Integral Formulation of the Boundary Value Problem in Waveguides.
Sancho, M.
1980-01-01
Presents an integral approach to the boundary value problem in waveguides deduced from the Kirchoff's integral formulation of the electromagnetic field. Also, the basis for the numerical solution of more general problems is given, including the example of the isosceles right triangular guide. (Author/SK)
Shih, H.R. [Jackson State Univ., MS (United States); Duffield, R.C.; Lin, J. [Univ. of Missouri, Columbia, MO (United States)
1996-10-01
An integral equation formulation and a numerical procedure for a boundary-finite element technique are developed for the static analysis of a stiffened plate with eccentric stiffeners. This formulation employs the fundamental solution associated with unstiffened plate bending and plane stress problems. With this approach, the resulting integral equation not only contained integrals along the perimeter of the stiffened but additional integrals along the stiffeners and the interface between the plate and its stiffeners. Thus the domain of the plate has to be divided into zones between the stiffeners. Each zone is modeled by boundary elements and stiffeners by finite elements. In this paper, the boundary element solution procedures for plate bending and in-plane problems are presented. The zone technique which permits coupling of unstiffened plate boundary element with stiffener finite elements is presented as well. Numerical example is given to demonstrate the effectiveness of this approach.
Boundary integral equation formulations for free-surface flow problems in two and three dimensions
Romate, J.E.; Zandbergen, P.J.
1989-01-01
To compute the transient solution of free-surface flow problems in two and three dimensions boundary integral equation formulations are considered. Consistent lower and higher order approximations based on small curvature expansions are compared and applied to a time-dependent, linear free-surface wave problem.
Corcelli, S.A.; Kress, J.D.; Pratt, L.R.
1995-08-07
This paper develops and characterizes mixed direct-iterative methods for boundary integral formulations of continuum dielectric solvation models. We give an example, the Ca{sup ++}{hor_ellipsis}Cl{sup {minus}} pair potential of mean force in aqueous solution, for which a direct solution at thermal accuracy is difficult and, thus for which mixed direct-iterative methods seem necessary to obtain the required high resolution. For the simplest such formulations, Gauss-Seidel iteration diverges in rare cases. This difficulty is analyzed by obtaining the eigenvalues and the spectral radius of the non-symmetric iteration matrix. This establishes that those divergences are due to inaccuracies of the asymptotic approximations used in evaluation of the matrix elements corresponding to accidental close encounters of boundary elements on different atomic spheres. The spectral radii are then greater than one for those diverging cases. This problem is cured by checking for boundary element pairs closer than the typical spatial extent of the boundary elements and for those cases performing an ``in-line`` Monte Carlo integration to evaluate the required matrix elements. These difficulties are not expected and have not been observed for the thoroughly coarsened equations obtained when only a direct solution is sought. Finally, we give an example application of hybrid quantum-classical methods to deprotonation of orthosilicic acid in water.
丁皓江; 江爱民
2003-01-01
To obtain the fundamental solutions for computation of magneto-electro-elastic media by the boundary element method, the general solutions in the case of distinct eigenvalues are derived and expressed in five harmonic functions from the governing equations and the strict differential operator theorem. On the basis of these general solutions, the fundamental solution of infinite magneto-electro-elastic solid are obtained with the method of trial-and-error. Finally, the boundary integral formulation is derived and the corresponding boundary element method program is implemented to perform two numerical calculations(a column under uni-axial tension, uniform electric displacement or uniform magnetic induction, an annular plate simply-supported on outer and inner surfaces under axial loads). The numerical results agree well with the analytical ones.
A new first kind boundary integral formulation for the Dirichlet-to-Neumann map in 2D
In this paper, we analyze the Dirichlet-to-Neumann (DtN) operator in the periodic case as a pseudodifferential operator represented through boundary integrals. We begin with some analytical results concerning the structure of the operator. In particular we exploit the freedom available in the choice of the kernel for the boundary integral representation to introduce a new logarithmic kernel for the fundamental solution of the Laplacian on a cylinder. We then use it to develop a superalgebraically convergent numerical method to compute DtN which proves very stable even for nonsmooth and large variation curves. An important step in the proposed procedure is the inversion of an integral equation of first kind. To deal with it, we introduce an efficient FFT-based preconditioner which performs well in combination with Nystrom's method and a decomposition of the operator based on 'flat geometry subtraction'
A "general boundary" formulation for quantum mechanics and quantum gravity
Oeckl, Robert
2003-01-01
I propose to formalize quantum theories as topological quantum field theories in a generalized sense, associating state spaces with boundaries of arbitrary (and possibly finite) regions of space-time. I further propose to obtain such ``general boundary'' quantum theories through a generalized path integral quantization. I show how both, non-relativistic quantum mechanics and quantum field theory can be given a ``general boundary'' formulation. Surprisingly, even in the non-relativistic case, ...
马杭; 黄兴
2003-01-01
Based on the fact that the singular boundary integrals in the sense of Cauchy principal value can be represented approxi-mately by the mean values of two companion nearly singular boundary integrals, a vary general approach was developed in the paper.In the approach, the approximate formulation before discretization was constructed to cope with the difficulties encountered in the cor-ner treatment in the formulations of hypersingular boundary integral equations. This makes it possible to solve the hypersingularboundary integral equation numerically in a non-regularized form and in a local manner by using conforming C0 quadratic boundary ele-ments and standard Gaussian quadratures similar to those employed in the conventional displacement-BIE formulations. The approxi-mate formulation is very convenient to use because the corner information is comprised naturally in the representations of those ap-proximate integrals. Numerical examples in plane elasticity show that with the present approach, the compatible or better results canbe achieved in comparison with those of the conventional BIE formulations.
Boundary conditions for hyperbolic formulations of the Einstein equations
Frittelli, Simonetta; Gomez, Roberto
2003-01-01
In regards to the initial-boundary value problem of the Einstein equations, we argue that the projection of the Einstein equations along the normal to the boundary yields necessary and appropriate boundary conditions for a wide class of equivalent formulations. We explicitly show that this is so for the Einstein-Christoffel formulation of the Einstein equations in the case of spherical symmetry.
Natarajan, Sundararajan; Ooi, Ean Tat; Chiong, Irene; Song, Chongmin
2013-01-01
Three different displacement based finite element formulations over arbitrary polygons are studied in this paper. The formulations considered are: the conventional polygonal finite element method (FEM) with Laplace interpolants, the cell-based smoothed polygonal FEM with simple averaging technique and the scaled boundary polygon formulation. For the purpose of numerical integration, we employ the sub-traingulation for the polygonal FEM and classical Gaussian quadrature for the smoothed FEM an...
A NOVEL BOUNDARY INTEGRAL EQUATION METHOD FOR LINEAR ELASTICITY--NATURAL BOUNDARY INTEGRAL EQUATION
Niu Zhongrong; Wang Xiuxi; Zhou Huanlin; Zhang Chenli
2001-01-01
The boundary integral equation (BIE) of displacement derivatives is put at a disadvantage for the difficulty involved in the evaluation of the hypersingular integrals. In this paper, the operators δij and εij are used to act on the derivative BIE. The boundary displacements, tractions and displacement derivatives are transformed into a set of new boundary tensors as boundary variables. A new BIE formulation termed natural boundary integral equation (NBIE) is obtained. The NBIE is applied to solving two-dimensional elasticity problems. In the NBIE only the strongly singular integrals are contained. The Cauchy principal value integrals occurring in the NBIE are evaluated. A combination of the NBIE and displacement BIE can be used to directly calculate the boundary stresses. The numerical results of several examples demonstrate the accuracy of the NBIE.
Path Integral Formulation of Noncommutative Quantum Mechanics
Acatrinei, C S
2001-01-01
We propose a phase-space path integral formulation of noncommutative quantum mechanics, and prove its equivalence to the operatorial formulation. As an illustration, the partition function of a noncommutative two-dimensional harmonic oscillator is calculated.
Completed Beltrami-Michell formulation for analyzing mixed boundary value problems in elasticity
Patnaik, Surya N.; Kaljevic, Igor; Hopkins, Dale A.; Saigal, Sunil
1995-01-01
In elasticity, the method of forces, wherein stress parameters are considered as the primary unknowns, is known as the Beltrami-Michell formulation (BMF). The existing BMF can only solve stress boundary value problems; it cannot handle the more prevalent displacement of mixed boundary value problems of elasticity. Therefore, this formulation, which has restricted application, could not become a true alternative to the Navier's displacement method, which can solve all three types of boundary value problems. The restrictions in the BMF have been alleviated by augmenting the classical formulation with a novel set of conditions identified as the boundary compatibility conditions. This new method, which completes the classical force formulation, has been termed the completed Beltrami-Michell formulation (CBMF). The CBMF can solve general elasticity problems with stress, displacement, and mixed boundary conditions in terms of stresses as the primary unknowns. The CBMF is derived from the stationary condition of the variational functional of the integrated force method. In the CBMF, stresses for kinematically stable structures can be obtained without any reference to the displacements either in the field or on the boundary. This paper presents the CBMF and its derivation from the variational functional of the integrated force method. Several examples are presented to demonstrate the applicability of the completed formulation for analyzing mixed boundary value problems under thermomechanical loads. Selected example problems include a cylindrical shell wherein membrane and bending responses are coupled, and a composite circular plate.
Spectral integration of linear boundary value problems
Viswanath, Divakar
2012-01-01
Spectral integration is a method for solving linear boundary value problems which uses the Chebyshev series representation of functions to avoid the numerical discretization of derivatives. It is occasionally attributed to Zebib (J. of Computational Physics vol. 53 (1984), p. 443-455) and more often to Greengard (SIAM J. on Numerical Analysis vol. 28 (1991), p. 1071-1080). Its advantage is believed to be its relative immunity to errors that arise when nearby grid points are used to approximate derivatives. In this paper, we reformulate the method of spectral integration by changing it in four different ways. The changes consist of a more convenient integral formulation, a different way to treat and interpret boundary conditions, treatment of higher order problems in factored form, and the use of piecewise Chebyshev grid points. Our formulation of spectral integration is more flexible and powerful as show by its ability to solve a problem that would otherwise take 8192 grid points using only 96 grid points. So...
Critical Review of Path Integral Formulation
Fujita, Takehisa
2008-01-01
The path integral formulation in quantum mechanics corresponds to the first quantization since it is just to rewrite the quantum mechanical amplitude into many dimensional integrations over discretized coordinates $x_n$. However, the path integral expression cannot be connected to the dynamics of classical mechanics, even though, superficially, there is some similarity between them. Further, the field theory path integral in terms of many dimensional integrations over fields does not correspo...
The reflection equation algebra of Sklyanin is extended to the supersymmetric case. A graded reflection equation algebra is proposed and the corresponding graded (supersymmetric) boundary quantum inverse scattering method (QISM) is formulated. As an application, integrable open-boundary conditions for the doped spin-1 chain of the supersymmetric t-J model are studied in the framework of the boundary QISM. Diagonal boundary K-matrices are found and four classes of integrable boundary terms are determined. (author)
Galerkin Boundary Integral Analysis for the 3D Helmholtz Equation
Swager, Melissa [Emporia State University; Gray, Leonard J [ORNL; Nintcheu Fata, Sylvain [ORNL
2010-01-01
A linear element Galerkin boundary integral analysis for the three-dimensional Helmholtz equation is presented. The emphasis is on solving acoustic scattering by an open (crack) surface, and to this end both a dual equation formulation and a symmetric hypersingular formulation have been developed. All singular integrals are defined and evaluated via a boundary limit process, facilitating the evaluation of the (finite) hypersingular Galerkin integral. This limit process is also the basis for the algorithm for post-processing of the surface gradient. The analytic integrations required by the limit process are carried out by employing a Taylor series expansion for the exponential factor in the Helmholtz fundamental solutions. For the open surface, the implementations are validated by comparing the numerical results obtained by using the two different methods.
A positive formalism for quantum theory in the general boundary formulation
Oeckl, Robert
2012-01-01
We introduce a new "positive formalism" for encoding quantum theories in the general boundary formulation, somewhat analogous to the mixed state formalism of the standard formulation. This makes the probability interpretation more natural and elegant, eliminates operationally irrelevant structure and opens the general boundary formulation to quantum information theory.
A Advanced Boundary Element Formulation for Acoustic Radiation and Scattering in Three Dimensions.
Soenarko, Benjamin
A computational method is presented for determining acoustic fields produced by arbitrary shaped three-dimensional bodies. The formulation includes both radiation and scattering problems. In particular an isoparametric element formulation is introduced in which both the surface geometry and the acoustic variables on the surface of the body are represented by second order shape functions within the local coordinate system. A general result for the surface velocity potential and the exterior field is derived. This result is applicable to non-smooth bodies, i.e. it includes the case where the surface may have a non-unique normal (e.g. at the edge of a cube). Test cases are shown involving spherical, cylindrical and cubical geometry for both radiation and scattering problems. The present formulation is also extended to include half-space problems in which the effect of the reflected wave from an infinite plane is taken into account. By selecting an appropriate Green's function, the surface integral over the plane is nullified; thus all the computational efforts can be performed only on the radiating or scattering body at issue and thereby greatly simplify the solution. A special formulation involving axisymmetric bodies and boundary conditions is also presented. For this special case, the surface integrals are reduced to line integrals and an integral over the angle of revolution. The integration over the angle is performed partly analytically in terms of elliptic integrals and partly numerically using simple Gaussian quadrature formula. Since the rest of the integrals involve only line integrals along the generator of the body, any discretization scheme can be easily obtained to achieve a desired degree of accuracy in evaluating these integrals.
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)
Adjoint Formulation for an Embedded-Boundary Cartesian Method
Nemec, Marian; Aftosmis, Michael J.; Murman, Scott M.; Pulliam, Thomas H.
2004-01-01
, which is based on the full-potential equation with viscous corrections. More recently, Dadone and Grossman presented an adjoint formulation for the Euler equations. In both approaches, a boundary condition is introduced to approximate the effects of the evolving surface shape that results in accurate gradient computation.
The formulation of gauge-Higgs unification with dynamical boundary conditions
Yamamoto, Kengo
2014-01-01
The boundary conditions on multiply connected extra dimensions play major roles in gauge-Higgs unification theory. Different boundary conditions, having been given in ad hoc manner so far, lead to different theories. To solve this arbitrariness problem of boundary conditions, we construct a formulation of gauge-Higgs unification with dynamics of boundary conditions on M4×S1/Z2 . As a result, it is found that only highly restricted sets of boundary conditions, which lead to nontrivial symmetry...
Perturbation theory and importance functions in integral transport formulations
Perturbation theory expressions for the static reactivity derived from the flux, collision density, birth-rate density, and fission-neutron density formulations of integral transport theory, and from the integro-differential formulation, are intercompared. The physical meaning and relation of the adjoint functions corresponding to each of the five formulations are established. It is found that the first-order approximation of the perturbation expressions depends on the transport theory formulation and on the adjoint function used. The approximations of the integro-differential formulation corresponding to different first-order approximations of the integral transport theory formulations are identified. It is found that the accuracy of all first-order approximations of the integral transport formulations examined is superior to the accuracy of first-order integro-differential perturbation theory
An integral formulation for wave propagation on weakly non-uniform potential flows
Mancini, Simone; Sinayoko, Samuel; Gabard, Gwenael; Tournour, Michel
2015-01-01
An integral formulation for acoustic radiation in moving flows is presented. It is based on a potential formulation for acoustic radiation on weakly non-uniform subsonic mean flows. This work is motivated by the absence of suitable kernels for wave propagation on non-uniform flow. The integral solution is formulated using a Green's function obtained by combining the Taylor and Lorentz transformations. Although most conventional approaches based on either transform solve the Helmholtz problem in a transformed domain, the current Green's function and associated integral equation are derived in the physical space. A dimensional error analysis is developed to identify the limitations of the current formulation. Numerical applications are performed to assess the accuracy of the integral solution. It is tested as a means of extrapolating a numerical solution available on the outer boundary of a domain to the far field, and as a means of solving scattering problems by rigid surfaces in non-uniform flows. The results...
Geometric Phase and Chiral Anomaly in Path Integral Formulation
Fujikawa, Kazuo
2007-01-01
All the geometric phases, adiabatic and non-adiabatic, are formulated in a unified manner in the second quantized path integral formulation. The exact hidden local symmetry inherent in the Schr\\"{o}dinger equation defines the holonomy. All the geometric phases are shown to be topologically trivial. The geometric phases are briefly compared to the chiral anomaly which is naturally formulated in the path integral.
A Boundary Integral Equation Approach for Boundary Problem of Laplace Equation
SUNJian-she; YELiu-qing
2003-01-01
Using the second Green formula, the boundary problem of Laplace equation satisfied by potential function of static electric field is transformed to the problem of the boundary integral equation,and then a boundary integral equation approach is established by partitioning boundary using linear boundary element.
Iterative solution of Hermite boundary integral equations
Gray, Leonard J [ORNL; Nintcheu Fata, Sylvain [ORNL; Ma, Ding [ORNL
2008-01-01
An efficient iterative method for the solution of the linear equations arising from a Hermite boundary integral approximation has been developed. Along with equations for the boundary unknowns, the Hermite system incorporates equations for the first-order surface derivatives (gradient) of the potential, and is therefore substantially larger than the matrix for a corresponding linear approximation. However, by exploiting the structure of the Hermite matrix, a two-level iterative algorithm has been shown to provide a very efficient solution algorithm. In this approach, the boundary function unknowns are treated separately from the gradient, taking advantage of the sparsity and near-positive definiteness of the gradient equations. In test problems, the new algorithm significantly reduced computation time compared to iterative solution applied to the full matrix. This approach should prove to be even more effective for the larger systems encountered in three-dimensional analysis, and increased efficiency should come from pre-conditioning of the non-sparse matrix component.
Boundary conditions for the Einstein-Christoffel formulation of Einstein's equations
Arnold, Douglas N.; Nicolae Tarfulea
2007-01-01
Specifying boundary conditions continues to be a challenge in numerical relativity in order to obtain a long time convergent numerical simulation of Einstein's equations in domains with artificial boundaries. In this paper, we address this problem for the Einstein--Christoffel (EC) symmetric hyperbolic formulation of Einstein's equations linearized around flat spacetime. First, we prescribe simple boundary conditions that make the problem well posed and preserve the constraints. Next, we indi...
RADIATION BOUNDARY CONDITIONS FOR MAXWELL'S EQUATIONS: A REVIEW OF ACCURATE TIME-DOMAIN FORMULATIONS
Thomas Hagstrom; Stephen Lau
2007-01-01
We review time-domain formulations of radiation boundary conditions for Maxwell's equations, focusing on methods which can deliver arbitrary accuracy at acceptable computational cost. Examples include fast evaluations of nonlocal conditions on symmetric and general boundaries, methods based on identifying and evaluating equivalent sources, and local approximations such as the perfectly matched layer and sequences of local boundary conditions. Complexity estimates are derived to assess work and storage requirements as a function of wavelength and simulation time.
Canonical formulation and path integral for local vacuum energy sequestering
Bufalo, R.; Klusoň, J.; Oksanen, M.
2016-01-01
We establish the Hamiltonian analysis and the canonical path integral for a local formulation of vacuum energy sequestering. In particular, by considering the state of the universe as a superposition of vacuum states corresponding to different values of the cosmological and gravitational constants, the path integral is extended to include integrations over the cosmological and gravitational constants. The result is an extension of the Ng-van Dam form of the path integral of unimodular gravity...
Kempka, S.N.; Strickland, J.H.; Glass, M.W.; Peery, J.S. [Sandia National Labs., Albuquerque, NM (United States); Ingber, M.S. [Univ. of New Mexico, Albuquerque, NM (United States)
1995-04-01
formulation to satisfy velocity boundary conditions for the vorticity form of the incompressible, viscous fluid momentum equations is presented. The tangential and normal components of the velocity boundary condition are satisfied simultaneously by creating vorticity adjacent to boundaries. The newly created vorticity is determined using a kinematical formulation which is a generalization of Helmholtz` decomposition of a vector field. Though it has not been generally recognized, these formulations resolve the over-specification issue associated with creating voracity to satisfy velocity boundary conditions. The generalized decomposition has not been widely used, apparently due to a lack of a useful physical interpretation. An analysis is presented which shows that the generalized decomposition has a relatively simple physical interpretation which facilitates its numerical implementation. The implementation of the generalized decomposition is discussed in detail. As an example the flow in a two-dimensional lid-driven cavity is simulated. The solution technique is based on a Lagrangian transport algorithm in the hydrocode ALEGRA. ALEGRA`s Lagrangian transport algorithm has been modified to solve the vorticity transport equation and the generalized decomposition, thus providing a new, accurate method to simulate incompressible flows. This numerical implementation and the new boundary condition formulation allow vorticity-based formulations to be used in a wider range of engineering problems.
Exact Boundary Derivative Formulation for Numerical Conformal Mapping Method
Wei-Lin Lo; Nan-Jing Wu; Chuin-Shan Chen; Ting-Kuei Tsay
2016-01-01
Conformal mapping is a useful technique for handling irregular geometries when applying the finite difference method to solve partial differential equations. When the mapping is from a hyperrectangular region onto a rectangular region, a specific length-to-width ratio of the rectangular region that fitted the Cauchy-Riemann equations must be satisfied. In this research, a numerical integral method is proposed to find the specific length-to-width ratio. It is conventional to employ the boundar...
Tezduyar, T. E.; Liou, J.
1991-01-01
Downstream boundary conditions equivalent to the homogeneous form of the natural boundary conditions associated with the velocity-pressure formulation of the Navier-Stokes equations are derived for the vorticity-stream function formulation of two-dimensional incompressible flows. Of particular interest are the zero normal and shear stress conditions at a downstream boundary.
Some integral formulations occurring in accelerator physics
In this paper a powerful and robust analytical-numerical approach to study the electromagnetic interaction between a bunch of particles and the discontinuities of the vacuum chamber of a particle accelerator is discussed. In particular the diffraction of the electromagnetic field created by a bunch of a bunch of charges travelling through an iris and a drift tube is considered. Choosing in both cases a spectral transform of the current density distribution on the scatterer as unknowns, an effective numerical model is obtained. These unknowns have to satisfy a system of dual integral equations. A general procedure to transform this system into only one Fredholm integral equation of the second kind (in the case of the iris) or to a system of linear algebraic equations by means of a Neumann series (in the case of the drift tube) is described. These models allow to compute the longitudinal coupling impedance with a good accuracy either in the low frequency limit or in the high frequency limit
Boundary integral method applied in chaotic quantum billiards
Li, B; Li, Baowen; Robnik, Marko
1995-01-01
The boundary integral method (BIM) is a formulation of Helmholtz equation in the form of an integral equation suitable for numerical discretization to solve the quantum billiard. This paper is an extensive numerical survey of BIM in a variety of quantum billiards, integrable (circle, rectangle), KAM systems (Robnik billiard) and fully chaotic (ergodic, such as stadium, Sinai billiard and cardioid billiard). On the theoretical side we point out some serious flaws in the derivation of BIM in the literature and show how the final formula (which nevertheless was correct) should be derived in a sound way and we also argue that a simple minded application of BIM in nonconvex geometries presents serious difficulties or even fails. On the numerical side we have analyzed the scaling of the averaged absolute value of the systematic error \\Delta E of the eigenenergy in units of mean level spacing with the density of discretization (b = number of numerical nodes on the boundary within one de Broglie wavelength), and we f...
De Corato, M.; Slot, J. J. M.; Hütter, M.; D'Avino, G.; Maffettone, P. L.; Hulsen, M. A.
