|
| ||
|
|
||
Boundary Values (boundary + value)
Terms modified by Boundary Values Selected AbstractsSum rules and exact relations for quantal Coulomb systemsCONTRIBUTIONS TO PLASMA PHYSICS, Issue 5-6 2003V.M. Adamyan Abstract A complex response function describing a reaction of a multi-particle system to a weak alternating external field is the boundary value of a Nevanlinna class function (i.e. a holomorphic function with non-negative imaginary part in the upper half-plane). Attempts of direct calculations of response functions based on standard approximations of the kinetic theory for real Coulomb condensed systems often result in considerable discrepancies with experiments and computer simulations. At the same time a relatively simple approach using only the exact values of leading asymptotic terms of the response function permits to restrict essentially a subset of Nevanlinna class functions containing this response function, and in this way