2016-07-01
In this paper, we present a finite element implementation of fluctuating hydrodynamics with a moving boundary fitted mesh for treating the suspended particles. The thermal fluctuations are incorporated into the continuum equations using the Landau and Lifshitz approach [1]. The proposed implementation fulfills the fluctuation-dissipation theorem exactly at the discrete level. Since we restrict the equations to the creeping flow case, this takes the form of a relation between the diffusion coefficient matrix and friction matrix both at the particle and nodal level of the finite elements. Brownian motion of arbitrarily shaped particles in complex confinements can be considered within the present formulation. A multi-step time integration scheme is developed to correctly capture the drift term required in the stochastic differential equation (SDE) describing the evolution of the positions of the particles. The proposed approach is validated by simulating the Brownian motion of a sphere between two parallel plates and the motion of a spherical particle in a cylindrical cavity. The time integration algorithm and the fluctuating hydrodynamics implementation are then applied to study the diffusion and the equilibrium probability distribution of a confined circle under an external harmonic potential.
We introduce a set of constraint preserving boundary conditions for the Baumgarte–Shapiro–Shibata–Nakamura formulation of the Einstein evolution equations in spherical symmetry, based on its hyperbolic structure. While the outgoing eigenfields are left to propagate freely off the numerical grid, boundary conditions are set to enforce that the incoming eigenfields don't introduce spurious reflections and, more importantly, that there are no fields introduced at the boundary that violate the constraint equations. In order to do this we adopt two different approaches to set boundary conditions for the extrinsic curvature, by expressing either the radial or the time derivative of its associated ingoing eigenfield in terms of the constraints. We find that these boundary conditions are very robust in practice, allowing us to perform long lasting evolutions that remain accurate and stable, and that converge to a solution that satisfies the constraints all the way to the boundary. (paper)
The formulation of gauge-Higgs unification with dynamical boundary conditions
Yamamoto, Kengo
2014-01-01
The boundary conditions on multiply connected extra dimensions play a major rolls in gauge-Higgs unification theory. Different boundary conditions, having been given in ad hoc manner so far, lead to different theories. To solve this arbitrariness problem of boundary condition, we construct a gauge-Higgs unification formulation with dynamics of boundary conditions on M^4 times S^1/Z_2. As a result, it is found that certain sets of boundary conditions which lead to nontrivial symmetry breaking practically contribute to the partition function. In particular, we show that for SU(5) gauge group, sets of boundary conditions which lead to SU(5) to SU(3) times SU(2) times U(1) symmetry breaking are naturally selected.
Cleansing Formulations That Respect Skin Barrier Integrity
Russel M. Walters
2012-01-01
Full Text Available Surfactants in skin cleansers interact with the skin in several manners. In addition to the desired benefit of providing skin hygiene, surfactants also extract skin components during cleansing and remain in the stratum corneum (SC after rinsing. These side effects disrupt SC structure and degrade its barrier properties. Recent applications of vibrational spectroscopy and two-photon microscopy in skin research have provided molecular-level information to facilitate our understanding of the interaction between skin and surfactant. In the arena of commercial skin cleansers, technologies have been developed to produce cleansers that both cleanse and respect skin barrier. The main approach is to minimize surfactant interaction with skin through altering its solution properties. Recently, hydrophobically modified polymers (HMPs have been introduced to create skin compatible cleansing systems. At the presence of HMP, surfactants assemble into larger, more stable structures. These structures are less likely to penetrate the skin, thereby resulting in less aggressive cleansers and the integrity of the skin barrier is maintained. In this paper, we reviewed our recent findings on surfactant and SC interactions at molecular level and provided an overview of the HM technology for developing cleansers that respect skin barrier.
Surface Integral Formulations for the Design of Plasmonic Nanostructures
Forestiere, Carlo; Iadarola, Giovanni; Rubinacci, Guglielmo; Tamburrino, Antonello; Dal Negro, Luca; Miano, Giovanni; Boston University Team; Universita'degli Studi di Napoli Federico Team, II; Universita'di Cassino e del Lazio Meridionale Team
2013-03-01
Numerical formulations based on surface integral equations (SIEs) provide an accurate and efficient framework for the solution of the electromagnetic scattering problem by three-dimensional plasmonic nanostructures in the frequency domain. In this work, we present a unified description of SIE formulations with both singular and nonsingular kernel and we study their accuracy in solving the scattering problem by metallic nanoparticles with spherical and nonspherical shape. In fact, the accuracy of the numerical solution, especially in the near zone, is of great importance in the analysis and design of plasmonic nanostructures, whose operation critically depends on the manipulation of electromagnetic hot spots. Four formulation types are considered: the N-combined region integral equations, the T-combined region integral equations, the combined field integral equations and the null field integral equations. A detailed comparison between their numerical solutions obtained for several nanoparticle shapes is performed by examining convergence rate and accuracy in both the far and near zone of the scatterer as a function of the number of degrees of freedom. A rigorous analysis of SIE formulations can have a high impact on the engineering of numerous nano-scale optical devices.
Bendapudi, Satyam [United Technologies Research Center, East Hartford, CT (United States); Braun, James E.; Groll, Eckhard A. [School of Mechanical Engineering, Purdue University, West Lafayette, IN 47907 (United States)
2008-12-15
Dynamic models of vapor compression systems are useful tools in developing feedback controllers and are gaining increasing attention in recent years. The dominant dynamics are typically those of the evaporator and condenser, which are difficult to model. Accuracy and execution speed of system models therefore are highly dependent on the modeling approach of the heat exchangers. The two common approaches are the finite-volume (FV) and the moving-boundary (MB) methods. Both have been used successfully and reported in the literature, but there is little discussion presented for either choice. This paper presents the development and comparative study of shell-and-tube heat exchanger dynamic models using both the FV and the MB approaches. Detailed model formulations are provided and stability is demonstrated as components and within a complete centrifugal chiller system model. The system models are validated using data from a 300 kW R134a centrifugal chiller test stand. The FV formulation is found to be more robust through start-up and all load-change transients, but executes slower. The moving-boundary method can handle all load-change transients but start-up stability is more sensitive to compressor and expansion valve formulations. The moving-boundary formulation also executes about three times faster than the finite-volume while maintaining nearly identical accuracy. With the homogenous two-phase assumption, charge prediction is seen to be less accurate in the moving-boundary approach. (author)
Cutanda Henriquez, Vicente; Juhl, Peter Møller
2013-01-01
The formulation presented in this paper is based on the Boundary Element Method (BEM) and implements Kirchhoff’s decomposition into viscous, thermal and acoustic components, which can be treated independently everywhere in the domain except on the boundaries. The acoustic variables with losses...... are solved using extended boundary conditions that account for: i) negligible temperature fluctuations at the boundary, and ii) normal and tangential matching of the boundary’s particle velocity. The proposed model does not require constructing a special mesh for the viscous and thermal boundary layers...... as is the case with the existing Finite Element Method (FEM) implementations with losses. The suitability of this approach is demonstrated using an axisymmetrical BEM and two test cases where the numerical results are compared with analytical solutions....
Quantum mechanics 1. Path-integral formulation and operator formalism
The first volume of this two-volume textbook gives a modern introduction to the quantum theory, which connects Feynman's path-integral formulation with the traditional operator formalism. In easily understandable form starting from the double-slit experiment the characteristic features and foundations of quantum theory are made accessible by means of the functional-integral approach. Just this approach makes a ''derivation'' of the Schroedinger equation from the principle of the interfering alternatives possible. In the following the author developes the traditional operator formulation of quantum mechanics, which is better suited for practical solution of elementary problems. However he then refers to the functional-integral approach, when this contributes to a better understanding. A further advance of this concept: The functional-integral approach facilitates essentially the later access to quantum field theory. The work is in like manner suited for the self-study as for the deepening accompanying of the course.
Canonical formulation and path integral for local vacuum energy sequestering
Bufalo, R; Oksanen, M
2016-01-01
We establish the Hamiltonian analysis and the canonical path integral for a local formulation of vacuum energy sequestering. In particular, by considering the state of the universe as a superposition of vacuum states corresponding to different values of the cosmological and gravitational constants, the path integral is extended to include integrations over the cosmological and gravitational constants. The result is an extension of the Ng-van Dam form of the path integral of unimodular gravity. It is argued to imply a relation between the fraction of the most likely values of the gravitational and cosmological constants and the average values of the energy density and pressure of matter over spacetime. Finally, we construct and analyze a BRST-exact formulation of the theory, which can be considered as a topological field theory.
Canonical formulation and path integral for local vacuum energy sequestering
Bufalo, R.; KlusoÅ, J.; Oksanen, M.
2016-08-01
We establish the Hamiltonian analysis and the canonical path integral for a local formulation of vacuum energy sequestering. In particular, by considering the state of the Universe as a superposition of vacuum states corresponding to different values of the cosmological and gravitational constants, the path integral is extended to include integrations over the cosmological and gravitational constants. The result is an extension of the Ng-van Dam form of the path integral of unimodular gravity. It is argued to imply a relation between the fraction of the most likely values of the gravitational and cosmological constants and the average values of the energy density and pressure of matter over spacetime. Finally, we construct and analyze a Becchi-Rouet-Stora-Tyutin-exact formulation of the theory, which can be considered as a topological field theory.
A path integral formulation of p-adic quantum mechanics
We propose a path integral formulation of some evolution operators with p-adic 'time', based on restrictions to nested invariant subspaces of test-functions. These restrictions turn the time variables into discrete ones and allow the usual path integral manipulations. We illustrate this definition with the example of the p-acid harmonic oscillator and point out realizations in the context of two-dimensional conformal field theories and Yang-Mills equations. (orig.)
Geometric formulations and variational integrators of discrete autonomous Birkhoff systems
The variational integrators of autonomous Birkhoff systems are obtained by the discrete variational principle. The geometric structure of the discrete autonomous Birkhoff system is formulated. The discretization of mathematical pendulum shows that the discrete variational method is as effective as symplectic scheme for the autonomous Birkhoff systems. (electromagnetism, optics, acoustics, heat transfer, classical mechanics, and fluid dynamics)
Second-order domain derivative of normal-dependent boundary integrals
Balzer, Jonathan
2010-03-17
Numerous reconstruction tasks in (optical) surface metrology allow for a variational formulation. The occurring boundary integrals may be interpreted as shape functions. The paper is concerned with the second-order analysis of such functions. Shape Hessians of boundary integrals are considered difficult to find analytically because they correspond to third-order derivatives of an, in a sense equivalent, domain integral. We complement previous results by considering cost functions depending explicitly on the surface normal. The correctness and practicability of our calculations are verified in the context of a Newton-type shape reconstruction method. © 2010 Birkhäuser / Springer Basel AG.
Integrated watershed planning across jurisdictional boundaries
Watts, A. W.; Roseen, R.; Stacey, P.; Bourdeau, R.
2014-12-01
We will present the foundation for an Coastal Watershed Integrated Plan for three communities in southern New Hampshire. Small communities are often challenged by complex regulatory requirements and limited resources, but are wary of perceived risks in engaging in collaborative projects with other communities. Potential concerns include loss of control, lack of resources to engage in collaboration, technical complexity, and unclear benefits. This project explores a multi-town subwatershed application of integrated planning across jurisdictional boundaries that addresses some of today's highest priority water quality issues: wastewater treatment plant upgrades for nutrient removal; green infrastructure stormwater management for developing and re-developing areas; and regional monitoring of ecosystem indicators in support of adaptive management to achieve nutrient reduction and other water quality goals in local and downstream waters. The project outcome is a collaboratively-developed inter-municipal integrated plan, and a monitoring framework to support cross jurisdictional planning and assess attainment of water quality management goals. This research project has several primary components: 1) assessment of initial conditions, including both the pollutant load inputs and the political, economic and regulatory status within each community, 2) a pollutant load model for point and non-point sources, 3) multi-criteria evaluation of load reduction alternatives 4) a watershed management plan optimized for each community, and for Subwatersheds combining multiple communities. The final plan will quantify the financial and other benefits/drawbacks to each community for both inter municipal and individual pollution control approaches. We will discuss both the technical and collaborative aspects of the work, with lessons learned regarding science to action, incorporation of social, economic and water quality assessment parameters, and stakeholder/researcher interaction.
Argeso, Hakan; Mengi, Yalcin
2014-02-01
A unified formulation is presented, based on the boundary element method, to perform the interaction analysis for the problems involving poroviscoelastic media. The proposed formulation permits the evaluation of all the elements of impedance and input motion matrices at a single step in terms of system matrices of boundary element method without solving any special problem, such as, unit displacement or load problem, as required by conventional methods. It further eliminates the complicated procedure and the need for using scattering analysis in the evaluation of input motion functions. The formulation is explained by considering a simple interaction problem involving an inclusion embedded in an infinite poroviscoelastic medium, which is under the influence of a dynamic excitation induced by seismic waves. In the formulation, an impedance relation is established for this interaction problem, suitable for performing the interaction analysis by substructure method, which permits carrying out the analysis for inclusion and its surrounding medium separately. The inclusion is first treated as poroviscoelastic, then viscoelastic and finally rigid, where the formulation in each of these cases is obtained consecutively as a special case of the previous one. It is remarkable to note that, a cavity problem where there is a hole in place of inclusion can be also considered within the framework of the present formulation. The formulation is assessed by applying it to some sample problems. The extension of the formulation to other types of interaction problems, such as, multi-inclusion problems, the analyses of foundations supported by a poroviscoelastic medium, etc., will be the subject of a separate study.
An Integrated Methodology for Emulsified Formulated Product Design
Mattei, Michele
significantly reduce both time and cost connected to product development by doing only the necessary experi- ments , and ensuring chances for innovation . The main contribution of this project i s the development of an integrated methodology for the design of emulsified formulated products. The methodology...... consists of three stages: the problem definition stage, the model - based design stage, and the experiment - based verification stage. In the probl em definition stage, the consumer needs are trans- lated into a set of target thermo - physical properties and into a list of categories of ingre- dients that...... the proposed formulation are measured by means of tailor - made exp eriments. The formulation is then validated or, if necessary, re- fined thanks to a systematic list of action. The problem definition stage relies on a robust knowledge base, which needs to system- atically generate quantitative...
Computing the Casimir force using regularized boundary integral equations
Kilen, Isak; Jakobsen, Per Kristen
2014-11-01
In this paper we use a novel regularization procedure to reduce the calculation of the Casimir force for 2D scalar fields between compact objects to the solution of a classical integral equation defined on the boundaries of the objects. The scalar fields are subject to Dirichlet boundary conditions on the object boundaries. We test the integral equation by comparing with what we get for parallel plates, concentric circles and adjacent circles using mode summation and the functional integral method. We show how symmetries in the shapes and configuration of boundaries can easily be incorporated into our method and that it leads to fast evaluation of the Casimir force for symmetric situations.
Islam, T; Chik, Z; Mustafa, M. M.; H. Sanusi
2012-01-01
This paper presents an efficient model for estimation of soil electric resistivity with depth and layer thickness in a multilayer earth structure. This model is the improvement of conventional two-layer earth model including Wenner resistivity formulations with boundary conditions. Two-layer soil model shows the limitations in specific soil characterizations of different layers with the interrelationships between soil apparent electrical resistivity (ρ) and several soil physical or chemical p...
Quantum Brans-Dicke Gravity in Euclidean Path Integral Formulation
Kim, Hongsu
1997-01-01
The conformal structure of Brans-Dicke gravity action is carefully studied. It is discussed that Brans-Dicke gravity action has definitely no conformal invariance. It is shown, however, that this lack of conformal invariance enables us to demonstrate that Brans-Dicke theory appears to have a better short-distance behavior than Einstein gravity as far as Euclidean path integral formulation for quantum gravity is concerned.
BOUNDARY INTEGRAL FORMULA OF ELASTIC PROBLEMS IN CIRCLE PLANE
DONG Zheng-zhu; LI Shun-cai; YU De-hao
2005-01-01
By bianalytic functions, the boundary integral formula of the stress function for the elastic problem in a circle plane is developed. But this integral formula includes a strongly singular integral and can not be directly calculated. After the stress function is expounded to Fourier series, making use of some formulas in generalized functions to the convolutions, the boundary integral formula which does not include strongly singular integral is derived further. Then the stress function can be got simply by the integration of the values of the stress function and its derivative on the boundary. Some examples are given. It shows that the boundary integral formula of the stress function for the elastic problem is convenient.
A spectral boundary integral equation method for the 2D Helmholtz equation
In this paper, we present a new numerical formulation of solving the boundary integral equations reformulated from the Helmholtz equation. The boundaries of the problems are assumed to be smooth closed contours. The solution on the boundary is treated as a periodic function, which is in turn approximated by a truncated Fourier series. A Fourier collocation method is followed in which the boundary integral equation is transformed into a system of algebraic equations. It is shown that in order to achieve spectral accuracy for the numerical formulation, the non-smoothness of the integral kernels, associated with the Helmholtz equation, must be carefully removed. The emphasis of the paper is on investigating the essential elements of removing the non-smoothness of the integral kernels in the spectral implementation. The present method is robust for a general smooth boundary contour. Aspects of efficient implementation of the method using FFT are also discussed. Numerical examples of wave scattering are given in which the exponential accuracy of the present numerical method is demonstrated. 15 refs., 3 figs., 4 tabs
Treatment of domain integrals in boundary element methods
Nintcheu Fata, Sylvain [ORNL
2012-01-01
A systematic and rigorous technique to calculate domain integrals without a volume-fitted mesh has been developed and validated in the context of a boundary element approximation. In the proposed approach, a domain integral involving a continuous or weakly-singular integrand is first converted into a surface integral by means of straight-path integrals that intersect the underlying domain. Then, the resulting surface integral is carried out either via analytic integration over boundary elements or by use of standard quadrature rules. This domain-to-boundary integral transformation is derived from an extension of the fundamental theorem of calculus to higher dimension, and the divergence theorem. In establishing the method, it is shown that the higher-dimensional version of the first fundamental theorem of calculus corresponds to the well-known Poincare lemma. The proposed technique can be employed to evaluate integrals defined over simply- or multiply-connected domains with Lipschitz boundaries which are embedded in an Euclidean space of arbitrary but finite dimension. Combined with the singular treatment of surface integrals that is widely available in the literature, this approach can also be utilized to effectively deal with boundary-value problems involving non-homogeneous source terms by way of a collocation or a Galerkin boundary integral equation method using only the prescribed surface discretization. Sample problems associated with the three-dimensional Poisson equation and featuring the Newton potential are successfully solved by a constant element collocation method to validate this study.
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.)
Boundary Integral Solutions to Three-Dimensional Unconfined Darcy's Flow
Lennon, Gerard P.; Liu, Philip L.-F.; Liggett, James A.
1980-08-01
The boundary integral equation method (BIEM) is used to solve three-dimensional potential flow problems in porous media. The problems considered here are time dependent and have a nonlinear boundary condition on the free surface. The entire boundary, including the moving free surface, discretized into linear finite elements for the purpose of evaluating the boundary integrals. The technique allows transient, three-dimensional problems to be solved with reasonable computational costs. Numerical examples include recharge through rectangular and circular areas and seepage flow from a surface pond. The examples are used to illustrate the method and show the nonlinear effects.
Ivanyshyn Yaman, Olha; Le Louër, Frédérique
2016-09-01
This paper deals with the material derivative analysis of the boundary integral operators arising from the scattering theory of time-harmonic electromagnetic waves and its application to inverse problems. We present new results using the Piola transform of the boundary parametrisation to transport the integral operators on a fixed reference boundary. The transported integral operators are infinitely differentiable with respect to the parametrisations and simplified expressions of the material derivatives are obtained. Using these results, we extend a nonlinear integral equations approach developed for solving acoustic inverse obstacle scattering problems to electromagnetism. The inverse problem is formulated as a pair of nonlinear and ill-posed integral equations for the unknown boundary representing the boundary condition and the measurements, for which the iteratively regularized Gauss-Newton method can be applied. The algorithm has the interesting feature that it avoids the numerous numerical solution of boundary value problems at each iteration step. Numerical experiments are presented in the special case of star-shaped obstacles.
Analytical Solution of Boundary Integral Equations for 2-D Steady Linear Wave Problems
J.M. Chuang
2005-01-01
Based on the Fourier transform, the analytical solution of boundary integral equations formulated for the complex velocity of a 2-D steady linear surface flow is derived. It has been found that before the radiation condition is imposed,free waves appear both far upstream and downstream. In order to cancel the free waves in far upstream regions, the eigensolution of a specific eigenvalue, which satisfies the homogeneous boundary integral equation, is found and superposed to the analytical solution. An example, a submerged vortex, is used to demonstrate the derived analytical solution. Furthermore,an analytical approach to imposing the radiation condition in the numerical solution of boundary integral equations for 2-D steady linear wave problems is proposed.
Radioisotope diffusion in grain textures by boundary integral method
Aim of this contribution is to deal with radioisotope diffusion in grain texture by Boundary Integral method (BIM). Governing partial integral equation is transformed to an equivalent boundary integral equation, which is written in a discrete form and a system of linear algebraic equations is thus obtained. Advantage of BIM is that the system of equations is solved only for unknown values on the boundary. values in the domain are calculated explicitly in a down stream procedure. A given example indicates a good agreement with analytical results. (author)
Boundary Integral Equations and A Posteriori Error Estimates
YU Dehao; ZHAO Longhua
2005-01-01
Adaptive methods have been rapidly developed and applied in many fields of scientific and engineering computing. Reliable and efficient a posteriori error estimates play key roles for both adaptive finite element and boundary element methods. The aim of this paper is to develop a posteriori error estimates for boundary element methods. The standard a posteriori error estimates for boundary element methods are obtained from the classical boundary integral equations. This paper presents hyper-singular a posteriori error estimates based on the hyper-singular integral equations. Three kinds of residuals are used as the estimates for boundary element errors. The theoretical analysis and numerical examples show that the hyper-singular residuals are good a posteriori error indicators in many adaptive boundary element computations.
Mitharwal, Rajendra
2015-01-01
This work presents a Boundary Element Method (BEM) formulation for contactless electromagnetic field assessments. The new scheme is based on a regularized BEM approach that requires the use of electric measurements only. The regularization is obtained by leveraging on an extension of Calderon techniques to rectangular systems leading to well-conditioned problems independent of the discretization density. This enables the use of highly discretized Huygens surfaces that can be consequently placed very near to the radiating source. In addition, the new regularized scheme is hybridized with both surfacic homogeneous and volumetric inhomogeneous forward BEM solvers accelerated with fast matrix-vector multiplication schemes. This allows for rapid and effective dosimetric assessments and permits the use of inhomogeneous and realistic head phantoms. Numerical results corroborate the theory and confirms the practical effectiveness of all newly proposed formulations.
Gomez-Sousa, Hipolito; Martinez-Lorenzo, Jose Angel
2015-01-01
The electromagnetic behavior of plasmonic structures can be predicted after discretizing and solving a linear system of equations, derived from a continuous surface integral equation (SIE) and the appropriate boundary conditions, using a method of moments (MoM) methodology. In realistic large-scale optical problems, a direct inversion of the SIE-MoM matrix cannot be performed due to its large size, and an iterative solver must be used instead. This paper investigates the performance of four iterative solvers (GMRES, TFQMR, CGS, and BICGSTAB) for five different SIE-MoM formulations (PMCHWT, JMCFIE, CTF, CNF, and MNMF). Moreover, under this plasmonic context, a set of suggested guidelines are provided to choose a suitable SIE formulation and iterative solver depending on the desired simulation error and available runtime resources.
Formulation of market strategies for Integrated Community Energy Systems (ICES)
None
1978-04-01
The ANL Energy and Environmental Systems Division has undertaken studies of implementation mechanisms and commercialization prospects for ''integrated community energy systems.'' Real Estate Research Corp. was commissioned to formulate marketing strategies appropriate to the implementation of ICES in the U.S. Objectives of this assignment are to: assist ICES program managers in formulating market strategies for the acceptance and widespread application of ICES systems; provide sufficient background information on the processes of development so that marketing strategies can be suitably tailored to particular concerns and characteristics of development projects; establish an information system for identifying areas, subareas, sites, or projects with substantial growth and development activity, as potential candidates for the application of ICES; test the information system to determine its potential usefulness for identifying candidate sites; and provide recommendations on strategies and techniques that might be used in a comprehensive marketing program for application of ICES systems. Chapter 2 presents information on the development process, which is used as a framework for other elements of the report. The project information system for identifying candidate projects for ICES applications is described in Chapter 3, and that system is subjected to a limited test and evaluation in Chapter 4. Description of the characteristics of development process appears in Chapter 5, and discussion of the formulation of marketing strategies in Chapter 6, and presentation of marketing techniques as part of an ICES marketing program in Chapter 7.
Two-point boundary value and Cauchy formulations in an axisymmetrical MHD equilibrium problem
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)
The functional integral formulation of the Schrieffer–Wolff transformation
Zamani, Farzaneh; Ribeiro, Pedro; Kirchner, Stefan
2016-06-01
We revisit the Schrieffer–Wolff transformation and present a path integral version of this important canonical transformation. The equivalence between the low-energy sector of the Anderson model in the so-called local moment regime and the spin-isotropic Kondo model is usually established via a canonical transformation performed on the Hamiltonian, followed by a projection. Here we present a path integral formulation of the Schrieffer–Wolff transformation which relates the functional integral form of the partition function of the Anderson model to that of its effective low-energy model. The resulting functional integral assumes the form of a spin path integral and includes a geometric phase factor, i.e. a Berry phase. Our approach stresses the underlying symmetries of the model and allows for a straightforward generalization of the transformation to more involved models. It thus not only sheds new light on a classic problem, it also offers a systematic route of obtaining effective low-energy models and higher order corrections. This is demonstrated by obtaining the effective low-energy model of a quantum dot attached to two ferromagnetic leads.
APPLICATION OF BOUNDARY INTEGRAL EQUATION METHOD FOR THERMOELASTICITY PROBLEMS
Vorona Yu.V.; Kara I.D.
2015-01-01
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.
APPLICATION OF BOUNDARY INTEGRAL EQUATION METHOD FOR THERMOELASTICITY PROBLEMS
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.
Hu, Fang Q.; Pizzo, Michelle E.; Nark, Douglas M.
2016-01-01
Based on the time domain boundary integral equation formulation of the linear convective wave equation, a computational tool dubbed Time Domain Fast Acoustic Scattering Toolkit (TD-FAST) has recently been under development. The time domain approach has a distinct advantage that the solutions at all frequencies are obtained in a single computation. In this paper, the formulation of the integral equation, as well as its stabilization by the Burton-Miller type reformulation, is extended to cases of a constant mean flow in an arbitrary direction. In addition, a "Source Surface" is also introduced in the formulation that can be employed to encapsulate regions of noise sources and to facilitate coupling with CFD simulations. This is particularly useful for applications where the noise sources are not easily described by analytical source terms. Numerical examples are presented to assess the accuracy of the formulation, including a computation of noise shielding by a thin barrier motivated by recent Historical Baseline F31A31 open rotor noise shielding experiments. Furthermore, spatial resolution requirements of the time domain boundary element method are also assessed using point per wavelength metrics. It is found that, using only constant basis functions and high-order quadrature for surface integration, relative errors of less than 2% may be obtained when the surface spatial resolution is 5 points-per-wavelength (PPW) or 25 points-per-wavelength squared (PPW2).
On the Implementation of 3D Galerkin Boundary Integral Equations
Nintcheu Fata, Sylvain [ORNL; Gray, Leonard J [ORNL
2010-01-01
In this article, a reverse contribution technique is proposed to accelerate the construction of the dense influence matrices associated with a Galerkin approximation of singular and hypersingular boundary integral equations of mixed-type in potential theory. In addition, a general-purpose sparse preconditioner for boundary element methods has also been developed to successfully deal with ill-conditioned linear systems arising from the discretization of mixed boundary-value problems on non-smooth surfaces. The proposed preconditioner, which originates from the precorrected-FFT method, is sparse, easy to generate and apply in a Krylov subspace iterative solution of discretized boundary integral equations. Moreover, an approximate inverse of the preconditioner is implicitly built by employing an incomplete LU factorization. Numerical experiments involving mixed boundary-value problems for the Laplace equation are included to illustrate the performance and validity of the proposed techniques.
A simple boundary element formulation for shape optimization of 2D continuous structures
For the design of nuclear equipment like pressure vessels, steam generators, and pipelines, among others, it is very important to optimize the shape of the structural systems to withstand prescribed loads such as internal pressures and prescribed or limiting referential values such as stress or strain. In the literature, shape optimization of frame structural systems is commonly found but the same is not true for continuous structural systems. In this work, the Boundary Element Method (BEM) is applied to simple problems of shape optimization of 2D continuous structural systems. The proposed formulation is based on the BEM and on deterministic optimization methods of zero and first order such as Powell's, Conjugate Gradient, and BFGS methods. Optimal characterization for the geometric configuration of 2D structure is obtained with the minimization of an objective function. Such function is written in terms of referential values (such as loads, stresses, strains or deformations) prescribed at few points inside or at the boundary of the structure. The use of the BEM for shape optimization of continuous structures is attractive compared to other methods that discretized the whole continuous. Several numerical examples of the application of the proposed formulation to simple engineering problems are presented. (authors)
Calculation of Turbulent Boundary Layers Using the Dissipation Integral Method
MatthiasBuschmann
1999-01-01
This paper gives an introduction into the dissipation integral method.The general integral equations for the three-dimensional case are derved.It is found that for a practical calculation algorithm the integral monentum equation and the integral energy equation are msot useful.Using Two different sets of mean velocity profiles the hyperbolical character of a dissipation integral method is shown.Test cases for two-and three-dimensional boundary layers are analysed and discussed.The paper concludes with a discussion of the advantages and limits of dissipation integral methods.
Diffraction of Elastic Waves in Fluid-Layered Solid Interfaces by an Integral Formulation
J. E. Basaldúa-Sánchez
2013-01-01
Full Text Available In the present communication, scattering of elastic waves in fluid-layered solid interfaces is studied. The indirect boundary element method is used to deal with this wave propagation phenomenon in 2D fluid-layered solid models. The source is represented by Hankel’s function of second kind and this is always applied in the fluid. Our method is an approximate boundary integral technique which is based upon an integral representation for scattered elastic waves using single-layer boundary sources. This approach is typically called indirect because the sources’ strengths are calculated as an intermediate step. In addition, this formulation is regarded as a realization of Huygens’ principle. The results are presented in frequency and time domains. Various aspects related to the different wave types that emerge from this kind of problems are emphasized. A near interface pulse generates changes in the pressure field and can be registered by receivers located in the fluid. In order to show the accuracy of our method, we validated the results with those obtained by the discrete wave number applied to a fluid-solid interface joining two half-spaces, one fluid and the other an elastic solid.
Explicit Expressions for 3D Boundary Integrals in Potential Theory
Nintcheu Fata, Sylvain [ORNL
2009-01-01
On employing isoparametric, piecewise linear shape functions over a flat triangular domain, exact expressions are derived for all surface potentials involved in the numerical solution of three-dimensional singular and hyper-singular boundary integral equations of potential theory. These formulae, which are valid for an arbitrary source point in space, are represented as analytic expressions over the edges of the integration triangle. They can be used to solve integral equations defined on polygonal boundaries via the collocation method or may be utilized as analytic expressions for the inner integrals in the Galerkin technique. Also, the constant element approximation can be directly obtained with no extra effort. Sample problems solved by the collocation boundary element method for the Laplace equation are included to validate the proposed formulae.
Boundary integral solution of potential problems arising in the modelling of electrified oil films
Chappell, David J
2014-01-01
We consider a class of potential problems on a periodic half-space for the modelling of electrified oil films, which are used in the development of novel switchable liquid optical devices (diffraction gratings). A boundary integral formulation which reduces the problem to the study of the oil-air interface alone is derived and solved in a highly efficient manner using the Nystr\\"{o}m method. The oil films encountered experimentally are typically very thin and thus an interface-only integral representation is important for avoiding the near-singularity problems associated with boundary integral methods for long slender domains. The super-algebraic convergence of the proposed methods is discussed and demonstrated via appropriate numerical experiments.
Path integral formulation and Feynman rules for phylogenetic branching models
A dynamical picture of phylogenetic evolution is given in terms of Markov models on a state space, comprising joint probability distributions for character types of taxonomic classes. Phylogenetic branching is a process which augments the number of taxa under consideration, and hence the rank of the underlying joint probability state tensor. We point out the combinatorial necessity for a second-quantized, or Fock space setting, incorporating discrete counting labels for taxa and character types, to allow for a description in the number basis. Rate operators describing both time evolution without branching, and also phylogenetic branching events, are identified. A detailed development of these ideas is given, using standard transcriptions from the microscopic formulation of non-equilibrium reaction-diffusion or birth-death processes. These give the relations between stochastic rate matrices, the matrix elements of the corresponding evolution operators representing them, and the integral kernels needed to implement these as path integrals. The 'free' theory (without branching) is solved, and the correct trilinear 'interaction' terms (representing branching events) are presented. The full model is developed in perturbation theory via the derivation of explicit Feynman rules which establish that the probabilities (pattern frequencies of leaf colourations) arising as matrix elements of the time evolution operator are identical with those computed via the standard analysis. Simple examples (phylogenetic trees with two or three leaves), are discussed in detail. Further implications for the work are briefly considered including the role of time reparametrization covariance
A kernel-free boundary integral method for elliptic boundary value problems
Ying, Wenjun; Henriquez, Craig S.
2007-12-01
This paper presents a class of kernel-free boundary integral (KFBI) methods for general elliptic boundary value problems (BVPs). The boundary integral equations reformulated from the BVPs are solved iteratively with the GMRES method. During the iteration, the boundary and volume integrals involving Green's functions are approximated by structured grid-based numerical solutions, which avoids the need to know the analytical expressions of Green's functions. The KFBI method assumes that the larger regular domain, which embeds the original complex domain, can be easily partitioned into a hierarchy of structured grids so that fast elliptic solvers such as the fast Fourier transform (FFT) based Poisson/Helmholtz solvers or those based on geometric multigrid iterations are applicable. The structured grid-based solutions are obtained with standard finite difference method (FDM) or finite element method (FEM), where the right hand side of the resulting linear system is appropriately modified at irregular grid nodes to recover the formal accuracy of the underlying numerical scheme. Numerical results demonstrating the efficiency and accuracy of the KFBI methods are presented. It is observed that the number of GMRES iterations used by the method for solving isotropic and moderately anisotropic BVPs is independent of the sizes of the grids that are employed to approximate the boundary and volume integrals. With the standard second-order FEMs and FDMs, the KFBI method shows a second-order convergence rate in accuracy for all of the tested Dirichlet/Neumann BVPs when the anisotropy of the diffusion tensor is not too strong.
The integrated Earth system model version 1: formulation and functionality
W. D. Collins
2015-07-01
Full Text Available The integrated Earth system model (iESM has been developed as a new tool for projecting the joint human/climate system. The iESM is based upon coupling an integrated assessment model (IAM and an Earth system model (ESM into a common modeling infrastructure. IAMs are the primary tool for describing the human–Earth system, including the sources of global greenhouse gases (GHGs and short-lived species (SLS, land use and land cover change (LULCC, and other resource-related drivers of anthropogenic climate change. ESMs are the primary scientific tools for examining the physical, chemical, and biogeochemical impacts of human-induced changes to the climate system. The iESM project integrates the economic and human-dimension modeling of an IAM and a fully coupled ESM within a single simulation system while maintaining the separability of each model if needed. Both IAM and ESM codes are developed and used by large communities and have been extensively applied in recent national and international climate assessments. By introducing heretofore-omitted feedbacks between natural and societal drivers, we can improve scientific understanding of the human–Earth system dynamics. Potential applications include studies of the interactions and feedbacks leading to the timing, scale, and geographic distribution of emissions trajectories and other human influences, corresponding climate effects, and the subsequent impacts of a changing climate on human and natural systems. This paper describes the formulation, requirements, implementation, testing, and resulting functionality of the first version of the iESM released to the global climate community.
The integrated Earth system model version 1: formulation and functionality
Collins, W. D.; Craig, A. P.; Truesdale, J. E.; Di Vittorio, A. V.; Jones, A. D.; Bond-Lamberty, B.; Calvin, K. V.; Edmonds, J. A.; Kim, S. H.; Thomson, A. M.; Patel, P.; Zhou, Y.; Mao, J.; Shi, X.; Thornton, P. E.; Chini, L. P.; Hurtt, G. C.
2015-07-01
The integrated Earth system model (iESM) has been developed as a new tool for projecting the joint human/climate system. The iESM is based upon coupling an integrated assessment model (IAM) and an Earth system model (ESM) into a common modeling infrastructure. IAMs are the primary tool for describing the human-Earth system, including the sources of global greenhouse gases (GHGs) and short-lived species (SLS), land use and land cover change (LULCC), and other resource-related drivers of anthropogenic climate change. ESMs are the primary scientific tools for examining the physical, chemical, and biogeochemical impacts of human-induced changes to the climate system. The iESM project integrates the economic and human-dimension modeling of an IAM and a fully coupled ESM within a single simulation system while maintaining the separability of each model if needed. Both IAM and ESM codes are developed and used by large communities and have been extensively applied in recent national and international climate assessments. By introducing heretofore-omitted feedbacks between natural and societal drivers, we can improve scientific understanding of the human-Earth system dynamics. Potential applications include studies of the interactions and feedbacks leading to the timing, scale, and geographic distribution of emissions trajectories and other human influences, corresponding climate effects, and the subsequent impacts of a changing climate on human and natural systems. This paper describes the formulation, requirements, implementation, testing, and resulting functionality of the first version of the iESM released to the global climate community.
The integrated Earth System Model Version 1: formulation and functionality
Collins, William D.; Craig, Anthony P.; Truesdale, John E.; Di Vittorio, Alan; Jones, Andrew D.; Bond-Lamberty, Benjamin; Calvin, Katherine V.; Edmonds, James A.; Kim, Son H.; Thomson, Allison M.; Patel, Pralit L.; Zhou, Yuyu; Mao, Jiafu; Shi, Xiaoying; Thornton, Peter E.; Chini, Louise M.; Hurtt, George C.
2015-07-23
The integrated Earth System Model (iESM) has been developed as a new tool for pro- jecting the joint human/climate system. The iESM is based upon coupling an Integrated Assessment Model (IAM) and an Earth System Model (ESM) into a common modeling in- frastructure. IAMs are the primary tool for describing the human–Earth system, including the sources of global greenhouse gases (GHGs) and short-lived species, land use and land cover change, and other resource-related drivers of anthropogenic climate change. ESMs are the primary scientific tools for examining the physical, chemical, and biogeochemical impacts of human-induced changes to the climate system. The iESM project integrates the economic and human dimension modeling of an IAM and a fully coupled ESM within a sin- gle simulation system while maintaining the separability of each model if needed. Both IAM and ESM codes are developed and used by large communities and have been extensively applied in recent national and international climate assessments. By introducing heretofore- omitted feedbacks between natural and societal drivers, we can improve scientific under- standing of the human–Earth system dynamics. Potential applications include studies of the interactions and feedbacks leading to the timing, scale, and geographic distribution of emissions trajectories and other human influences, corresponding climate effects, and the subsequent impacts of a changing climate on human and natural systems. This paper de- scribes the formulation, requirements, implementation, testing, and resulting functionality of the first version of the iESM released to the global climate community.
Surface-integral formulation of scattering theory for charged particles
Full text: Collisions in the realm of atomic and nuclear physics not only have many practical applications, but also form the testing ground for the underlying quantum collision theory. The last decade has seen extraordinary theoretical progress in the field of electron-impact atomic breakup problem [1]. This problem was challenging to solve due to formal and computational difficulties associated with the long-range Coulomb potential. Presently, however, the electron-induced breakup processes can be calculated accurately for simple targets such as atomic hydrogen and helium, in the kinematically complete form. We report on how the computational progress has resulted in a deeper understanding of the formal theory of Coulomb few-body scattering [2] and how corresponding calculations of nuclear breakup reactions can benefit from this development. In quantum collision theory it is customary to define the scattering amplitude in terms of the scattering wave function and the potential of interaction. Despite the fact that the Coulomb wave function and the Coulomb potential are both known analytically, the conventional theory is not able to provide such a standard definition for the amplitude of scattering of two charged particles, which yields the Rutherford cross section. As far as breakup of a bound state of two particles in a system of three charged particles is concerned, here again the theory fails to give a formal definition for calculating the breakup amplitude in the post form in terms of the total scattering wave function describing the process. The reason for this failure is that charged particles continue to interact with each other even at infinite separation due to the long-range nature of the Coulomb potential, something the conventional theory cannot handle. We present a new formulation of scattering theory applicable to arbitrary two and three-body systems with both short-range and Coulomb long-range potentials [2]. The formalism is based on a surface-integral
Li, Ping
2014-07-01
This paper presents an algorithm hybridizing discontinuous Galerkin time domain (DGTD) method and time domain boundary integral (BI) algorithm for 3-D open region electromagnetic scattering analysis. The computational domain of DGTD is rigorously truncated by analytically evaluating the incoming numerical flux from the outside of the truncation boundary through BI method based on the Huygens\\' principle. The advantages of the proposed method are that it allows the truncation boundary to be conformal to arbitrary (convex/ concave) scattering objects, well-separated scatters can be truncated by their local meshes without losing the physics (such as coupling/multiple scattering) of the problem, thus reducing the total mesh elements. Furthermore, low frequency waves can be efficiently absorbed, and the field outside the truncation domain can be conveniently calculated using the same BI formulation. Numerical examples are benchmarked to demonstrate the accuracy and versatility of the proposed method.
Advanced applications of boundary-integral equation methods
The BIE (boundary integral equation) method is based on the numerical solution of a set of integral constraint equations which couple boundary tractions (stresses) to boundary displacements. Thus the dimensionality of the problem is reduced by one; only boundary geometry and data are discretized. Stresses at any set of selected interior points are computed following the boundary solution without any further numerical approximations. Thus, the BIE method has inherently greater resolution capability for stress gradients than does the finite element method. Conversely, the BIE method is not efficient for problems involving significant inhomogeneity such as in multi-thin-layered materials, or in elastoplasticity. Some progress in applyiing the BIE method to the latter problem has been made but much more work remains. Further, the BIE method is only optional for problems with significant stress risers, and only when boundary stresses are most important. Interior stress calculations are expensive, per point, and can drive the solution costs up rapidly. The current report summarizes some of the advanced elastic applications of fracture mechanics and three-dimensional stress analysis, while referencing some of the much broader developmental effort. Future emphasis is needed to exploit the BIE method in conjunction with other techniques such as the finite element method through the creation of hybrid stress analysis methods
Advanced applications of boundary-integral equation methods
Numerical analysis has become the basic tool for both design and research problems in solid mechanics. The boundary-integral equation (BIE) method is based on classical mathematical techniques but is finding new life as a basic stress analysis tool for engineering applications. The BIE method is based on the numerical solution of a set of integral constraint equations which couple boundary tractions (stresses) to boundary displacements. Thus the dimensionality of the problem is reduced by one; only boundary geometry and data are discretized. Stresses at any set of selected interior points are computed following the boundary solution without any further numerical approximations. Thus, the BIE method has inherently greater resolution capability for stress gradients than does the finite element method. Conversely, the BIE method is not efficient for problems involving significant inhomogeneity such as in multi-thin-layered materials, or in elastoplasticity. Some progress in applying the BIE method to the latter problem has been made but much more work remains. Further, the BIE method is only optional for problems with significant stress risers, and only when boundary stresses are more important. Interior stress calculations are expensive, per point, and can drive the solution costs up rapidly. The current report summarizes some of the advanced elastic applications of fracture mechanics and three-dimensional stress analysis, while referring some of the much broader developmental effort. (Auth.)
The D(D3)-anyon chain: integrable boundary conditions and excitation spectra
Finch, Peter E.; Frahm, Holger
2013-05-01
Chains of interacting non-Abelian anyons with local interactions invariant under the action of the Drinfeld double of the dihedral group D3 are constructed. Formulated as a spin chain the Hamiltonians are generated from commuting transfer matrices of an integrable vertex model for periodic and braided as well as open boundaries. A different anyonic model with the same local Hamiltonian is obtained within the fusion path formulation. This model is shown to be related to an integrable fusion interaction round the face model. Bulk and surface properties of the anyon chain are computed from the Bethe equations for the spin chain. The low-energy effective theories and operator content of the models (in both the spin chain and fusion path formulation) are identified from analytical and numerical studies of the finite-size spectra. For all boundary conditions considered the continuum theory is found to be a product of two conformal field theories. Depending on the coupling constants the factors can be a Z4 parafermion or a {M}_{(5,6)} minimal model.
Study of flow and mass transport in multilayered aquifers using boundary integral method
Zakikhani, M.
1988-01-01
In recent years, the boundary integral element method (BIEM) has been widely used in the area of ground-water modeling. This method, based on Green's theorem, has a variety of advantages over domain methods. Earlier applications of the BIEM to multilayer aquifer problems were restricted to steady-state flows. In these applications, layered aquifer systems were solved iteratively using the Bessel function as the principal Green function. In this formulation, the argument of the Bessel function is a function of hydraulic properties of the aquifer-aquitard system. Such an approach reduces the efficiency of the computations and yields less accurate numerical results. In the study presented here, a non-iterative boundary integral equation formulation (NIBIEM) for multilayer aquifer systems with or without a well network is developed. In this procedure, the coefficients of the singular points associated with pumping or recharge wells are included in the analysis in an analytic sense. This improves the efficiency and the accuracy of the computation. The formulation presented is developed for three different phases of flow.
Erzincanli, Belkis; Sahin, Mehmet
2013-12-01
An Arbitrary Lagrangian-Eulerian (ALE) formulation based on the unstructured finite volume method is proposed for solving moving boundary problems with large displacements and rotations. The numerical method is based on the side-centered arrangement of the primitive variables that does not require any ad-hoc modifications in order to enhance pressure coupling. The continuity equation is satisfied within each element at machine precision and the summation of the continuity equations can be exactly reduced to the domain boundary, which is important for the global mass conservation. A special attention is given to construct an ALE algorithm obeying the discrete geometric conservation law (DGCL). The mesh deformation algorithm is based on the indirect Radial Basis Function (RBF) algorithm at each time level while avoiding remeshing in order to enhance numerical robustness. For the parallel solution of resulting large-scale algebraic equations in a fully coupled form, a matrix factorization is introduced similar to that of the projection method for the whole system and the parallel algebraic multigrid solver BoomerAMG is used for the scaled discrete Laplacian provided by the HYPRE library which we access through the PETSc library. The present numerical algorithm is initially validated for the decaying Taylor-Green vortex flow, the flow past an oscillating circular cylinder in a channel and the flow induced by an oscillating sphere in a cubic cavity. Then the numerical algorithm is applied to the numerical simulation of flow field around a pair of flapping Drosophila wings in hover flight. The time variation of the Eulerian coherent structures in the near wake is shown along with the aerodynamic loads.
Optimal control problems for impulsive systems with integral boundary conditions
Allaberen Ashyralyev
2013-03-01
Full Text Available In this article, the optimal control problem is considered when the state of the system is described by the impulsive differential equations with integral boundary conditions. Applying the Banach contraction principle the existence and uniqueness of the solution is proved for the corresponding boundary problem by the fixed admissible control. The first and second variation of the functional is calculated. Various necessary conditions of optimality of the first and second order are obtained by the help of the variation of the controls.
Open two-species exclusion processes with integrable boundaries
We give a complete classification of integrable Markovian boundary conditions for the asymmetric simple exclusion process with two species (or classes) of particles. Some of these boundary conditions lead to non-vanishing particle currents for each species. We explain how the stationary state of all these models can be expressed in a matrix product form, starting from two key components, the Zamolodchikov–Faddeev and Ghoshal–Zamolodchikov relations. This statement is illustrated by studying in detail a specific example, for which the matrix ansatz (involving nine generators) is explicitly constructed and physical observables (such as currents, densities) calculated. (paper)
An integrated approach to marketing strategy formulation and implementation
Akroush, Mamoun Nadim Awwad
2003-01-01
The overall aim of the thesis was to address the issues involved in marketing strategy formulation, implementation and company performance by developing a framework for the marketing of insurance services in Jordan. In order to achieve this aim the research developed a comprehensive framework involving three parts; marketing strategy formulation components, marketing strategy implementation, and company performance. The research population included all the insurance companies t...
3D transient eddy current fields using the u-v integral-eigenvalue formulation
The three-dimensional eddy current transient field problem is formulated using the u-v method. This method breaks the vector Helmholtz equation into two scalar Helmholtz equations. Null field integral equations and the appropriate boundary conditions are used to set up an identification matrix which is independent of null field point locations. Embedded in the identification matrix are the unknown eigenvalues of the problem representing its impulse response in time. These eigenvalues are found by equating the determinant of the identification matrix to zero. When the initial transient forcing function is Fourier decomposed into its spatial harmonics, each Fourier component can be associated with a unique eigenvalue by this technique. The true transient solution comes through a convolution of the impulse response, so obtained with the particular external field decay governing the problem at hand. The technique is applied to the FELIX (fusion electromagnetic induction experiments) medium cylinder experiment; computed results are compared with data. A pseudoanalytic confirmation of the eigenvalues so obtained is formulated to validate the procedure
Convergence of a Boundary Integral Method for Water Waves
Beale, J. Thomas; Hou, Thomas Y.; Lowengrub, John
1996-01-01
We prove nonlinear stability and convergence of certain boundary integral methods for time-dependent water waves in a two-dimensional, inviscid, irrotational, incompressible fluid, with or without surface tension. The methods are convergent as long as the underlying solution remains fairly regular (and a sign condition holds in the case without surface tension). Thus, numerical instabilities are ruled out even in a fully nonlinear regime. The analysis is based on delicate energy estimates, fo...
Numerical comparison of spectral properties of volume-integral-equation formulations
Markkanen, Johannes; Ylä-Oijala, Pasi
2016-07-01
We study and compare spectral properties of various volume-integral-equation formulations. The equations are written for the electric flux, current, field, and potentials, and discretized with basis functions spanning the appropriate function spaces. Each formulation leads to eigenvalue distributions of different kind due to the effects of discretization procedure, namely, the choice of basis and testing functions. The discrete spectrum of the potential formulation reproduces the theoretically predicted spectrum almost exactly while the spectra of other formulations deviate from the ideal one. It is shown that the potential formulation has the spectral properties desired from the preconditioning perspective.
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.
Mazzotti, M. [Department of Civil, Chemical, Environmental and Materials Engineering – DICAM, University of Bologna, DICAM Viale del Risorgimento 2, Bologna 40136 (Italy); Civil, Architectural and Environmental Engineering Department, Drexel University, 3141 Chestnut St., Philadelphia, PA 19104 (United States); Bartoli, I. [Civil, Architectural and Environmental Engineering Department, Drexel University, 3141 Chestnut St., Philadelphia, PA 19104 (United States); Marzani, A., E-mail: alessandro.marzani@unibo.it [Department of Civil, Chemical, Environmental and Materials Engineering – DICAM, University of Bologna, DICAM Viale del Risorgimento 2, Bologna 40136 (Italy); Viola, E. [Department of Civil, Chemical, Environmental and Materials Engineering – DICAM, University of Bologna, DICAM Viale del Risorgimento 2, Bologna 40136 (Italy)
2013-09-01
Highlights: •Dispersive properties of viscoelastic waveguides and cavities are computed using a regularized 2.5D BEM. •Linear viscoelasticity is introduced at the constitutive level by means of frequency dependent complex moduli. •A contour integral algorithm is used to solve the nonlinear eigenvalue problem. •The Sommerfeld radiation condition is used to select the permissible Riemann sheets. •Attenuation of surface waves in cavities approaches the attenuation of Rayleigh waves. -- Abstract: A regularized 2.5D boundary element method (BEM) is proposed to predict the dispersion properties of damped stress guided waves in waveguides and cavities of arbitrary cross-section. The wave attenuation, induced by material damping, is introduced using linear viscoelastic constitutive relations and described in a spatial manner by the imaginary component of the axial wavenumber. The discretized dispersive wave equation results in a nonlinear eigenvalue problem, which is solved obtaining complex axial wavenumbers for a fixed frequency using a contour integral algorithm. Due to the singular characteristics and the multivalued feature of the wave equation, the requirement of holomorphicity inside the contour region over the complex wavenumber plane is fulfilled by the introduction of the Sommerfeld branch cuts and by the choice of the permissible Riemann sheets. A post processing analysis is developed for the extraction of the energy velocity of propagative guided waves. The reliability of the method is demonstrated by comparing the results obtained for a rail and a bar with square cross-section with those obtained from a 2.5D Finite Element formulation also known in literature as Semi Analytical Finite Element (SAFE) method. Next, to show the potential of the proposed numerical framework, dispersion properties are predicted for surface waves propagating along cylindrical cavities of arbitrary cross-section. It is demonstrated that the attenuation of surface waves
Highlights: •Dispersive properties of viscoelastic waveguides and cavities are computed using a regularized 2.5D BEM. •Linear viscoelasticity is introduced at the constitutive level by means of frequency dependent complex moduli. •A contour integral algorithm is used to solve the nonlinear eigenvalue problem. •The Sommerfeld radiation condition is used to select the permissible Riemann sheets. •Attenuation of surface waves in cavities approaches the attenuation of Rayleigh waves. -- Abstract: A regularized 2.5D boundary element method (BEM) is proposed to predict the dispersion properties of damped stress guided waves in waveguides and cavities of arbitrary cross-section. The wave attenuation, induced by material damping, is introduced using linear viscoelastic constitutive relations and described in a spatial manner by the imaginary component of the axial wavenumber. The discretized dispersive wave equation results in a nonlinear eigenvalue problem, which is solved obtaining complex axial wavenumbers for a fixed frequency using a contour integral algorithm. Due to the singular characteristics and the multivalued feature of the wave equation, the requirement of holomorphicity inside the contour region over the complex wavenumber plane is fulfilled by the introduction of the Sommerfeld branch cuts and by the choice of the permissible Riemann sheets. A post processing analysis is developed for the extraction of the energy velocity of propagative guided waves. The reliability of the method is demonstrated by comparing the results obtained for a rail and a bar with square cross-section with those obtained from a 2.5D Finite Element formulation also known in literature as Semi Analytical Finite Element (SAFE) method. Next, to show the potential of the proposed numerical framework, dispersion properties are predicted for surface waves propagating along cylindrical cavities of arbitrary cross-section. It is demonstrated that the attenuation of surface waves
El-Awady, J.; Biner, S.; Ghoniem, N.
2007-11-07
We present a self-consistent formulation of 3-D parametric dislocation dynamics (PDD) with the boundary element method (BEM) to describe dislocation motion, and hence microscopic plastic flow in finite volumes. We develop quantitative measures of the accuracy and convergence of the method by considering a comparison with known analytical solutions. It is shown that the method displays absolute convergence with increasing the number of quadrature points on the dislocation loop and the surface mesh density. The error in the image force on a screw dislocation approaching a free surface is shown to increase as the dislocation approaches the surface, but is nevertheless controllable. For example, at a distance of one lattice parameter from the surface, the relative error is less than 5% for a surface mesh with an element size of 1000 x 2000 (in units of lattice parameter), and 64 quadrature points. The Eshelby twist angle in a finite-length cylinder containing a coaxial screw dislocation is also used to benchmark the method. Finally, large scale 3-D simulation results of single slip behavior in cylindrical microcrystals are presented. Plastic flow characteristics and the stress-strain behavior of cylindrical microcrystals under compression are shown to be in agreement with experimental observations. It is shown that the mean length of dislocations trapped at the surface is the dominant factor in determining the size effects on hardening of single crystals. The influence of surface image fields on the flow stress is finally explored. It is shown that the flow stress is reduced by as much as 20% for small single crystals of size less than 0.15 {micro}m.
Bird, G. E.; Trevelyan, J; Augarde, C.E.
2010-01-01
Issues relating to the practical implementation of the coupled boundary element–scaled boundary finite element method are addressed in this paper. A detailed approach highlights fully the process of applying boundary conditions, including the treatment of examples in which the assumptions made in previous work are no longer valid. Verification of the method is undertaken by means of estimating stress intensity factors and comparing them against analytical solutions. The coupled algorithm show...
Revisit boundary conditions for the self-adjoint angular flux formulation
Wang, Yaqi [Idaho National Lab. (INL), Idaho Falls, ID (United States); Gleicher, Frederick N. [Idaho National Lab. (INL), Idaho Falls, ID (United States)
2015-03-01
We revisit the boundary conditions for SAAF. We derived the equivalent parity variational form ready for coding up. The more rigorous approach of evaluating odd parity should be solving the odd parity equation coupled with the even parity. We proposed a symmetric reflecting boundary condition although neither positive definiteness nor even-odd decoupling is achieved. A simple numerical test verifies the validity of these boundary conditions.
Tokamak plasma shape identification based on the boundary integral equations
A necessary condition for tokamak plasma shape identification is discussed and a new identification method is proposed in this article. This method is based on the boundary integral equations governing a vacuum region around a plasma with only the measurement of either magnetic fluxes or magnetic flux intensities. It can identify various plasmas with low to high ellipticities with the precision determined by the number of the magnetic sensors. This method is applicable to real-time control and visualization using a 'table-look-up' procedure. (author)
Integrability of a deterministic cellular automaton driven by stochastic boundaries
Prosen, Tomaž; Mejía-Monasterio, Carlos
2016-05-01
We propose an interacting many-body space–time-discrete Markov chain model, which is composed of an integrable deterministic and reversible cellular automaton (rule 54 of Bobenko et al 1993 Commun. Math. Phys. 158 127) on a finite one-dimensional lattice {({{{Z}}}2)}× n, and local stochastic Markov chains at the two lattice boundaries which provide chemical baths for absorbing or emitting the solitons. Ergodicity and mixing of this many-body Markov chain is proven for generic values of bath parameters, implying the existence of a unique nonequilibrium steady state. The latter is constructed exactly and explicitly in terms of a particularly simple form of matrix product ansatz which is termed a patch ansatz. This gives rise to an explicit computation of observables and k-point correlations in the steady state as well as the construction of a nontrivial set of local conservation laws. The feasibility of an exact solution for the full spectrum and eigenvectors (decay modes) of the Markov matrix is suggested as well. We conjecture that our ideas can pave the road towards a theory of integrability of boundary driven classical deterministic lattice systems.
Geng, Weihua; Krasny, Robert
2013-08-01
We present a treecode-accelerated boundary integral (TABI) solver for electrostatics of solvated biomolecules described by the linear Poisson-Boltzmann equation. The method employs a well-conditioned boundary integral formulation for the electrostatic potential and its normal derivative on the molecular surface. The surface is triangulated and the integral equations are discretized by centroid collocation. The linear system is solved by GMRES iteration and the matrix-vector product is carried out by a Cartesian treecode which reduces the cost from O(N2) to O(NlogN), where N is the number of faces in the triangulation. The TABI solver is applied to compute the electrostatic solvation energy in two cases, the Kirkwood sphere and a solvated protein. We present the error, CPU time, and memory usage, and compare results for the Poisson-Boltzmann and Poisson equations. We show that the treecode approximation error can be made smaller than the discretization error, and we compare two versions of the treecode, one with uniform clusters and one with non-uniform clusters adapted to the molecular surface. For the protein test case, we compare TABI results with those obtained using the grid-based APBS code, and we also present parallel TABI simulations using up to eight processors. We find that the TABI solver exhibits good serial and parallel performance combined with relatively simple implementation, efficient memory usage, and geometric adaptability.
Intrinsic Formulation of Geometric Integrability and Generation of Conservation Laws
Bracken, Paul
2007-01-01
An intrinsic version of the integrability theorem for the classical Backlund theorem is presented. It is characterized by a one-form which can be put in the form of a Riccati system. It is shown how this system can be linearized. Based on this, a procedure for generating an infinite number of conservation laws is given.
Pun, Kit Fai
2003-01-01
Performance measurement quantifies the efficiency and effectiveness of action that helps organisations translate their strategies into results and fixes accountability to improve performance. This research identifies two problem statements: First, can integrating strategy formulation with measurement initiatives safeguard the performance goals in manufacturing enterprises? And second, how can manufacturing enterprises derive an integrated approach that meet their requirements and needs for ...
Advanced applications of boundary-integral equation methods
Numerical analysis has become the basic tool for both design and research problems in solid mechanics. The need for accuracy and detail, plus the availablity of the high speed computer has led to the development of many new modeling methods ranging from general purpose structural analysis finite element programs to special purpose research programs. The boundary-integral equation (BIE) method is based on classical mathematical techniques but is finding new life as a basic stress analysis tool for engineering applications. The paper summarizes some advanced elastic applications of fracture mechanics and three-dimensional stress analysis, while referencing some of the much broader developmental effort. Future emphasis is needed to exploit the BIE method in conjunction with other techniques such as the finite element method through the creation of hybrid stress analysis methods. (Auth.)
A coupled finite-element, boundary-integral method for simulating ultrasonic flowmeters.
Bezdĕk, Michal; Landes, Hermann; Rieder, Alfred; Lerch, Reinhard
2007-03-01
Today's most popular technology of ultrasonic flow measurement is based on the transit-time principle. In this paper, a numerical simulation technique applicable to the analysis of transit-time flowmeters is presented. A flowmeter represents a large simulation problem that also requires computation of acoustic fields in moving media. For this purpose, a novel boundary integral method, the Helmholtz integral-ray tracing method (HIRM), is derived and validated. HIRM is applicable to acoustic radiation problems in arbitrary mean flows at low Mach numbers and significantly reduces the memory demands in comparison with the finite-element method (FEM). It relies on an approximate free-space Green's function which makes use of the ray tracing technique. For simulation of practical acoustic devices, a hybrid simulation scheme consisting of FEM and HIRM is proposed. The coupling of FEM and HIRM is facilitated by means of absorbing boundaries in combination with a new, reflection-free, acoustic-source formulation. Using the coupled FEM-HIRM scheme, a full three-dimensional (3-D) simulation of a complete transit-time flowmeter is performed for the first time. The obtained simulation results are in good agreement with measurements both at zero flow and under flow conditions. PMID:17375833
Radiolysis Model Formulation for Integration with the Mixed Potential Model
Buck, Edgar C.; Wittman, Richard S.
2014-07-10
The U.S. Department of Energy Office of Nuclear Energy (DOE-NE), Office of Fuel Cycle Technology has established the Used Fuel Disposition Campaign (UFDC) to conduct the research and development activities related to storage, transportation, and disposal of used nuclear fuel (UNF) and high-level radioactive waste. Within the UFDC, the components for a general system model of the degradation and subsequent transport of UNF is being developed to analyze the performance of disposal options [Sassani et al., 2012]. Two model components of the near-field part of the problem are the ANL Mixed Potential Model and the PNNL Radiolysis Model. This report is in response to the desire to integrate the two models as outlined in [Buck, E.C, J.L. Jerden, W.L. Ebert, R.S. Wittman, (2013) “Coupling the Mixed Potential and Radiolysis Models for Used Fuel Degradation,” FCRD-UFD-2013-000290, M3FT-PN0806058
A new class preconditioners for one class of two-or three-dimensional elliptic operators with highly varying coefficients is developed. The construction is based on domain decomposition method when the substructure contains internal cross points. The approximation of the initial equation is based on the Galerkin method for special subspaces of Sobolev's spaces H1. The general estimates of the condition number for the preconditioned operator are given. This number does not depend on the variation range of the coefficient of the initial operator and slightly (logarithmically) depends on a step of the domain triangulation. The preconditioner operators provide means for constructing the cost-effective methods for solution of magnetostatic equations in incomplete-nonlinear formulation as well as in formulation of the Maxwell equation for the scale potential representation. These operators are easily inverible both for parallel and for traditional computing achitectures. 36 refs.; 1 tab
Influence of the plasma boundary on the line-integrated emissivity
In tokamak plasma radiation diagnostics, if the width of a detected plasma chord is comparable with the plasma minor radius, the plasma boundary may influence the line-integrated emissivity considerably and make it a weighted integral of the width-averaged emissivity. The explicit formula for the line-integrated emissivity with taking into account the plasma boundary effect is presented
Ntouyas SotirisK
2011-01-01
Full Text Available This paper studies a boundary value problem of nonlinear fractional differential equations of order with three-point integral boundary conditions. Some new existence and uniqueness results are obtained by using standard fixed point theorems and Leray-Schauder degree theory. Our results are new in the sense that the nonlocal parameter in three-point integral boundary conditions appears in the integral part of the conditions in contrast to the available literature on three-point boundary value problems which deals with the three-point boundary conditions restrictions on the solution or gradient of the solution of the problem. Some illustrative examples are also discussed.
Keck, Rolf-Erik; Veldkamp, Dick; Wedel-Heinen, Jens Jakob;
This thesis describes the further development and validation of the dynamic meandering wake model for simulating the flow field and power production of wind farms operating in the atmospheric boundary layer (ABL). The overall objective of the conducted research is to improve the modelling...... of the wind industry, four areas were identified as high prioritizations for further research: 1. the turbulence distribution in a single wake 2. multiple wake deficits and build-up of turbulence over a row of turbines 3. the effect of the atmospheric boundary layer on wake turbulence and wake deficit...... evolution 4. atmospheric stability effects on wake deficit evolution and meandering The conducted research is to a large extent based on detailed wake investigations and reference data generated through computational fluid dynamics simulations, where the wind turbine rotor has been represented...
Boundary conditions and the generalized metric formulation of the double sigma model
Ma, Chen-Te
2015-09-01
Double sigma model with strong constraints is equivalent to the ordinary sigma model by imposing a self-duality relation. The gauge symmetries are the diffeomorphism and one-form gauge transformation with the strong constraints. We consider boundary conditions in the double sigma model from three ways. The first way is to modify the Dirichlet and Neumann boundary conditions with a fully O (D, D) description from double gauge fields. We perform the one-loop β function for the constant background fields to find low-energy effective theory without using the strong constraints. The low-energy theory can also have O (D, D) invariance as the double sigma model. The second way is to construct different boundary conditions from the projectors. The third way is to combine the antisymmetric background field with field strength to redefine an O (D, D) generalized metric. We use this generalized metric to reconstruct a consistent double sigma model with the classical and quantum equivalence.
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.
Stenroos, Matti
2016-01-01
Boundary element methods (BEM) are used for forward computation of bioelectromagnetic fields in multi-compartment volume conductor models. Most BEM approaches assume that each compartment is in contact with at most one external compartment. In this work, I present a general surface integral equation and BEM discretization that remove this limitation and allow BEM modeling of general piecewise-homogeneous medium. The new integral equation allows positioning of field points at junctioned boundary of more than two compartments, enabling the use of linear collocation BEM in such a complex geometry. A modular BEM implementation is presented for linear collocation and Galerkin approaches, starting from standard formulation. The approach and resulting solver are verified in three ways, including comparison to finite element method (FEM). In a two-compartment split-sphere model with two spaced monopoles, the results obtained with high-resolution FEM and the BEMs were almost identical (relative difference < 0.003).
Coarse projective kMC integration: forward/reverse initial and boundary value problems
In 'equation-free' multiscale computation a dynamic model is given at a fine, microscopic level; yet we believe that its coarse-grained, macroscopic dynamics can be described by closed equations involving only coarse variables. These variables are typically various low-order moments of the distributions evolved through the microscopic model. We consider the problem of integrating these unavailable equations by acting directly on kinetic Monte Carlo microscopic simulators, thus circumventing their derivation in closed form. In particular, we use projective multi-step integration to solve the coarse initial value problem forward in time as well as backward in time (under certain conditions). Macroscopic trajectories are thus traced back to unstable, source-type, and even sometimes saddle-like stationary points, even though the microscopic simulator only evolves forward in time. We also demonstrate the use of such projective integrators in a shooting boundary value problem formulation for the computation of 'coarse limit cycles' of the macroscopic behavior, and the approximation of their stability through estimates of the leading 'coarse Floquet multipliers'
Boundary Conditions and the Generalized Metric Formulation of the Double Sigma Model
Ma, Chen-Te
2015-01-01
Double sigma model with the strong constraints is equivalent to the normal sigma model by imposing the self-duality relation. The gauge symmetries are the diffeomorphism and one-form gauge transformation with the strong constraints. We modify the Dirichlet and Neumann boundary conditions with the fully $O(D, D)$ description from the doubled gauge fields. We perform the one-loop $\\beta$ function for the constant background fields to find low energy effective theory without using the strong constraints. The low energy theory can also be $O(D,D)$ invariant as the double sigma model. We use the other one way to construct different boundary conditions from the projectors. Finally, we combine the antisymmetric background field with the field strength to redefine a different $O(D, D)$ generalized metric. We use this generalized metric to construct a consistent double sigma model with the classical and quantum equivalence. We show the one-loop $\\beta$ function for the constant background fields and obtain the normal ...
A New Integral Formulation for Eddy Current Computation in Thin Conductive Shells
Le Duc, Tung; Meunier, Gérard; Chadebec, Olivier; Guichon, Jean-Michel
2012-01-01
In order to compute eddy current distributions in thin conductive nonmagnetic shells, a new integral formulation is proposed. The method is based on a surface impedance condition which takes into account the field variation through depth due to skin effect. It is general and enables the modeling of various problems whatever their skin-depth and avoiding the meshing of the air region.
Integrable systems on so(4) related to XXX spin chains with boundaries
We consider two-site XXX Heisenberg magnets with different boundary conditions, which are integrable systems on so(4) possessing additional cubic and quartic integrals of motion. The separated variables for these models are constructed using the Sklyanin method
Formulation of natural convection around repository for dual reciprocity boundary element solution
The disposal of high-level radioactive wastes in deep geological formations is of pronounced technological importance for nuclear safety. The understanding of related fluid flow, heat and mass transport in geological systems is of great interest. This article prepares necessary physical, mathematical and numerical fundamentals for computational modeling of related phenomena. The porous media is described by the simple Darcy law and momentum-energy coupling is due to Boussinesq approximation. The Dual Reciprocity of Boundary Element Method (DRBEM) is used for solving coupled mass, momentum and energy equations in two-dimensions for the steady buoyancy induced convection problem in an semi-infinite porous media. It is structured by weighting with the fundamental solution of the Laplace equation. The inverse multi quadrics are used in the DRBEM transformation. The solution is obtained in an iterative way.(author)
BOUNDARY INTEGRAL FORMULAS FOR ELASTIC PLANE PROBLEM OF EXTERIOR CIRCULAR DOMAIN
DONG Zheng-zhu; LI Shun-cai; YU De-hao
2006-01-01
After the stress function and the normal derivative on the boundary for the plane problem of exterior circular domain are expanded into Laurent series, comparing them with the Laurent series of the complex stress function and making use of some formulas in Fourier series and the convolutions, the boundary integral formula of the stress function is derived further. Then the stress function can be obtained directly by the integration of the stress function and its normal derivative on the boundary. Some examples are given. It shows that the boundary integral formula of the stress function is convenient to be used for solving the elastic plane problem of exterior circular domain.
High Order Projection Plane Method for Evaluation of Supersingular Curved Boundary Integrals in BEM
Miao Cui; Wei-zhe Feng; Xiao-wei Gao; Kai Yang
2016-01-01
Boundary element method (BEM) is a very promising approach for solving various engineering problems, in which accurate evaluation of boundary integrals is required. In the present work, the direct method for evaluating singular curved boundary integrals is developed by considering the third-order derivatives in the projection plane method when expanding the geometry quantities at the field point as Taylor series. New analytical formulas are derived for geometry quantities defined on the curve...
Piloting and Path Integration within and across Boundaries
Mou, Weimin; Wang, Lin
2015-01-01
Three experiments investigated whether navigation is less efficient across boundaries than within boundaries. In an immersive virtual environment, participants learned objects' locations in a large room or a small room. Participants then pointed to the objects' original locations after physically walking a circuitous path without vision.…
The impact of a boundary layer height formulation on the GEOS-5 model climate
McGrath-Spangler, E. L.
2016-04-01
Planetary boundary layer (PBL) processes are important for the estimation of surface-atmosphere exchanges that impact global climate. One way of characterizing the strength of these processes is the PBL depth. In the Goddard Earth Observing System (GEOS-5) atmospheric general circulation model, the PBL depth is also used in calculating the turbulent length scale, which, in turn, is used in estimating the turbulence and vertical mixing within the model. Therefore, changing the PBL depth definition directly affects the model climate. This study evaluates the climatological model response of two long-term simulations using different PBL depth definitions. The first definition is based on a bulk Richardson number; the second uses a combination of the same bulk Richardson number definition over land plus a definition based on the turbulent eddy diffusion coefficient over water. The two simulations produce different spatiotemporal patterns of temperature, specific humidity, and wind speed related to the differences in turbulence. The largest differences, as expected, are present over water. Due to differences in atmospheric stability, the relationship between the two PBL depth estimates differ among the majority of the oceans and off the west coasts of continents, affecting the climatic response. Due to its optimization of the climatic response while maintaining a realistic diurnal cycle of PBL depth, the mixed PBL depth configuration is preferred.
We present a method to solve initial-boundary-value problems for linear and integrable nonlinear differential-difference evolution equations. The method is the discrete version of the one developed by A S Fokas to solve initial-boundary-value problems for linear and integrable nonlinear partial differential equations via an extension of the inverse scattering transform. The method takes advantage of the Lax pair formulation for both linear and nonlinear equations, and is based on the simultaneous spectral analysis of both parts of the Lax pair. A key role is also played by the global algebraic relation that couples all known and unknown boundary values. Even though additional technical complications arise in discrete problems compared to continuum ones, we show that a similar approach can also solve initial-boundary-value problems for linear and integrable nonlinear differential-difference equations. We demonstrate the method by solving initial-boundary-value problems for the discrete analogue of both the linear and the nonlinear Schrödinger equations, comparing the solution to those of the corresponding continuum problems. In the linear case we also explicitly discuss Robin-type boundary conditions not solvable by Fourier series. In the nonlinear case, we also identify the linearizable boundary conditions, we discuss the elimination of the unknown boundary datum, we obtain explicitly the linear and continuum limit of the solution, and we write the soliton solutions
Cutanda Henríquez, Vicente; Juhl, Peter Møller
2008-01-01
) when field points are calculated very close to the boundary. The difficulty is due to the near-singularity of the integrand, which causes failure of the numerical integration over the element. There are a number of techniques to overcome this problem, in many cases involving a reformulation of the...... interest. The subdivision is adapted to the strength of the near-singularity and is only performed when needed, not adding excessive calculation time and storage. The implementation is examined and verified with test cases....
Liu, Enru; Zhang, Z.; Yue, J.H.; Dobson, Andy
2008-01-01
We present a semi-analytic method based on the propagation matrix formulation of indirect boundary element method to compute response of elastic (and acoustic) waves in multi-layered media with irregular interfaces. The method works recursively starting from the top-most free surface at which a stress-free boundary condition is applied, and the displacement-stress boundary conditions are then subsequently applied at each interface. The basic idea behind this method is the matrix formulation o...
A formulation for vertically integrated groundwater flow in a stratified coastal aquifer
Strack, O. D. L.; Ausk, B. K.
2015-08-01
We present the comprehensive discharge potential for steady three-dimensional flow in horizontally stratified coastal aquifers with a horizontal base and a vertical coastline. The gradient of this comprehensive potential gives the vertically integrated discharge throughout the aquifer, i.e., the specific discharge vector as a function of three-dimensional space integrated over the saturated portion of the aquifer. The boundary values of the comprehensive potential along the coast can be computed precisely, given the geometry of the aquifer: the hydraulic conductivities of the strata, the elevations of the horizontal planes that separate the strata, and the elevation of the impermeable base of the aquifer relative to sea level. Boundary conditions of the comprehensive potential may either be given in terms of its gradient, or computed from given heads along the boundaries. The governing equation of the comprehensive potential is the Poisson equation in areas of infiltration and the Laplace equation elsewhere. The computation of interface elevations, piezometric heads, and the vertical distribution of flow requires that an assumption be made regarding the relation between the comprehensive potential and piezometric heads. We adopt the Dupuit-Forchheimer approximation for this purpose and make use of the Ghyben-Herzberg equation. We present several applications of the approach and find that the stratification may have a significant effect on the boundary value of the comprehensive potential, and thus on the flow rates in the aquifer.
Guo, J. Y.; Shang, K.; Jekeli, C.; Shum, C. K.
2015-04-01
Two approaches have been formulated to compute the gravitational potential difference using low-low satellite-to-satellite tracking data based on energy integral: one in the geocentric inertial reference system, and the other in the terrestrial reference system. The focus of this work is on the approach in the geocentric inertial reference system, where a potential rotation term appears in addition to the potential term. In former formulations, the contribution of the time-variable components of the gravitational potential to the potential term was included, but their contribution to the potential rotation term was neglected. In this work, an improvement to the former formulations is made by reformulating the potential rotation term to include the contribution of the time-variable components of the gravitational potential. A simulation shows that our more accurate formulation of the potential rotation term is necessary to achieve the accuracy for recovering the temporal variation of the Earth's gravity field, such as for use to the Gravity Recovery And Climate Experiment GRACE observation data based on this approach.
Integrated Multi-Strategic Web Document Pre-Processing for Sentence and Word Boundary Detection.
Shim, Junhyeok; Kim, Dongseok; Cha, Jeongwon; Lee, Gary Geunbae; Seo, Jungyun
2002-01-01
Discussion of natural language processing focuses on a multi-strategic integrated text preprocessing method for difficult problems of sentence boundary disambiguation and word boundary disambiguation of Web texts. Describes an evaluation of the method using Korean Web document collections. (Author/LRW)
Algebraic Bethe Ansatz for O(2N) sigma models with integrable diagonal boundaries
Gombor, Tamas
2015-01-01
The finite volume problem of O(2N) sigma models with integrable diagonal boundaries on a finite interval is investigated. The double row transfer matrix is diagonalized by Algebraic Bethe Ansatz. The boundary Bethe Yang equations for the particle rapidities and the accompanying Bethe Ansatz equations are derived.
Mouffak Benchohra; Fatima-Zohra Mostefai
2012-01-01
The aim of this paper is to investigate a class of boundary value problems for fractional differential equations involving nonlinear integral conditions. The main tool used in our considerations is the technique associated with measures of weak noncompactness.
Multiple integral representation for the trigonometric SOS model with domain wall boundaries
Using the dynamical Yang-Baxter algebra we derive a functional equation for the partition function of the trigonometric SOS model with domain wall boundary conditions. The solution of the equation is given in terms of a multiple contour integral.
Multiple integral representation for the trigonometric SOS model with domain wall boundaries
Galleas, W.
2012-05-01
Using the dynamical Yang-Baxter algebra we derive a functional equation for the partition function of the trigonometric SOS model with domain wall boundary conditions. The solution of the equation is given in terms of a multiple contour integral.
WODC
2007-01-01
The project's aim is to contribute to the building of a common system of indicators to measure immigrant integration in Europe, providing the input of states, countries and affected groups: immigrants (and women in particular in this group) as well as the host population. The responsibility of this project is in the hands of the General Directorate for Immigrant Integration of the Ministry of Labour and Social Affairs in Spain. It has been supported by a transnational network involving the pa...
Adel A.K. Mohsen
2010-07-01
Full Text Available The problem of nonuniqueness (NU of the solution of exterior acoustic problems via boundary integral equations is discussed in this article. The efficient implementation of the CHIEF (Combined Helmholtz Integral Equations Formulation method to axisymmetric problems is studied. Interior axial fields are used to indicate the solution error and to select proper CHIEF points. The procedure makes full use of LU-decomposition as well as the forward solution derived in the solution. Implementations of the procedure for hard spheres are presented. Accurate results are obtained up to a normalised radius of ka = 20.983, using only one CHIEF point. The radiation from a uniformly vibrating sphere is also considered. Accurate results for ka up to 16.927 are obtained using two CHIEF points.
Boriskina, Svetlana V; Sewell, Phillip; Benson, Trevor M; Nosich, Alexander I
2004-03-01
A fast and accurate method is developed to compute the natural frequencies and scattering characteristics of arbitrary-shape two-dimensional dielectric resonators. The problem is formulated in terms of a uniquely solvable set of second-kind boundary integral equations and discretized by the Galerkin method with angular exponents as global test and trial functions. The log-singular term is extracted from one of the kernels, and closed-form expressions are derived for the main parts of all the integral operators. The resulting discrete scheme has a very high convergence rate. The method is used in the simulation of several optical microcavities for modern dense wavelength-division-multiplexed systems. PMID:15005404
Isolation, Integration, and Ethnic Boundaries in Rural Guatemala
Pebley, Anne R.; Goldman, Noreen; Robles, Arodys
2002-01-01
The Guatemalan Indigenous population is engaged in a process of ethnic reorganization that closely parallels that of contemporary American Indians. We investigate the consequences of this process on the use of two key ethnic boundary markers for women -- dress and language use – using data from a 1995 social survey. The results show that social isolation and education are key factors in knowledge and use of Indigenous languages. By contrast, use of Indigenous dress does not vary substantially...
Classical Mechanics in Hilbert Space: Path Integral Formulation, and a Quantum Correction
Shee, James
2015-01-01
While it is well-known that quantum mechanics can be reformulated in terms of a path integral representation, it will be shown that such a formulation is also possible in the case of classical mechanics. From Koopman-von Neumann theory, which recasts classical mechanics in terms of a Hilbert space wherein the Liouville operator acts as the generator of motion, we derive a path integral representation of the classical propagator and suggest an efficient numerical implementation using fast fourier transform techniques. We then include a first quantum correction to derive a revealing expression for the semi-classical path integral, which augments the classical picture of a single trajectory through phase space with additional wave-like spreading.
Shape integral method for magnetospheric shapes. [boundary layer calculations
Michel, F. C.
1979-01-01
A method is developed for calculating the shape of any magnetopause to arbitrarily high precision. The method uses an integral equation which is evaluated for a trial shape. The resulting values of the integral equation as a function of auxiliary variables indicate how close one is to the desired solution. A variational method can then be used to improve the trial shape. Some potential applications are briefly mentioned.
High Order Projection Plane Method for Evaluation of Supersingular Curved Boundary Integrals in BEM
Miao Cui
2016-01-01
Full Text Available Boundary element method (BEM is a very promising approach for solving various engineering problems, in which accurate evaluation of boundary integrals is required. In the present work, the direct method for evaluating singular curved boundary integrals is developed by considering the third-order derivatives in the projection plane method when expanding the geometry quantities at the field point as Taylor series. New analytical formulas are derived for geometry quantities defined on the curved line/plane, and unified expressions are obtained for both two-dimensional and three-dimensional problems. For the two-dimensional boundary integrals, analytical expressions for the third-order derivatives are derived and are employed to verify the complex-variable-differentiation method (CVDM which is used to evaluate the high order derivatives for three-dimensional problems. A few numerical examples are given to show the effectiveness and the accuracy of the present method.
Light-front Hamiltonian and path integral formulations of large N scalar QCD2
Recently Grinstein, Jora and Polosa (2009) have studied a model of large N scalar quantum chromodynamics (QCD) in one-space one-time dimensions (cf. G. 't Hooft (1974) ). This theory admits a Bethe-Salpeter equation describing the discrete spectrum of qq¯ bound states. They consider the gauge fields in the adjoint representation of SU(N) and the scalar fields in the fundamental representation. The theory is asymptotically free and linearly confining. In this work, we present the light-front quantization of this theory using the Hamiltonian and path integral formulations under appropriate light-cone gauges.
Light-front Hamiltonian and path integral formulations of large N scalar QCD{sub 2}
Kulshreshtha, Usha, E-mail: ushakulsh@gmail.com [Department of Physics, Kirori Mal College, University of Delhi, Delhi-110007 (India); Kulshreshtha, D.S., E-mail: dskulsh@gmail.com [Department of Physics and Astrophysics, University of Delhi, Delhi-110007 (India); Vary, J.P., E-mail: jvary@iastate.edu [Department of Physics and Astronomy, Iowa State University, Ames, IA 50011 (United States)
2012-02-14
Recently Grinstein, Jora and Polosa (2009) have studied a model of large N scalar quantum chromodynamics (QCD) in one-space one-time dimensions (cf. G. 't Hooft (1974) ). This theory admits a Bethe-Salpeter equation describing the discrete spectrum of qq{sup Macron} bound states. They consider the gauge fields in the adjoint representation of SU(N) and the scalar fields in the fundamental representation. The theory is asymptotically free and linearly confining. In this work, we present the light-front quantization of this theory using the Hamiltonian and path integral formulations under appropriate light-cone gauges.
Light-front Hamiltonian and path integral formulations of large N scalar QCD2
Kulshreshtha, Usha; Kulshreshtha, D. S.; Vary, J. P.
2012-02-01
Recently Grinstein, Jora and Polosa (2009) [5] have studied a model of large N scalar quantum chromodynamics (QCD) in one-space one-time dimensions (cf. G. 't Hooft (1974) [6]). This theory admits a Bethe-Salpeter equation describing the discrete spectrum of qqbar bound states. They consider the gauge fields in the adjoint representation of SU (N) and the scalar fields in the fundamental representation. The theory is asymptotically free and linearly confining. In this work, we present the light-front quantization of this theory using the Hamiltonian and path integral formulations under appropriate light-cone gauges.
Jokela, Niko; Kytölä, Kalle
2013-01-01
We study the probabilities with which chordal Schramm-Loewner Evolutions (SLE) visit small neighborhoods of boundary points. We find explicit formulas for general chordal SLE boundary visiting probability amplitudes, also known as SLE boundary zig-zags or order refined SLE multi-point Green's functions on the boundary. Remarkably, an exact answer can be found to this important SLE question for an arbitrarily large number of marked points. The main technique employed is a spin chain - Coulomb gas correspondence between tensor product representations of a quantum group and functions given by Dotsenko-Fateev type integrals. We show how to express these integral formulas in terms of regularized real integrals, and we discuss their numerical evaluation. The results are universal in the sense that apart from an overall multiplicative constant the same formula gives the amplitude for many different formulations of the SLE boundary visit problem. The formula also applies to renormalized boundary visit probabilities f...
Three-dimensional layerwise modeling of layered media with boundary integral equations
Kokkinos, Filis-Triantaphyllos T.
1995-01-01
A hybrid method is presented for the analysis of layers, plates, and multi-layered systems consisting of isotropic and linear elastic materials. The problem is formulated for the general case of a multi-layered system using a total potential energy formulation and employing the layerwise laminate theory of Reddy. A one-dimensional finite element model is used for the analysis of the multi-layered system through its thickness, and integral Fourier transforms are used to obtai...
Gomez-Sousa, Hipolito; Martinez-Lorenzo, Jose Angel; Arias-Acuña, Marcos
2015-01-01
This paper presents a new method, based on the well-known method of moments (MoM), for the numerical electromagnetic analysis of scattering and radiation from metallic or dielectric structures, or both structure types in the same simulation, that are in contact with other metallic or dielectric structures. The proposed method for solving the MoM junction problem consists of two separate algorithms, one of which comprises a generalization for bodies in contact of the surface integral equation (SIE) formulations. Unlike some other published SIE generalizations in the field of computational electromagnetics, this generalization does not require duplicating unknowns on the dielectric separation surfaces. Additionally, this generalization is applicable to any ordinary single-scatterer SIE formulations employed as baseline. The other algorithm deals with enforcing boundary conditions and Kirchhoff's Law, relating the surface current flow across a junction edge. Two important features inherent to this latter algorit...
The Brown-Henneaux's central charge from the path-integral boundary condition
Terashima, Hiroaki
2000-01-01
We derive Brown-Henneaux's commutation relation and central charge in the framework of the path integral. If we use the leading part of the asymptotic symmetry to derive the Ward-Takahashi identity, we can see the central charge arises from the fact that the boundary condition of the path integral is not invariant under the transformation.
RESTRICTED NONLINEAR APPROXIMATION AND SINGULAR SOLUTIONS OF BOUNDARY INTEGRAL EQUATIONS
Reinhard Hochmuth
2002-01-01
This paper studies several problems, which are potentially relevant for the construction of adaptive numerical schemes. First, biorthogonal spline wavelets on [0,1 ] are chosen as a starting point for characterizations of functions in Besov spaces B , (0,1) with 0＜σ＜∞ and (1+σ)-1＜τ＜∞. Such function spaces are known to be related to nonlinear approximation. Then so called restricted nonlinear approximation procedures with respect to Sobolev space norms are considered. Besides characterization results Jackson type estimates for various tree-type and tresholding algorithms are investigated. Finally known approximation results for geometry induced singularity functions of boundary integeral equations are combined with the characterization results for restricted nonlinear approximation to show Besov space regularity results.
Boundary integral equation Neumann-to-Dirichlet map method for gratings in conical diffraction.
Wu, Yumao; Lu, Ya Yan
2011-06-01
Boundary integral equation methods for diffraction gratings are particularly suitable for gratings with complicated material interfaces but are difficult to implement due to the quasi-periodic Green's function and the singular integrals at the corners. In this paper, the boundary integral equation Neumann-to-Dirichlet map method for in-plane diffraction problems of gratings [Y. Wu and Y. Y. Lu, J. Opt. Soc. Am. A26, 2444 (2009)] is extended to conical diffraction problems. The method uses boundary integral equations to calculate the so-called Neumann-to-Dirichlet maps for homogeneous subdomains of the grating, so that the quasi-periodic Green's functions can be avoided. Since wave field components are coupled on material interfaces with the involvement of tangential derivatives, a least squares polynomial approximation technique is developed to evaluate tangential derivatives along these interfaces for conical diffraction problems. Numerical examples indicate that the method performs equally well for dielectric or metallic gratings. PMID:21643404
Hijazzi, Norshamirra; Thiruchelvam, Sivadass; Sabri Muda, Rahsidi; Nasharuddin Mustapha, Kamal; Che Muda, Zakaria; Ghazali, Azrul; Kamal Kadir, Ahmad; Hakimie, Hazlinda; Sahari, Khairul Salleh Mohamed; Hasini, Hasril; Mohd Sidek, Lariyah; Itam, Zarina; Fadhli Mohamad, Mohd; Razad, Azwin Zailti Abdul
2016-03-01
Dams, however significant their contributions are to the society, are not immune to failures and diminishing lifespan not unlike other structural elements in our infrastructure. Despite continuing efforts on design, construction, operation, and maintenance of dams to improve the safety of the dams, the possibility of unforeseen events of dam failures is still possible. Seeing that dams are usually integrated into close approximities with the community, dam failures may consequent in tremendous loss of lives and properties. The aims of formulation of Integrated Community Based Disaster Management (ICBDM) is to simulate evacuation modelling and emergency planning in order to minimize loss of life and property damages in the event of a dam-related disaster. To achieve the aim above, five main pillars have been identified for the formulation of ICBDM. A series of well-defined program inclusive of hydrological 2-D modelling, life safety modelling, community based EWS and CBTAP will be conducted. Finally, multiple parties’ engagement is to be carried out in the form of table top exercise to measure the readiness of emergency plans and response capabilities of key players during the state of a crisis.
This report deals with the formulation and numerical integration of constitutive models in the framework of finite deformation thermomechanics. Based on the concept of dual variables, plasticity and viscoplasticity models exhibiting nonlinear kinematic hardening as well as nonlinear isotropic hardening rules are presented. Care is taken that the evolution equations governing the hardening response fulfill the intrinsic dissipation inequality in every admissible process. In view of the development of an efficient numerical integration procedure, simplified versions of these constitutive models are supposed. In these versions, the thermoelastic strains are assumed to be small and a simplified kinematic hardening rule is considered. Additionally, in view of an implementation into the ABAQUS finite element code, the elasticity law is approximated by a hypoelasticity law. For the simplified onstitutive models, an implicit time-integration algorithm is developed. First, in order to obtain a numerical objective integration scheme, use is made of the HUGHES-WINGET-Algorithm. In the resulting system of ordinary differential equations, it can be distinguished between three differential operators representing different physical effects. The structure of this system of differential equations allows to apply an operator split scheme, which leads to an efficient integration scheme for the constitutive equations. By linearizing the integration algorithm the consistent tangent modulus is derived. In this way, the quadratic convergence of Newton's method used to solve the basic finite element equations (i.e. the finite element discretization of the governing thermomechanical field equations) is preserved. The resulting integration scheme is implemented as a user subroutine UMAT in ABAQUS. The properties of the applied algorithm are first examined by test calculations on a single element under tension-compression-loading. For demonstrating the capabilities of the constitutive theory
Integrity of fuelling machine pressure boundary under flow reversal during defuelling
Wahba, N.N.; Bayoumi, M.H. [Ontario Power Generation, Inc., Nuclear Safety Analysis Division, Fuel and Fuel Channel Analysis Dept., Toronto, Ontario (Canada)
2002-07-01
This paper documents the calculated loads and stresses of various components of the fuelling machine pressure boundary, pressure tube and fixed-end positioning-assembly stud due to reverse flow bundle impact if an inlet feeder break is postulated to occur during flow defuelling. The information was required to support pressure tube inspection during outage for Darlington NGS. The results indicate that the integrity of the pressure boundary is maintained under the postulated scenario. (author)
Tetervin, Neal; Lin, Chia Chiao
1951-01-01
A general integral form of the boundary-layer equation, valid for either laminar or turbulent incompressible boundary-layer flow, is derived. By using the experimental finding that all velocity profiles of the turbulent boundary layer form essentially a single-parameter family, the general equation is changed to an equation for the space rate of change of the velocity-profile shape parameter. The lack of precise knowledge concerning the surface shear and the distribution of the shearing stress across turbulent boundary layers prevented the attainment of a reliable method for calculating the behavior of turbulent boundary layers.
Integral equation solution for truncated slab structures by using a fringe current formulation
Jørgensen, Erik; Toccafondi, A.; Maci, S.
1999-01-01
Full-wave solutions of truncated dielectric slab problems are interesting for a variety of engineering applications, in particular patch antennas on finite ground planes. For this application a canonical reference solution is that of a semi-infinite slab illuminated by a line source. Standard...... integral equation (IE) techniques are not easily applied to this problem, since unknown equivalent currents have to be distributed on a semi-infinite domain. In this paper we present a surface/surface approach, applied to an IE which is based on a non-conventional formulation. More precise, the unknowns of...... this IE are the difference between the actual currents and the currents of the infinite structure (without truncation)...
Formulation of invariant functional integrals and applications to the quantization of gauge theories
Introducting a metrical structure into the Configuration Space of Quantum Field Theories with Infinite-Dimensional symetry group, a formulation of Invariant Functional Integrals suitable for their quantization, is obtained. It is apllied to Gauge Theories of Yang-Mills and Polyakov's Bosonic String; obtaining several new facts about them, as well as reproducing some well known results. By following the general idea of invariant functional measures; a fermionic (chiral) change of variables in the fermionic sector of two-dimensional massless Quantum-Chromodynamics is implemented obtaining by the first time, a pure gluonic effective action for the model. In adittion, the complete solution for the Rothe-Stamatesu Model, is obtained. (author)
Correct Path-Integral Formulation of Quantum Thermal Field Theory in Coherent State Representation
SU Jun-Chen; ZHENG Fu-Hou
2005-01-01
The path-integral quantization of thermal scalar, vector, and spinor fields is performed newly in the coherent-state representation. In doing this, we choose the thermal electrodynamics and ψ4 theory as examples. By this quantization, correct expressions of the partition functions and the generating functionals for the quantum thermal electrodynamics and ψ4 theory are obtained in the coherent-state representation. These expressions allow us to perform analytical calculations of the partition functions and generating functionals and therefore are useful in practical applications. Especially, the perturbative expansions of the generating functionals are derived specifically by virtue of the stationary-phase method. The generating functionals formulated in the position space are re-derived from the ones given in the coherent-state representation.
Integrating Sustainability into the Curriculum: Crossing Disciplinary Boundaries
Pushnik, J.
2012-12-01
The next generation will confront an increased number of global issues that interface the complexities of socioeconomic perspectives, environmental stability, poverty and development. Recently California State University Chico undertook a general education reform, providing a unique opportunity to craft a general education pathway to prepare students for these challenges by focusing a curriculum on sustainability. The Sustainability Pathway emphasizes a system thinking approach to help students understand and be able to address a set of problems involving the biosphere processes, human institutions and the economic vitality. The curriculum intentionally integrates courses from across the disciplines of natural sciences, social sciences, agriculture, engineering, economics, arts and humanities into a central focused theme of sustainability. The diverse backgrounds and academic focus of the participating faculty has necessitate the development of a common language and a cohesion within the curriculum. To address these needs a faculty learning community (FLC) was established to build on a common set of case studies. Three regional environmental water related issues were selected that had demonstrable socioeconomic, equity/ethical dimensions and environmental consequences. These case studies are Klamath River basin in northern California, the Bay-Delta project in the central part of the state and the Sultan Sea in southern California. Members of the FLC has contributed a perspective from their academic discipline which includes proposed reading lists, web based resources and PowerPoint presentations which are housed in common web- based resource repository. The pedagogical rational is to create linkages and cohesion among the courses in the curriculum by iteratively examining these case studies as basis for development of a multidisciplinary perspective as students progress through their general education.
Explicit expressions for three-dimensional boundary integrals in linear elasticity
Nintcheu Fata, Sylvain [ORNL
2011-01-01
On employing isoparametric, piecewise linear shape functions over a flat triangle, exact formulae are derived for all surface potentials involved in the numerical treatment of three-dimensional singular and hyper-singular boundary integral equations in linear elasticity. These formulae are valid for an arbitrary source point in space and are represented as analytical expressions along the edges of the integration triangle. They can be employed to solve integral equations defined on triangulated surfaces via a collocation method or may be utilized as analytical expressions for the inner integrals in a Galerkin technique. A numerical example involving a unit triangle and a source point located at various distances above it, as well as sample problems solved by a collocation boundary element method for the Lame equation are included to validate the proposed formulae.
The thesis addresses the numerical simulation of non-destructive testing (NDT) using eddy currents, and more precisely the computation of induced electromagnetic fields by a transmitter sensor in a healthy part. This calculation is the first step of the modeling of a complete control process in the CIVA software platform developed at CEA LIST. Currently, models integrated in CIVA are restricted to canonical (modal computation) or axially-symmetric geometries. The need for more diverse and complex configurations requires the introduction of new numerical modeling tools. In practice the sensor may be composed of elements with different shapes and physical properties. The inspected parts are conductive and may contain dielectric or magnetic elements. Due to the cohabitation of different materials in one configuration, different regimes (static, quasi-static or dynamic) may coexist. Under the assumption of linear, isotropic and piecewise homogeneous material properties, the surface integral equation (SIE) approach allows to reduce a volume-based problem to an equivalent surface-based problem. However, the usual SIE formulations for the Maxwell's problem generally suffer from numerical noise in asymptotic situations, and especially at low frequencies. The objective of this study is to determine a version that is stable for a range of physical parameters typical of eddy-current NDT applications. In this context, a block-iterative scheme based on a physical decomposition is proposed for the computation of primary fields. This scheme is accurate and well-conditioned. An asymptotic study of the integral Maxwell's problem at low frequencies is also performed, allowing to establish the eddy-current integral problem as an asymptotic case of the corresponding Maxwell problem. (author)
Integration of the SL(2,R)/U(1) Gauged WZNW Model with Periodic Boundary Conditions
Mueller, Uwe; Weigt, Gerhard
1999-01-01
Gauged WZNW models are integrable conformal field theories. We integrate the classical \\slu{} theory with periodic boundary conditions, which describes closed strings moving in a curved target-space geometry. We calculate its Poisson bracket structure by solving an initial state problem. The results differ from previous field-theoretic calculations due to zero modes. For a future exact canonical quantization the physical fields are (non-locally) transformed onto canonical free fields.
Integration of the SL(2,(R/U(1)) gauged WZNW model with periodic boundary conditions
Mueller, Uwe; Weigt, Gerhard
2000-02-28
Gauged WZNW models are integrable conformal field theories. We integrate the classical SL(2,R/U(1)) theory with periodic boundary conditions, which describes closed strings moving in a curved target-space geometry. We calculate its Poisson bracket structure by solving an initial state problem. The results differ from previous field-theoretic calculations due to zero-modes. For a future exact canonical quantization the physical fields are (non-locally) transformed onto canonical free fields.
Yan Sun
2015-01-01
Under some conditions concerning the first eigenvalues corresponding to the relevant linear operator, we obtain sharp optimal criteria for the existence of positive solutions for p-Laplacian problems with integral boundary conditions. The main methods in the paper are constructing an available integral operator and combining fixed point index theory. The interesting point of the results is that the nonlinear term contains all lower-order derivatives explicitly. Finally, we give some examples ...
Histone crosstalk directed by H2B ubiquitination is required for chromatin boundary integrity.
Meiji Kit-Wan Ma
2011-07-01
Full Text Available Genomic maps of chromatin modifications have provided evidence for the partitioning of genomes into domains of distinct chromatin states, which assist coordinated gene regulation. The maintenance of chromatin domain integrity can require the setting of boundaries. The HS4 insulator element marks the 3' boundary of a heterochromatin region located upstream of the chicken β-globin gene cluster. Here we show that HS4 recruits the E3 ligase RNF20/BRE1A to mediate H2B mono-ubiquitination (H2Bub1 at this insulator. Knockdown experiments show that RNF20 is required for H2Bub1 and processive H3K4 methylation. Depletion of RNF20 results in a collapse of the active histone modification signature at the HS4 chromatin boundary, where H2Bub1, H3K4 methylation, and hyperacetylation of H3, H4, and H2A.Z are rapidly lost. A remarkably similar set of events occurs at the HSA/HSB regulatory elements of the FOLR1 gene, which mark the 5' boundary of the same heterochromatin region. We find that persistent H2Bub1 at the HSA/HSB and HS4 elements is required for chromatin boundary integrity. The loss of boundary function leads to the sequential spreading of H3K9me2, H3K9me3, and H4K20me3 over the entire 50 kb FOLR1 and β-globin region and silencing of FOLR1 expression. These findings show that the HSA/HSB and HS4 boundary elements direct a cascade of active histone modifications that defend the FOLR1 and β-globin gene loci from the pervasive encroachment of an adjacent heterochromatin domain. We propose that many gene loci employ H2Bub1-dependent boundaries to prevent heterochromatin spreading.
Mouffak Benchohra
2012-01-01
Full Text Available The aim of this paper is to investigate a class of boundary value problems for fractional differential equations involving nonlinear integral conditions. The main tool used in our considerations is the technique associated with measures of weak noncompactness.
Bethe ansatz for the Temperley–Lieb spin chain with integrable open boundaries
In this paper we study the spectrum of the spin-1 Temperley–Lieb spin chain with integrable open boundary conditions. We obtain the eigenvalue expressions as well as its associated Bethe ansatz equations by means of the coordinate Bethe ansatz. These equations provide the complete description of the spectrum of the model. (paper)
Brahim Tellab
2016-01-01
Full Text Available In this paper, we investigate the existence and uniqueness of solutions for second order nonlinear fractional differential equation with integral boundary conditions. Our result is an application of the Banach contraction principle and the Krasnoselskii fixed point theorem.
Chen, Ke [Univ. of Liverpool (United Kingdom)
1996-12-31
We study various preconditioning techniques for the iterative solution of boundary integral equations, and aim to provide a theory for a class of sparse preconditioners. Two related ideas are explored here: singularity separation and inverse approximation. Our preliminary conclusion is that singularity separation based preconditioners perform better than approximate inverse based while it is desirable to have both features.
2012-01-01
This thesis explores Norwegian majority members’ role in incorporating and integrating immigrant minorities from a broad social psychological perspective on intergroup relations. It consists of four studies which investigate changing symbolic boundaries of immigrants and the majority as reflected in media discourse, and majority members’ attitudes toward proactively incorporating immigrant minorities. These different studies aim to develop better understandings of how immigrant minorities may...
A well-conditioned boundary integral equation for transmission problems of electromagnetism
Levadoux, David; Millot, Florence; Pernet, Sébastien
2015-01-01
We propose a new well-conditioned boundary integral equation to solve transmission problems of electromagnetism. This equation is well posed and appears as a compact perturbation of the identity leading to fast iterative solutions without the help of any preconditioner. Some numerical experiments confirm this result.
Kao, Gloria Yi-Ming; Lin, Sunny S. J.; Sun, Chuen-Tsai
2008-01-01
The authors address the role of computer support for building conceptual self-awareness--that is, enabling students to think outside of concept boundaries in hope of enhancing creative potential. Based on meta-cognition theory, we developed an integrated concept mapping system (ICMSys) to improve users' conceptual self-awareness in addition to…
Sareni, Bruno; Krähenbühl, Laurent; Beroual, Abderrahmane; Nicolas, Alain; Brosseau, C.
1997-01-01
We present a numerical method based upon the resolution of boundary integral equations for the calculation of the effective permittivity of a lossless composite structure consisting of a two component mixture, each with its own dielectric anti shape characteristics. The topological arrangements considered are periodic lattices inhomogeneities. Our numerical simulations are compared to the effective medium approach and with results of previous works.
N{sup ±}-integrals and boundary values of Cauchy-type integrals of finite measures
Aliev, R. A., E-mail: aliyevrashid@hotmail.ru, E-mail: alievrashid@box.az [Baku State University (Azerbaijan)
2014-07-31
Let Γ be a simple closed Lyapunov contour with finite complex measure ν, and let G{sup +} be the bounded and G{sup −} the unbounded domains with boundary Γ. Using new notions (so-called N-integration and N{sup +}- and N{sup −}-integrals), we prove that the Cauchy-type integrals F{sup +}(z), z∈G{sup +}, and F{sup −}(z), z∈G{sup −}, of ν are Cauchy N{sup +}- and N{sup −}-integrals, respectively. In the proof of the corresponding results, the additivity property and the validity of the change-of-variable formula for the N{sup +}- and N{sup −}-integrals play an essential role. Bibliography: 21 titles. (paper)
The integrated Earth System Model (iESM: formulation and functionality
W. D. Collins
2015-01-01
Full Text Available The integrated Earth System Model (iESM has been developed as a new tool for projecting the joint human/climate system. The iESM is based upon coupling an Integrated Assessment Model (IAM and an Earth System Model (ESM into a common modeling infrastructure. IAMs are the primary tool for describing the human–Earth system, including the sources of global greenhouse gases (GHGs and short-lived species, land use and land cover change, and other resource-related drivers of anthropogenic climate change. ESMs are the primary scientific tools for examining the physical, chemical, and biogeochemical impacts of human-induced changes to the climate system. The iESM project integrates the economic and human dimension modeling of an IAM and a fully coupled ESM within a single simulation system while maintaining the separability of each model if needed. Both IAM and ESM codes are developed and used by large communities and have been extensively applied in recent national and international climate assessments. By introducing heretofore-omitted feedbacks between natural and societal drivers, we can improve scientific understanding of the human–Earth system dynamics. Potential applications include studies of the interactions and feedbacks leading to the timing, scale, and geographic distribution of emissions trajectories and other human influences, corresponding climate effects, and the subsequent impacts of a changing climate on human and natural systems. This paper describes the formulation, requirements, implementation, testing, and resulting functionality of the first version of the iESM released to the global climate community.
$A_n^{(1)}$ affine Toda field theories with integrable boundary conditions revisited
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 relies 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 conser...
In recent years, several rapid-mold-heating techniques that can be used for the injection molding of thin-walled parts or micro/nano structures have been developed. High-frequency induction heating, which involves heating by electromagnetic induction, is an efficient method for the rapid heating of mold surfaces. The present study proposes an integrated numerical model of the high-frequency induction heating process and the resulting injection molding process. To take into account the effects of thermal boundary conditions in induction heating, we carry out a fully integrated numerical analysis that combines electromagnetic field calculation, heat transfer analysis, and injection molding simulation. The proposed integrated simulation is extended to the injection molding of a thin-wall part, and the simulation results are compared with the experimental findings. The validity of the proposed simulation is discussed according to the ways of the boundary condition imposition
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
POSITIVE SOLUTIONS OF A NONLINEAR THREE-POINT EIGENVALUE PROBLEM WITH INTEGRAL BOUNDARY CONDITIONS
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.
Fisher, Travis C.; Carpenter, Mark H.; Nordstroem, Jan; Yamaleev, Nail K.; Swanson, R. Charles
2011-01-01
Simulations of nonlinear conservation laws that admit discontinuous solutions are typically restricted to discretizations of equations that are explicitly written in divergence form. This restriction is, however, unnecessary. Herein, linear combinations of divergence and product rule forms that have been discretized using diagonal-norm skew-symmetric summation-by-parts (SBP) operators, are shown to satisfy the sufficient conditions of the Lax-Wendroff theorem and thus are appropriate for simulations of discontinuous physical phenomena. Furthermore, special treatments are not required at the points that are near physical boundaries (i.e., discrete conservation is achieved throughout the entire computational domain, including the boundaries). Examples are presented of a fourth-order, SBP finite-difference operator with second-order boundary closures. Sixth- and eighth-order constructions are derived, and included in E. Narrow-stencil difference operators for linear viscous terms are also derived; these guarantee the conservative form of the combined operator.
Gao－LianLiu
1996-01-01
By introducing an image plane,the inverse heat conduction problem with free boundary is transformed into one with completely known boundary,which is much simpler to handle,as a by-product ,the classical Krichhoff's transformation for accounting for varialble conductivity is rederived and an invariance proerty of the inverse problem solution with respect to variable conductivity is indicated.Then a pair of complementary extremum principles are established on the image plane.providing a sound theoretical foundation for the Ritz's method and finite element method (FEM),An example solved by FEM is also given.
Field, J. H.
2011-01-01
It is shown how the time-dependent Schrodinger equation may be simply derived from the dynamical postulate of Feynman's path integral formulation of quantum mechanics and the Hamilton-Jacobi equation of classical mechanics. Schrodinger's own published derivations of quantum wave equations, the first of which was also based on the Hamilton-Jacobi…
Arsalis, Alexandros; Nielsen, Mads Pagh; Kær, Søren Knudsen
2013-01-01
A 1 kWe micro combined heat and power (CHP) system based on high temperature proton exchange membrane fuel cell (PEMFC) technology is modeled and optimized by formulation and application of a process integration methodology. The system can provide heat and electricity for a singlefamily household...
With the adoption of the Kyoto Protocol in 1997 national leaders have started investigating options for reducing carbon emissions within national borders. Despite confronting similar energy issues, every country that adopted the Kyoto Protocol has a unique energy strategy - being characterized by a different context, social, economic or environmental that influences the way different nations deal with climate change and other energy-related issues. Finding that currently available energy models are often too detailed or narrowly focused to inform longer-term policy formulation and evaluation holistically, the present study proposes the utilization of an integrated cross-sectoral medium to longer-term research and modeling approach, incorporating various methodologies to minimize exogenous assumptions and endogenously represent the key drivers of the system analyzed. The framework proposed includes feedback, delays and non-linearity and focuses on structure, scenarios and policies, requires a profound customization of the model that goes beyond a new parameterization. The inclusion of social and environmental factors, in addition to economic ones, all unique to the geographical area analyzed, allows for a wider analysis of the implication of policies by identifying potential side effect or longer-term bottlenecks for socio-economic development and environmental preservation arising from cross-sectoral relations. (author)
Cassiani, Massimo; Stohl, Andreas; Brioude, Jerome
2015-03-01
A correction for the vertical gradient of air density has been incorporated into a skewed probability density function formulation for turbulence in the convective boundary layer. The related drift term for Lagrangian stochastic dispersion modelling has been derived based on the well-mixed condition. Furthermore, the formulation has been extended to include unsteady turbulence statistics and the related additional component of the drift term obtained. These formulations are an extension of the drift formulation reported by Luhar et al. (Atmos Environ 30:1407-1418, 1996) following the well-mixed condition proposed by Thomson (J Fluid Mech 180:529-556, 1987). Comprehensive tests were carried out to validate the formulations including consistency between forward and backward simulations and preservation of a well-mixed state with unsteady conditions. The stationary state CBL drift term with density correction was incorporated into the FLEXPART and FLEXPART-WRF Lagrangian models, and included the use of an ad hoc transition function that modulates the third moment of the vertical velocity based on stability parameters. Due to the current implementation of the FLEXPART models, only a steady-state horizontally homogeneous drift term could be included. To avoid numerical instability, in the presence of non-stationary and horizontally inhomogeneous conditions, a re-initialization procedure for particle velocity was used. The criteria for re-initialization and resulting errors were assessed for the case of non-stationary conditions by comparing a reference numerical solution in simplified unsteady conditions, obtained using the non-stationary drift term, and a solution based on the steady drift with re-initialization. Two examples of "real-world" numerical simulations were performed under different convective conditions to demonstrate the effect of the vertical gradient in density on the particle dispersion in the CBL.
Regularized boundary integral representations for dislocations and cracks in smart media
This paper presents a complete set of singularity-reduced boundary integral relations for isolated discontinuities embedded in three-dimensional infinite media. The development is carried out within a broad context that allows the treatment of a well-known class of smart media such as linear piezoelectric, linear piezomagnetic and linear piezoelectromagnetic materials. In addition, resulting boundary integral representations are applicable to general discontinuities of arbitrary geometry and possessing a general jump distribution. The latter aspect allows the treatment of two special kinds of discontinuities: dislocations and cracks. The most attractive feature of the current development is that all integral relations for field quantities such as state variables and their gradients, the body flux, and the generalized interaction energy produced by dislocations are expressed only in terms of line integrals over the dislocation loops and, for cracks, the key governing boundary integral equation is established in a symmetric weak form and contains only weakly singular kernels of O(1/r). Results for the former case are fundamental and useful in the context of dislocation mechanics and modeling while the resulting weakly singular, weak form integral equation constitutes a basis for the development of a well-known numerical technique, called a symmetric Galerkin boundary element method (SGBEM), for analysis of cracked bodies. The weakly singular nature of such an integral equation allows low order interpolations to be used in the numerical approximation. The key ingredient for achieving such development of integral representations is the use of certain special decompositions in the derivative-transferring process via Stokes's theorem. Existence of such decompositions is ensured by a careful consideration of the singularity nature of the kernels, and a particular solution of the weakly singular functions involved is obtained by solving a system of partial differential
Retarded potentials and time domain boundary integral equations a road map
Sayas, Francisco-Javier
2016-01-01
This book offers a thorough and self-contained exposition of the mathematics of time-domain boundary integral equations associated to the wave equation, including applications to scattering of acoustic and elastic waves. The book offers two different approaches for the analysis of these integral equations, including a systematic treatment of their numerical discretization using Galerkin (Boundary Element) methods in the space variables and Convolution Quadrature in the time variable. The first approach follows classical work started in the late eighties, based on Laplace transforms estimates. This approach has been refined and made more accessible by tailoring the necessary mathematical tools, avoiding an excess of generality. A second approach contains a novel point of view that the author and some of his collaborators have been developing in recent years, using the semigroup theory of evolution equations to obtain improved results. The extension to electromagnetic waves is explained in one of the appendices...
Pan Xiaomin; Sheng Xinqing
2008-01-01
A general and efficient parallel approach is proposed for the first time to parallelize the hybrid finite-element-boundary-integral-multi-level fast multipole algorithm (FE-BI-MLFMA). Among many algorithms of FE-BI-MLFMA, the decomposition algorithm (DA) is chosen as a basis for the parallelization of FE-BI-MLFMA because of its distinct numerical characteristics suitable for parallelization. On the basis of the DA, the parallelization of FE-BI-MLFMA is carried out by employing the parallelized multi-frontal method for the matrix from the finite-element method and the parallelized MLFMA for the matrix from the boundary integral method respectively. The programming and numerical experiments of the proposed parallel approach are carried out in the high perfor-mance computing platform CEMS-Liuhui. Numerical experiments demonstrate that FE-BI-MLFMA is efficiently parallelized and its computational capacity is greatly improved without losing accuracy, efficiency, and generality.
Expanded boundary integral method and chaotic time-reversal doublets in quantum billiards
Veble, G.; Prosen, T.; Robnik, M.
2007-01-01
We present the expanded boundary integral method for solving the planar Helmholtz problem, which combines the ideas of the boundary integral method and the scaling method and is applicable to arbitrary shapes. We apply the method to a chaotic billiard with unidirectional transport, where we demonstrate the existence of doublets of chaotic eigenstates, which are quasi-degenerate due to time-reversal symmetry, and a very particular level spacing distribution that attains a chaotic Shnirelman peak at short energy ranges and exhibits Gaussian Unitary Ensemble (GUE) like statistics for large energy ranges. We show that, as a consequence of such particular level statistics or algebraic tunnelling between disjoint chaotic components connected by time-reversal operation, the system exhibits quantum current reversals.
Epitaxial integration of a nanoscale BiFeO3 phase boundary with silicon
Liang, Wen-I.; Peng, Chun-Yen; Huang, Rong; Kuo, Wei-Cheng; Huang, Yen-Chin; Adamo, Carolina; Chen, Yi-Chun; Chang, Li; Juang, Jenh-Yih; Schlom, Darrel G.; Chu, Ying-Hao
2016-01-01
The successful integration of the strain-driven nanoscale phase boundary of BiFeO3 onto a silicon substrate is demonstrated with extraordinary ferroelectricity and ferromagnetism. The detailed strain history is delineated through a reciprocal space mapping technique. We have found that a distorted monoclinic phase forms prior to a tetragonal-like phase, a phenomenon which may correlates with the thermal strain induced during the growth process.
Edwards, S.; Reuther, J.; Chattot, J. J.
The objective of this paper is to present a control theory approach for the design of airfoils in the presence of viscous compressible flows. A coupled system of the integral boundary layer and the Euler equations is solved to provide rapid flow simulations. An adjoint approach consistent with the complete coupled state equations is employed to obtain the sensitivities needed to drive a numerical optimization algorithm. Design to a target pressure distribution is demonstrated on an RAE 2822 airfoil at transonic speeds.
Pai, Ravindra
1991-01-01
A numerical method has been developed for computing the steady state flow about arbitrary shaped three dimensional bodies on or below the free surface using a Boundary Integral Element Method ( Panel Method). The method uses a singularity distribution over the body surface and the free surface. The method can solve for the potential distribution as well as the source density distribution. In this study a constant source distribution is assumed on each panel. The free surface bo...
Fatma Kanca
2013-01-01
This paper investigates the inverse problem of finding a time-dependent diffusion coefficient in a parabolic equation with the periodic boundary and integral overdetermination conditions. Under some assumption on the data, the existence, uniqueness, and continuous dependence on the data of the solution are shown by using the generalized Fourier method. The accuracy and computational efficiency of the proposed method are verified with the help of the numerical examples.
Integrable approach to simple exclusion processes with boundaries. Review and progress
We study the matrix ansatz in the quantum group framework, applying integrable systems techniques to statistical physics models. We start by reviewing the two approaches, and then show how one can use the former to get new insight into the latter. We illustrate our method by solving a model of reaction-diffusion. An eigenvector for the transfer matrix for the XXZ spin chain with non-diagonal boundary is obtained using a matrix ansatz. (paper)
Yang Xiao-Jun
2015-01-01
Full Text Available In the present paper we investigate the fractal boundary value problems for the Fredholm\\Volterra integral equations, heat conduction and wave equations by using the local fractional decomposition method. The operator is described by the local fractional operators. The four illustrative examples are given to elaborate the accuracy and reliability of the obtained results. [Projekat Ministarstva nauke Republike Srbije, br. OI 174001, III41006 i br. TI 35006
Integrable Boundary Conditions and W-Extended Fusion in the Logarithmic Minimal Models LM(1,p)
Pearce, Paul A; Ruelle, Philippe
2008-01-01
We consider the logarithmic minimal models LM(1,p) as `rational' logarithmic conformal field theories with extended W symmetry. To make contact with the extended picture starting from the lattice, we identify 4p-2 boundary conditions as specific limits of integrable boundary conditions of the underlying Yang-Baxter integrable lattice models. Specifically, we identify 2p integrable boundary conditions to match the 2p known irreducible W-representations. These 2p extended representations naturally decompose into infinite sums of the irreducible Virasoro representations (r,s). A further 2p-2 reducible yet indecomposable W-representations of rank 2 are generated by fusion and these decompose as infinite sums of indecomposable rank-2 Virasoro representations. The fusion rules in the extended picture are deduced from the known fusion rules for the Virasoro representations of LM(1,p) and are found to be in agreement with previous works. The closure of the fusion algebra on a finite number of representations in the e...
Conservation laws in field dynamics or why boundary motion is exactly integrable?
Mineev-Weinstein, M B
1995-01-01
An infinite number of conserved quantities in the field dynamics \\phi_t = L\\,U(\\phi) + \\rho for a linear Hermitian (or anti-Hermitian) operator L, an arbitrary function U and a given source \\rho are presented. These integrals of motion are the multipole moments of the potential created by \\phi in the far-field. In the singular limit of a bistable scalar field \\phi = \\phi_{\\pm} (i.e. Ising limit) this theory describes a dissipative boundary motion (such as Stefan or Saffman-Taylor problem that is the continuous limit of the DLA-fractal growth) and can be exactly integrable. These conserved quantities are the polynomial conservation laws attributed to the integrability. The criterion for integrability is the uniqueness of the inverse potential problem's solution.
Christov, Ivan C
2013-01-01
Most mathematics and engineering textbooks describe the process of "subtracting off" the steady state of a linear parabolic partial differential equation as a technique for obtaining a boundary-value problem with homogeneous boundary conditions that can be solved by separation of variables (i.e., eigenfunction expansions). While this method produces the correct solution for the start-up of the flow of, e.g., a Newtonian fluid between parallel plates, it can lead to erroneous solutions to the corresponding problem for a class of non-Newtonian fluids. We show that the reason for this is the non-rigorous enforcement of the start-up condition in the textbook approach, which leads to a violation of the principle of causality. Nevertheless, these boundary-value problems can be solved correctly using eigenfunction expansions, and we present the formulation that makes this possible (in essence, an application of Duhamel's principle). The solutions obtained by this new approach are shown to agree identically with thos...
The most important data for describing the influence of the MHD expansion group (consisting of nozzle, duct and diffuser) on the characteristic parameters of the overall cycle, in particular on the overall efficiency, are the thermodynamic-state quantities at the entrance of the nozzle and at the exit of the diffuser, ''the outer boundary values''. With these data unchanged, variation of the shape of the expansion line does not affect the overall performance of the process. Therefore the question arises which expansion shape is best from the point of view of an MHD generator, if the outer boundary values are fixed,or, in general, as a function of the outer boundary values. As the generator duct is the most complicated and, especially with the magnet, the most expensive element of the expansion group, minimizing of the duct volume is a reasonable criterion to be applied in the determination of the expansion shape. The paper shows how this criterion leads to a simple differential relationship between the electrical conductivity of the working gas, the gas velocity and the cross-section of the channel. If this relationship is used to complete the system of differential equations governing the energy conversion process, the resulting expansion shape is optimal with respect to minimum duct volume. Usually a somewhat arbitrary condition is taken to determine the expansion shape, e. g. the gas velocity or Mach number is postulated to be constant. There are some optimization procedures known in the literature which, however, refer to either the inlet or the outlet state of the duct, i.e. only one point of the expansion line falls on the optimum line. These computations are included as special cases in the more general treatment of the present paper. Finally an example is calculated for the MHD expansion under consideration of the optimization criterion. (author)
Application of the boundary-integral-equation method to the three-dimensional thermoelastic problem
It is possible to solve three-dimensional steady state thermoelastic problems from data of temperature, fluxes, tractions, and displacements on the boundary alone. The numerical discretisation of these integral equations is based on a technique similar to that of finite elements. The boundary alone needs to be discretised. Two-dimensional examples are given to prove the accuracy and the feasibility. In the case of three-dimensional problems, the surface is represented by eight nodes quadrilateral elements and six nodes triangular elements. The unknown (temperature, flux, displacement, traction) may be considered to vary linearly, quadratically, or cubically, with respect to he intrinsic coordinates of each element. The integration is performed numerically using Gaussian quadrature formulas, for which the number of integration points is chosen automatically by the program, so that the upper bound of error in integration is minimized. In order to obtain a banded form matrix and also to be able to study elongated structures, the body is divided into subregions, for each of which the integral equations are written. The thermoelastic stress and deformation field are obtained from two successive calculations on the same mesh. The first gives the thermal field. The second, taking account of the thermal field, calculates the thermoelastic displacement and stress field. This type of approach is especially suited to complicated three-dimensional thick structures for which finite element procedures are very expensive. The data are simple to generate, for data on the boundary alone have to be given. Much time can be saved by the user of the program in data generations and data checks
A time-domain finite element boundary integration method for ultrasonic nondestructive evaluation.
Shi, Fan; Choi, Wonjae; Skelton, Elizabeth A; Lowe, Michael J S; Craster, Richard V
2014-12-01
A 2-D and 3-D numerical modeling approach for calculating the elastic wave scattering signals from complex stress-free defects is evaluated. In this method, efficient boundary integration across the complex boundary of the defect is coupled with a time-domain finite element (FE) solver. The model is designed to simulate time-domain ultrasonic nondestructive evaluation in bulk media. This approach makes use of the hybrid concept of linking a local numerical model to compute the near-field scattering behavior and theoretical mathematical formulas for postprocessing to calculate the received signals. It minimizes the number of monitoring signals from the FE calculation so that the computation effort in postprocessing decreases significantly. In addition, by neglecting the conventional regular monitoring box, the region for FE calculation can be made smaller. In this paper, the boundary integral method is implemented in a commercial FE code, and it is validated by comparing the scattering signals with results from corresponding full FE models. The coupled method is then implemented in real inspection scenarios in both 2-D and 3-D, and the accuracy and the efficiency are demonstrated. The limitations of the proposed model and future works are also discussed. PMID:25474780
Integrity of the reactor coolant boundary of the European pressurized water reactor (EPR)
Goetsch, D.; Bieniussa, K.; Schulz, H.; Jalouneix, J.
1997-04-01
This paper is an abstract of the work performed in the frame of the development of the IPSN/GRS approach in view of the EPR conceptual safety features. EPR is a pressurized water reactor which will be based on the experience gained by utilities and designers in France and in Germany. The reactor coolant boundary of a PWR includes the reactor pressure vessel (RPV), those parts of the steam generators (SGs) which contain primary coolant, the pressurizer (PSR), the reactor coolant pumps (RCPs), the main coolant lines (MCLs) with their branches as well as the other connecting pipes and all branching pipes including the second isolation valves. The present work covering the integrity of the reactor coolant boundary is mainly restricted to the integrity of the main coolant lines (MCLs) and reflects the design requirements for the main components of the reactor coolant boundary. In the following the conceptual aspects, i.e. design, manufacture, construction and operation, will be assessed. A main aspect is the definition of break postulates regarding overall safety implications.
Anti-Periodic Boundary Conditions in Supersymmetric DLCQ
Pinsky, S.; Trittmann, U.
2000-01-01
It is of considerable importance to have a numerical method for solving supersymmetric theories that can support a non-zero central charge. The central charge in supersymmetric theories is in general a boundary integral and therefore vanishes when one uses periodic boundary conditions. One is therefore prevented from studying BPS states in the standard supersymmetric formulation of DLCQ (SDLCQ). We present a novel formulation of SDLCQ where the fields satisfy anti-periodic boundary conditions...
Solution of the Stokes system by boundary integral equations and fixed point iterative schemes
The solution to the exterior three dimensional Stokes problem is sought in the form of a single layer potential of unknown density. This reduces the problem to a boundary integral equation of the first kind whose operator is the velocity component of the single layer potential. It is shown that this component is an isomorphism between two appropriate Sobolev spaces containing the unknown densities and the data respectively. The isomorphism corresponds to a variational problem with coercive bilinear form. The latter property allows us to consider various fixed point iterative schemes that converge to the unique solution of the integral equation. Explicit error estimates are also obtained. The successive approximations are also considered in a more computable form by using the product integration method of Atkinson. (author). 47 refs
Kitanine, N; Niccoli, G
2014-01-01
We solve the longstanding problem to define a functional characterization of the spectrum of the transfer matrix associated to the most general spin-1/2 representations of the 6-vertex reflection algebra for general inhomogeneous chains. The corresponding homogeneous limit reproduces the spectrum of the Hamiltonian of the spin-1/2 open XXZ and XXX quantum chains with the most general integrable boundaries. The spectrum is characterized by a second order finite difference functional equation of Baxter type with an inhomogeneous term which vanishes only for some special but yet interesting non-diagonal boundary conditions. This functional equation is shown to be equivalent to the known separation of variable (SOV) representation hence proving that it defines a complete characterization of the transfer matrix spectrum. The polynomial character of the Q-function allows us then to show that a finite system of equations of generalized Bethe type can be similarly used to describe the complete transfer matrix spectru...
无
2010-01-01
This paper investigates the existence and multiplicity of nonnegative solutions to a singular nonlinear boundary value problem of second order differential equations with integral boundary conditions in a Banach space. The arguments are based on the construction of a nonempty bounded open convex set and fixed point index theory. Our nonlinearity possesses singularity and first derivative which makes it different with that in [10].
Pinckney, John
2010-01-01
With the advent of high speed computing Monte Carlo ray tracing techniques has become the preferred method for evaluating spacecraft orbital heats. Monte Carlo has its greatest advantage where there are many interacting surfaces. However Monte Carlo programs are specialized programs that suffer from some inaccuracy, long calculation times and high purchase cost. A general orbital heating integral is presented here that is accurate, fast and runs on MathCad, a generally available engineering mathematics program. The integral is easy to read, understand and alter. The integral can be applied to unshaded primitive surfaces at any orientation. The method is limited to direct heating calculations. This integral formulation can be used for quick orbit evaluations and spot checking Monte Carlo results.
BRST cohomology and Hilbert spaces of non-Abelian models in the decoupled path integral formulation
Rothe, K.D. [Institut fuer Theoretische Physik, Universitaet Heidelberg, Philosophenweg 16, 69120 Heidelberg (Germany); Scholtz, F.G.; Theron, A.N. [Institute of Theoretical Physics, University of Stellenbosch, Stellenbosch 7600 (South Africa)
1997-03-01
The existence of several nilpotent Noether charges in the decoupled formulation of two-dimensional gauge theories does not imply that all of these are required to annihilate the physical states. We elucidate this matter in the context of simple quantum mechanical and field theoretical models, where the structure of the Hilbert space is known. We provide a systematic procedure for deciding which of the BRST conditions is to be imposed on the physical states in order to ensure the equivalence of the decoupled formulation to the original, coupled one. {copyright} 1997 Academic Press, Inc.
A Fast Spectral Galerkin Method for Hypersingular Boundary Integral Equations in Potential Theory
Nintcheu Fata, Sylvain [ORNL; Gray, Leonard J [ORNL
2009-01-01
This research is focused on the development of a fast spectral method to accelerate the solution of three-dimensional hypersingular boundary integral equations of potential theory. Based on a Galerkin approximation, the Fast Fourier Transform and local interpolation operators, the proposed method is a generalization of the Precorrected-FFT technique to deal with double-layer potential kernels, hypersingular kernels and higher-order basis functions. Numerical examples utilizing piecewise linear shape functions are included to illustrate the performance of the method.
TIME–HARMONIC BEHAVIOUR OF CRACKED PIEZOELECTRIC SOLID BY BOUNDARY INTEGRAL EQUATION METHOD
Rangelov Tsviatko
2014-03-01
Full Text Available Anti-plane cracked functionally graded finite piezoelectric solid under time-harmonic elecromechanical load is studied by a non-hypersingular traction boundary integral equation method (BIEM. Exponentially varying material properties are considered. Numerical solutions are obtained by using Mathematica. The dependance of the intensity factors (IF - mechanical stress intensity factor (SIF and electrical field intensity factor (FIF on the inhomogeneous material parameters, on the type and frequency of the dynamic load and on the crack position are analyzed by numerical illustrative examples
Analysis of Well-Clear Boundary Models for the Integration of UAS in the NAS
Upchurch, Jason M.; Munoz, Cesar A.; Narkawicz, Anthony J.; Chamberlain, James P.; Consiglio, Maria C.
2014-01-01
The FAA-sponsored Sense and Avoid Workshop for Unmanned Aircraft Systems (UAS) defnes the concept of sense and avoid for remote pilots as "the capability of a UAS to remain well clear from and avoid collisions with other airborne traffic." Hence, a rigorous definition of well clear is fundamental to any separation assurance concept for the integration of UAS into civil airspace. This paper presents a family of well-clear boundary models based on the TCAS II Resolution Advisory logic. Analytical techniques are used to study the properties and relationships satisfied by the models. Some of these properties are numerically quantifed using statistical methods.
Young, D. P.; Woo, A. C.; Bussoletti, J. E.; Johnson, F. T.
1986-01-01
A general method is developed combining fast direct methods and boundary integral equation methods to solve Poisson's equation on irregular exterior regions. The method requires O(N log N) operations where N is the number of grid points. Error estimates are given that hold for regions with corners and other boundary irregularities. Computational results are given in the context of computational aerodynamics for a two-dimensional lifting airfoil. Solutions of boundary integral equations for lifting and nonlifting aerodynamic configurations using preconditioned conjugate gradient are examined for varying degrees of thinness.
Boundary integral equation methods and numerical solutions thin plates on an elastic foundation
Constanda, Christian; Hamill, William
2016-01-01
This book presents and explains a general, efficient, and elegant method for solving the Dirichlet, Neumann, and Robin boundary value problems for the extensional deformation of a thin plate on an elastic foundation. The solutions of these problems are obtained both analytically—by means of direct and indirect boundary integral equation methods (BIEMs)—and numerically, through the application of a boundary element technique. The text discusses the methodology for constructing a BIEM, deriving all the attending mathematical properties with full rigor. The model investigated in the book can serve as a template for the study of any linear elliptic two-dimensional problem with constant coefficients. The representation of the solution in terms of single-layer and double-layer potentials is pivotal in the development of a BIEM, which, in turn, forms the basis for the second part of the book, where approximate solutions are computed with a high degree of accuracy. The book is intended for graduate students and r...
Boundary-integral equation in engineering stress and fracture mechanics. Technical report
A boundary-integral equation (BIE) method, as employed by a computer program called PESTIE (Plane Elastic Solution Technique of Integral Equations), is described for application to engineering stress and fracture mechanics problems of interest to the electric power generating industry. The paper describes a unique combination of several numerical analysis capabilities and user-oriented features that produce significant advantages over finite element programs and earlier BIE programs. These advantages are demonstrated by comparing numerical results and performance of PESTIE with those of other programs for a series of stress concentration and stress intensity factor problems. The examples include the effect of closely spaced notches (e.g. as encountered in the rim area of a turbine rotor spindle), and the stress intensity factor of a shallow wide crack (e.g. a longitudinal crack in a large diameter pipe)
Boundary integral equation method for added mass in arrays of cylinders
The dynamic behavior of a group of cylinders in fluid, such as heat exchanger tubes and nuclear fuel assemblies, is strongly influenced by the surrounding fluid. Although, the added mass of such clusters of cylinders has been studied by many researchers with various analytical methods and numerical methods, no attempt has been made so far to analyze these problems by the Boundary Integral Equation Method (BIEM). This paper presents a BIEM model simulating the added mass arising when clusters of cylinders vibrate in an inviscid and incompressible fluid. In this model, perturbed fluid pressure is described by a two- dimensional Laplace equation. The primary advantage of this approach compared with other numerical methods, e.g., the finite element method (FEM), is that the integration and discretization of the model are only needed on boundary rather than in whole domain. Therefore, the proposed approach is much more economical than the finite element method. Various numerical examples are subsequently presented in this paper to illustrate the methodology and to demonstrate its accuracy
Integrable and conformal twisted boundary conditions for sl(2) A-D-E lattice models
We study integrable realizations of conformal twisted boundary conditions for sl(2) unitary minimal models on a torus. These conformal field theories are realized as the continuum scaling limit of critical G = A, D, E lattice models with positive spectral parameter u > 0 and Coxeter number g. Integrable seams are constructed by fusing blocks of elementary local face weights. The usual A-type fusions are labelled by the Kac labels (r, s) and are associated with the Verlinde fusion algebra. We introduce a new type of fusion in the two braid limits u → ±i∞ associated with the graph fusion algebra, and labelled by nodes a, b element of G respectively. When combined with automorphisms, they lead to general integrable seams labelled by x = (r, a, b, κ) element of (Ag-2, H, H, Z2) where H is the graph G for type I theories and its parent for type II theories. Identifying our construction labels with the conformal labels of Petkova and Zuber, we find that the integrable seams are in one-to-one correspondence with the conformal seams. The distinct seams are thus associated with the nodes of the Ocneanu quantum graph. The quantum symmetries and twisted partition functions are checked numerically for |G| ≤ 6. We also show, in the case of D2l, that the non-commutativity of the Ocneanu algebra of seams arises because the automorphisms do not commute with the fusions
Bammann, Douglas J.; Johnson, G. C. (University of California, Berkeley, CA); Marin, Esteban B.; Regueiro, Richard A. (University of Colorado, Boulder, CO)
2006-01-01
In this report we present the formulation of the physically-based Evolving Microstructural Model of Inelasticity (EMMI) . The specific version of the model treated here describes the plasticity and isotropic damage of metals as being currently applied to model the ductile failure process in structural components of the W80 program . The formulation of the EMMI constitutive equations is framed in the context of the large deformation kinematics of solids and the thermodynamics of internal state variables . This formulation is focused first on developing the plasticity equations in both the relaxed (unloaded) and current configurations. The equations in the current configuration, expressed in non-dimensional form, are used to devise the identification procedure for the plasticity parameters. The model is then extended to include a porosity-based isotropic damage state variable to describe the progressive deterioration of the strength and mechanical properties of metals induced by deformation . The numerical treatment of these coupled plasticity-damage constitutive equations is explained in detail. A number of examples are solved to validate the numerical implementation of the model.
Betcke, Timo; Graham, Ivan G; Langdon, Stephen; Lindner, Marko
2010-01-01
We consider the classical coupled, combined-field integral equation formulations for time-harmonic acoustic scattering by a sound soft bounded obstacle. In recent work, we have proved lower and upper bounds on the $L^2$ condition numbers for these formulations, and also on the norms of the classical acoustic single- and double-layer potential operators. These bounds to some extent make explicit the dependence of condition numbers on the wave number $k$, the geometry of the scatterer, and the coupling parameter. For example, with the usual choice of coupling parameter they show that, while the condition number grows like $k^{1/3}$ as $k\\to\\infty$, when the scatterer is a circle or sphere, it can grow as fast as $k^{7/5}$ for a class of `trapping' obstacles. In this paper we prove further bounds, sharpening and extending our previous results. In particular we show that there exist trapping obstacles for which the condition numbers grow as fast as $\\exp(\\gamma k)$, for some $\\gamma>0$, as $k\\to\\infty$ through so...
Multigrid solution of a path integral formulation for the hydrogen atom
Bai, D
2004-01-01
An efficient multigrid Monte-Carlo algorithm for calculating the ground state of the hydrogen atom using path integral is presented. The algorithm uses a unigrid approach. The action integral near r=0 is modified so that the correct values of observables are obtained. It is demonstrated that the critical slow down (CSD) is eliminated. Finally, the algorithm is compared to the staging algorithm.
Advanced Amine Solvent Formulations and Process Integration for Near-Term CO2 Capture Success
Fisher, Kevin S.; Searcy, Katherine; Rochelle, Gary T.; Ziaii, Sepideh; Schubert, Craig
2007-06-28
This Phase I SBIR project investigated the economic and technical feasibility of advanced amine scrubbing systems for post-combustion CO2 capture at coal-fired power plants. Numerous combinations of advanced solvent formulations and process configurations were screened for energy requirements, and three cases were selected for detailed analysis: a monoethanolamine (MEA) base case and two “advanced” cases: an MEA/Piperazine (PZ) case, and a methyldiethanolamine (MDEA) / PZ case. The MEA/PZ and MDEA/PZ cases employed an advanced “double matrix” stripper configuration. The basis for calculations was a model plant with a gross capacity of 500 MWe. Results indicated that CO2 capture increased the base cost of electricity from 5 cents/kWh to 10.7 c/kWh for the MEA base case, 10.1 c/kWh for the MEA / PZ double matrix, and 9.7 c/kWh for the MDEA / PZ double matrix. The corresponding cost per metric tonne CO2 avoided was 67.20 $/tonne CO2, 60.19 $/tonne CO2, and 55.05 $/tonne CO2, respectively. Derated capacities, including base plant auxiliary load of 29 MWe, were 339 MWe for the base case, 356 MWe for the MEA/PZ double matrix, and 378 MWe for the MDEA / PZ double matrix. When compared to the base case, systems employing advanced solvent formulations and process configurations were estimated to reduce reboiler steam requirements by 20 to 44%, to reduce derating due to CO2 capture by 13 to 30%, and to reduce the cost of CO2 avoided by 10 to 18%. These results demonstrate the potential for significant improvements in the overall economics of CO2 capture via advanced solvent formulations and process configurations.
Advances in the study of boundary value problems for nonlinear integrable PDEs
In this review I summarize some of the most significant advances of the last decade in the analysis and solution of boundary value problems for integrable partial differential equations (PDEs) in two independent variables. These equations arise widely in mathematical physics, and in order to model realistic applications, it is essential to consider bounded domain and inhomogeneous boundary conditions. I focus specifically on a general and widely applicable approach, usually referred to as the unified transform or Fokas transform, that provides a substantial generalization of the classical inverse scattering transform. This approach preserves the conceptual efficiency and aesthetic appeal of the more classical transform approaches, but presents a distinctive and important difference. While the inverse scattering transform follows the ‘separation of variables’ philosophy, albeit in a nonlinear setting, the unified transform is based on the idea of synthesis, rather than separation, of variables. I will outline the main ideas in the case of linear evolution equations, and then illustrate their generalization to certain nonlinear cases of particular significance. (invited article)
Advances in the study of boundary value problems for nonlinear integrable PDEs
Pelloni, Beatrice
2015-02-01
In this review I summarize some of the most significant advances of the last decade in the analysis and solution of boundary value problems for integrable partial differential equations (PDEs) in two independent variables. These equations arise widely in mathematical physics, and in order to model realistic applications, it is essential to consider bounded domain and inhomogeneous boundary conditions. I focus specifically on a general and widely applicable approach, usually referred to as the unified transform or Fokas transform, that provides a substantial generalization of the classical inverse scattering transform. This approach preserves the conceptual efficiency and aesthetic appeal of the more classical transform approaches, but presents a distinctive and important difference. While the inverse scattering transform follows the ‘separation of variables’ philosophy, albeit in a nonlinear setting, the unified transform is based on the idea of synthesis, rather than separation, of variables. I will outline the main ideas in the case of linear evolution equations, and then illustrate their generalization to certain nonlinear cases of particular significance.
PAN Zhong-liang; CHEN Ling
2009-01-01
The integrated circuit chip with high performance has a high sensitivity to the defects in manufacturing environments. When there are defects on a wafer, the defects may lead to the degradation of chip performance. It is necessary to design effective detection approaches for the defects in order to ensure the reliability of wafer. In this paper, a new method based on image boundary extraction is presented for the detection of defects on a wafer. The method uses island model genetic algorithms to perform the segmentation of wafer images, and gets the optimal threshold values. The island model genetic algorithm uses two distinct subpopulations, it is a coarse grain parallel model. The individuals migration can occur between the two subpopulations to share genetic materials. A lot of experimental results show that the defect detection method proposed in this paper can obtain the features of defects effectively.
Bhattacharya, Amitabh
2013-11-01
An efficient algorithm for simulating Stokes flow around particles is presented here, in which a second order Finite Difference method (FDM) is coupled to a Boundary Integral method (BIM). This method utilizes the strong points of FDM (i.e. localized stencil) and BIM (i.e. accurate representation of particle surface). Specifically, in each iteration, the flow field away from the particles is solved on a Cartesian FDM grid, while the traction on the particle surface (given the the velocity of the particle) is solved using BIM. The two schemes are coupled by matching the solution in an intermediate region between the particle and surrounding fluid. We validate this method by solving for flow around an array of cylinders, and find good agreement with Hasimoto's (J. Fluid Mech. 1959) analytical results.
Boundary integral equation method calculations of surface regression effects in flame spreading
Altenkirch, R. A.; Rezayat, M.; Eichhorn, R.; Rizzo, F. J.
1982-01-01
A solid-phase conduction problem that is a modified version of one that has been treated previously in the literature and is applicable to flame spreading over a pyrolyzing fuel is solved using a boundary integral equation (BIE) method. Results are compared to surface temperature measurements that can be found in the literature. In addition, the heat conducted through the solid forward of the flame, the heat transfer responsible for sustaining the flame, is also computed in terms of the Peclet number based on a heated layer depth using the BIE method and approximate methods based on asymptotic expansions. Agreement between computed and experimental results is quite good as is agreement between the BIE and the approximate results.
A Family of Well-Clear Boundary Models for the Integration of UAS in the NAS
Munoz, Cesar A.; Narkawicz, Anthony; Chamberlain, James; Consiglio, Maria; Upchurch, Jason
2014-01-01
The FAA-sponsored Sense and Avoid Workshop for Unmanned Aircraft Systems (UAS) defines the concept of sense and avoid for remote pilots as "the capability of a UAS to remain well clear from and avoid collisions with other airborne traffic." Hence, a rigorous definition of well clear is fundamental to any separation assurance concept for the integration of UAS into civil airspace. This paper presents a family of well-clear boundary models based on the TCAS II Resolution Advisory logic. For these models, algorithms that predict well-clear violations along aircraft current trajectories are provided. These algorithms are analogous to conflict detection algorithms but instead of predicting loss of separation, they predict whether well-clear violations will occur during a given lookahead time interval. Analytical techniques are used to study the properties and relationships satisfied by the models.
The formalism of Martin, Siggia and Rose is utilized to write a functional-integral representation for generating functionals in plasma transport theory, following Nakayama and Dawson. Parallel treatments of Navier-Stokes turbulence (attempted by Rosen) and of critical dynamics, by Kawasaki, are compared to illustrate the application of common field-theory techniques, such as the effective action. Quasi-classical methods for functional integrals are discussed
Kulshreshtha, Usha; Kulshreshtha, Daya Shankar; Vary, James P.
2016-01-01
Recently (in a series of papers) we have studied the vector Schwinger model with a photon mass term describing one-space one-time dimensional electrodynamics with mass-less fermions in the so-called standard regularization. In the present work, we study this model in the Faddeevian regularization (FR). This theory in the FR is seen to be gauge-non-invariant (GNI). We study the Hamiltonian and path integral quantization of this GNI theory. We then construct a gauge-invariant (GI) theory corresponding to this GNI theory using the Stueckelberg mechanism and recover the physical content of the original GNI theory from the newly constructed GI theory under some special gauge-choice. Further, we study the Hamiltonian, path integral and Becchi-Rouet-Stora and Tyutin formulations of the newly constructed GI theory under appropriate gauge-fixing conditions.
Alsaedi Ahmed
2009-01-01
Full Text Available A generalized quasilinearization technique is developed to obtain a sequence of approximate solutions converging monotonically and quadratically to a unique solution of a boundary value problem involving Duffing type nonlinear integro-differential equation with integral boundary conditions. The convergence of order for the sequence of iterates is also established. It is found that the work presented in this paper not only produces new results but also yields several old results in certain limits.
Mooranian A
2014-09-01
Full Text Available Armin Mooranian,1 Rebecca Negrulj,1 Nigel Chen-Tan,2 Gerald F Watts,3 Frank Arfuso,4 Hani Al-Salami11Biotechnology and Drug Development Research Laboratory, School of Pharmacy, Curtin Health Innovation Research Institute, Biosciences Research Precinct, Curtin University, 2Faculty of Science and Engineering, Curtin University, 3School of Medicine and Pharmacology, Royal Perth Hospital, University of Western Australia, 4School of Biomedical Science, Curtin Health Innovation Research Institute, Biosciences Research Precinct, Curtin University, Perth, AustraliaAbstract: The authors have previously designed, developed, and characterized a novel microencapsulated formulation as a platform for the targeted delivery of therapeutics in an animal model of type 2 diabetes, using the drug probucol (PB. The aim of this study was to optimize PB microcapsules by incorporating the bile acid deoxycholic acid (DCA, which has good permeation-enhancing properties, and to examine its effect on microcapsules’ morphology, rheology, structural and surface characteristics, and excipients’ chemical and thermal compatibilities. Microencapsulation was carried out using a BÜCHI-based microencapsulating system established in the authors’ laboratory. Using the polymer sodium alginate (SA, two microencapsulated formulations were prepared: PB-SA (control and PB-DCA-SA (test at a constant ratio (1:30 and 1:3:30, respectively. Complete characterization of the microcapsules was carried out. The incorporation of DCA resulted in better structural and surface characteristics, uniform morphology, and stable chemical and thermal profiles, while size and rheological parameters remained similar to control. In addition, PB-DCA-SA microcapsules showed good excipients’ compatibilities, which were supported by data from differential scanning calorimetry, Fourier transform infrared spectroscopy, scanning electron microscopy, and energy dispersive X-ray studies, suggesting
Preconditioning first and second kind integral formulations of the capacitance problem
Tausch, J.; White, J.
1996-12-31
Engineering programs which compute electrostatic capacitances for complicated arrangements of conductors commonly set up the electrostatic potential u as a superposition of surface carges {sigma} u(x) = {integral}{sub s}G(x, y){sigma}(y) dS(y). Where G(x, y) = {1/4}{pi}{vert_bar}x - y{vert_bar} is the Green`s function for the Laplacian in the three-space. For a specified potential on the conductor surface(s) S, this approach leads to an integral equation of the first kind on S for the charge density {sigma}. The capacitance is the net-charge on the conductors and is given by the surface integral of {sigma}.
跨共振的周期-积分边值问题%Periodic-Integral Boundary Value Problems across Resonance
宋新; 杨雪
2011-01-01
研究二阶微分方程周期-积分边值问题,应用最优控制理论给出了跨多个共振情形下的二阶微分方程周期-积分边值问题唯一可解的最优条件.%The periodic-integral boundary value problems for second order differential equations were considered. On the basis of optimal control theory method, we gave an optimal condition of the unique solvability to the periodic-integral boundary value problems for second order differential equations across multiple resonance.
Bracken, Paul
An intrinsic version of the integrability theorem for the classical Backlund theorem is presented. It is characterized by a one-form which can be put in the form of a Riccati system. It is shown how this system can be linearized. Based on this, a procedure for generating an infinite number of conservation laws is given.
Scattering of electromagnetic waves by discrete, randomly distributed objects is addressed. In general, the non-intersecting scattering objects can be of arbitrary form, material and shape. The main aim of this paper is to calculate the coherent reflection and transmission characteristics of a slab containing discrete, randomly distributed scatterers. The integral representation of the solution of the deterministic problem constitutes the underlying framework of the stochastic problem. Conditional averaging and the employment of the Quasi Crystalline Approximation lead to a system of integral equations in the unknown expansion coefficients. Of special interest is the slab geometry, which implies a system of integral equations in the depth variable. Explicit solutions for tenuous media and low frequency approximations can be obtained for spherical obstacles. - Highlights: • We analyze electromagnetic scattering by a collection of randomly distributed scatterers. • The coherent scattering contribution of the reflected and transmitted fields is emphasized. • The null field approach is employed to find the solution of the deterministic problem. • A system of integral equations is the main equation to find the desired solution
On the determination of phase boundaries via thermodynamic integration across coexistence regions
Specialized Monte Carlo methods are nowadays routinely employed, in combination with thermodynamic integration (TI), to locate phase boundaries of classical many-particle systems. This is especially useful for the fluid-solid transition, where a critical point does not exist and both phases may notoriously go deeply metastable. Using the Lennard-Jones model for demonstration, we hereby investigate on the alternate possibility of tracing reasonably accurate transition lines directly by integrating the pressure equation of state computed in a canonical-ensemble simulation with local moves. The recourse to this method would become a necessity when the stable crystal structure is not known. We show that, rather counterintuitively, metastability problems can be alleviated by reducing (rather than increasing) the size of the system. In particular, the location of liquid-vapor coexistence can exactly be predicted by just TI. On the contrary, TI badly fails in the solid-liquid region, where a better assessment (to within 10% accuracy) of the coexistence pressure can be made by following the expansion, until melting, of the defective solid which has previously emerged from the decay of the metastable liquid
On the determination of phase boundaries via thermodynamic integration across coexistence regions
Abramo, Maria Concetta, E-mail: mcabramo@unime.it; Caccamo, Carlo, E-mail: caccamo@unime.it; Costa, Dino, E-mail: dcosta@unime.it; Giaquinta, Paolo V., E-mail: paolo.giaquinta@unime.it; Malescio, Gianpietro, E-mail: malescio@unime.it; Munaò, Gianmarco, E-mail: gmunao@unime.it [Dipartimento di Fisica e di Scienze della Terra, Università degli Studi di Messina, Contrada Papardo, I-98166 Messina (Italy); Prestipino, Santi, E-mail: sprestipino@unime.it [Dipartimento di Fisica e di Scienze della Terra, Università degli Studi di Messina, Contrada Papardo, I-98166 Messina (Italy); CNR-IPCF, Viale F. Stagno d’Alcontres 37, I-98158 Messina (Italy)
2015-06-07
Specialized Monte Carlo methods are nowadays routinely employed, in combination with thermodynamic integration (TI), to locate phase boundaries of classical many-particle systems. This is especially useful for the fluid-solid transition, where a critical point does not exist and both phases may notoriously go deeply metastable. Using the Lennard-Jones model for demonstration, we hereby investigate on the alternate possibility of tracing reasonably accurate transition lines directly by integrating the pressure equation of state computed in a canonical-ensemble simulation with local moves. The recourse to this method would become a necessity when the stable crystal structure is not known. We show that, rather counterintuitively, metastability problems can be alleviated by reducing (rather than increasing) the size of the system. In particular, the location of liquid-vapor coexistence can exactly be predicted by just TI. On the contrary, TI badly fails in the solid-liquid region, where a better assessment (to within 10% accuracy) of the coexistence pressure can be made by following the expansion, until melting, of the defective solid which has previously emerged from the decay of the metastable liquid.
Kim, Oleksiy S.
2016-01-01
A new technique for estimating the impedance frequency bandwidth of electrically small antennas loaded with magneto-dielectric material from a single-frequency simulation in a surface integral equation solver is presented. The estimate is based on the inverse of the radiation Q computed using new...... derived expressions for the stored energy and the radiated power of arbitrary coupled electric and magnetic currents in free space.......A new technique for estimating the impedance frequency bandwidth of electrically small antennas loaded with magneto-dielectric material from a single-frequency simulation in a surface integral equation solver is presented. The estimate is based on the inverse of the radiation Q computed using newly...
Parsonage, Catherine; Fadnes, Petter Frost; Taylor, James
2007-01-01
Academic study has become a more significant part of a conservatoire education in recent times, but it has not always informed performance as effectively as it might. There is a need for further development of an academic curriculum that is specifically relevant to performers, in which the links between theory and practice are made explicit rather than expecting students to construct these for themselves. This article reports on research into the integration of theory and practice at Leeds Co...
ZHAO Ming-hao; LI Dong-xia; SHEN Ya-peng
2005-01-01
The integral-differential equations for three-dimensional planar interfacial cracks of arbitrary shape in transversely isotropic bimaterials were derived by virtue of the Somigliana identity and the fundamental solutions, in which the displacement discontinuities across the crack faces are the unknowns to be determined. The interface is parallel to both the planes of isotropy. The singular behaviors of displacement and stress near the crack border were analyzed and the stress singularity indexes were obtained by integral equation method. The stress intensity factors were expressed in terms of the displacement discontinuities. In the non-oscillatory case, the hyper-singular boundary integral-differential equations were reduced to hyper-singular boundary integral equations similar to those of homogeneously isotropie materials.
Arraut, Ivan
2015-01-01
If we apply the path integral formulation in order to analyze the particle creation process of black-holes inside the non-linear formulation of massive gravity, it is possible to demonstrate that the effect of the extra-degrees of freedom is to deform the periodicity of the poles of the propagator in the complex $t$-plane. This might create the effect of extra-particle creation process at scales where the extra-degrees of freedom become relevant. For stationary solutions, depending on the values taken by the free parameters of the theory, the periodicity structure of the propagator reveal two effects. The first one is a shift on the positions of the pole of the propagator with respect to the GR case, affecting then the instant at which the particles are detected. The second one is the existence of branch points, affecting then the perception of particles. The branch point can be finite (including the zero order case) or infinite depending on the free-parameters of the theory.
Nittaya Pongarm
2013-01-01
Full Text Available This paper studies sufficient conditions for the existence of solutions to the problem of sequential derivatives of nonlinear q-difference equations with three-point q-integral boundary conditions. Our results are concerned with several quantum numbers of derivatives and integrals. By using Banach's contraction mapping, Krasnoselskii's fixed-point theorem, and Leray-Schauder degree theory, some new existence results are obtained. Two examples illustrate our results.
Gao, Y.; Balaram, P.; Islam, S.
2009-12-01
Water issues and problems have bewildered humankind for a long time yet a systematic approach for understanding such issues remain elusive. This is partly because many water-related problems are framed from a contested terrain in which many actors (individuals, communities, businesses, NGOs, states, and countries) compete to protect their own and often conflicting interests. We argue that origin of many water problems may be understood as a dynamic consequence of competition, interconnections, and feedback among variables in the Natural and Societal Systems (NSSs). Within the natural system, we recognize that triple constraints on water- water quantity (Q), water quality (P), and ecosystem (E)- and their interdependencies and feedback may lead to conflicts. Such inherent and multifaceted constraints of the natural water system are exacerbated often at the societal boundaries. Within the societal system, interdependencies and feedback among values and norms (V), economy (C), and governance (G) interact in various ways to create intractable contextual differences. The observation that natural and societal systems are linked is not novel. Our argument here, however, is that rigid disciplinary boundaries between these two domains will not produce solutions to the water problems we are facing today. The knowledge needed to address water problems need to go beyond scientific assessment in which societal variables (C, G, and V) are treated as exogenous or largely ignored, and policy research that does not consider the impact of natural variables (E, P, and Q) and that coupling among them. Consequently, traditional quantitative methods alone are not appropriate to address the dynamics of water conflicts, because we cannot quantify the societal variables and the exact mathematical relationships among the variables are not fully known. On the other hand, conventional qualitative study in societal domain has mainly been in the form of individual case studies and therefore
Chang, Ruinan
The ability to have a good understanding of and to manipulate electromagnetic elds has been increasingly important for many hardware technologies. There is a strong need for advanced numeric algorithms that yield fast and accuracy controllable solvers for electromagnetic and micromagnetic simulations. The first part of the dissertation presents methods constituting the core of the high-performance simulator FastMag. FastMag derives its high speed from three aspects. First, it leverages the state-of-the-art graphics processing unit computational architectures, which can be hundreds of times faster than a single central processing unit. Moreover, ecient and and accurate implementations of numeric quadrature was invoked. Thirdly, we provide an analytic method for Jacobian vector products. Some advanced features are provided in FastMag. Quadratic basis functions are used to provide better accuracy. Hexahedral elements were also implemented because they are more accurate, consume less memory. The second part of the dissertation is devoted to electromagnetic scattering problems. We developed new algorithms that signicantly improved the traditional methods. First of all, potential volume integral equations were implemented, where the potential quantities (vector and scalar potential). Another important contribution of this disertation is quadrilateral barycentric basis functions (QBBFs). The QBBFs can serve as a fundamental block for primary basis functions (PBFs) and dual basis functions (DBFs). The PBFs and DBFs, when applied in combination into traditional electric and magnetic eld integral equations (EFIE and MFIE), give rise to accurate and robust results. Moreover, the DBFs make the famous Calderon preconditioner multiplicative.
Friedrich, Johannes; Fetzer, Ingo; Cornell, Sarah
2016-04-01
The planetary boundaries framework is an approach to global sustainability that emphasises non-linear threshold behavior in anthropogenically perturbed Earth system processes. However, knowledge about the characteristics and positions of thresholds, and the scope for management of the boundaries is not well established. Global integrated models can help to improve this understanding, by reflecting the complex feedbacks between human and environmental systems. This study analyses the current state of integrated models with regard to the main processes identified as 'critical Earth system processes' in the planetary boundaries framework, and identifies gaps and suggests priorities for future improvements. Our approach involves creating a common ontology of model descriptions, and performing a network analysis on the state of system integration in models. The distinct clusters of specific biophysical and social-economic systems obviously has enabled progress in those specific areas of global change, but it now constrains analysis of important human-driven Earth system dynamics. The modeling process therefore has to be improved through technical integration, scientific gap-filling, and also changes in scientific institutional dynamics. Combined, this can advance model potentials that may help us to find sustainable pathways within planetary boundaries.
Chatthai Thaiprayoon
2014-01-01
Full Text Available By developing a new comparison result and using the monotone iterative technique, we are able to obtain existence of minimal and maximal solutions of periodic boundary value problems for first-order impulsive functional integrodifferential equations with integral-jump conditions. An example is also given to illustrate our results.
Moving Towards Integrated Policy Formulation and Evaluation: The Green Economy Model
Bassi Andrea M.
2015-12-01
Full Text Available The mainstreaming of concepts related to the Green Economy, an action-oriented approach to reach sustainable development, has increased demands for integrated models that can shed light on the complex relations existing across social, economic and environmental indicators. A gap exists, whereby our thinking is rapidly evolving, but the tools available are still in the vast majority of cases sectorial, leading to planning processes taking place in silos. To avoid the emergence of side effects, and anticipate future threats and opportunities, a more systemic approach is needed. The Green Economy Model (GEM was created taking into account four main capitals and their interconnections: physical capital, human capital, social capital and natural capital. The application of GEM in 10 countries has shown its capability to coherently represent reality and generate results that can more effectively inform decision making.
Moving Towards Integrated Policy Formulation and Evaluation: The Green Economy Model
Bassi, Andrea M.
2015-12-01
The mainstreaming of concepts related to the Green Economy, an action-oriented approach to reach sustainable development, has increased demands for integrated models that can shed light on the complex relations existing across social, economic and environmental indicators. A gap exists, whereby our thinking is rapidly evolving, but the tools available are still in the vast majority of cases sectorial, leading to planning processes taking place in silos. To avoid the emergence of side effects, and anticipate future threats and opportunities, a more systemic approach is needed. The Green Economy Model (GEM) was created taking into account four main capitals and their interconnections: physical capital, human capital, social capital and natural capital. The application of GEM in 10 countries has shown its capability to coherently represent reality and generate results that can more effectively inform decision making.
Agustina Abdullah; Ali, Hikmah M.; Syamsu, Jasmal A.
2013-01-01
The study aims to formulate a strategy for strengthening the farmers in the adoption of technology for the development of integrated beef cattle with paddy. Research was conducted in Pinrang South Sulawesi province for seven months. Primary Data obtained by using questionnaires, interviews and focus group discussion. In this study also was involved expert respondents. Flow implementation strategy formulation is done using analytical hierarchy process (AHP) techniques. The results showed that ...
Zeng, Y. Y.; Guo, J. Y.; Shang, K.; Shum, C. K.; Yu, J. H.
2015-09-01
Two methods for computing gravitational potential difference (GPD) between the GRACE satellites using orbit data have been formulated based on energy integral; one in geocentric inertial frame (GIF) and another in Earth fixed frame (EFF). Here we present a rigorous theoretical formulation in EFF with particular emphasis on necessary approximations, provide a computational approach to mitigate the approximations to negligible level, and verify our approach using simulations. We conclude that a term neglected or ignored in all former work without verification should be retained. In our simulations, 2 cycle per revolution (CPR) errors are present in the GPD computed using our formulation, and empirical removal of the 2 CPR and lower frequency errors can improve the precisions of Stokes coefficients (SCs) of degree 3 and above by 1-2 orders of magnitudes. This is despite of the fact that the result without removing these errors is already accurate enough. Furthermore, the relation between data errors and their influences on GPD is analysed, and a formal examination is made on the possible precision that real GRACE data may attain. The result of removing 2 CPR errors may imply that, if not taken care of properly, the values of SCs computed by means of the energy integral method using real GRACE data may be seriously corrupted by aliasing errors from possibly very large 2 CPR errors based on two facts: (1) errors of bar C_{2,0} manifest as 2 CPR errors in GPD and (2) errors of bar C_{2,0} in GRACE data-the differences between the CSR monthly values of bar C_{2,0} independently determined using GRACE and SLR are a reasonable measure of their magnitude-are very large. Our simulations show that, if 2 CPR errors in GPD vary from day to day as much as those corresponding to errors of bar C_{2,0} from month to month, the aliasing errors of degree 15 and above SCs computed using a month's GPD data may attain a level comparable to the magnitude of gravitational potential
Boundary integral simulations of dissolving drops in segmented two-phase flows
Ramchandran, Arun; Leary, Thomas
2015-11-01
Recent years have seen an upsurge in the literature reporting the microfluidic measurement of the kinetics of `fast' gas-liquid reactions by recording the shrinkage of bubbles in segmented flows of these gas-liquid combinations in microfluidic channels. A critical aspect of the data analysis in these experiments is the knowledge of how dissolution influences the velocity field in the liquid slug, and hence, the mass transport characteristics. Unfortunately, there is no literature on this connection for dissolving bubbles. Our research addresses this gap using boundary integral simulations. The effects of the dissolution rate on the film thickness and the inter-drop separation are examined as a function of the capillary number and the viscosity ratio. The results demonstrate that dissolution can enhance the degree of mixing appreciably from one slug to the next. A curious result is that the film thickness and the droplet separation distance can change significantly beyond a critical capillary number, producing flow patterns completely different from those known for the undissolving bubble case. These results will guide the selection of operating regimes that enable convenient interpretation of data from experiments to deduce kinetic constants.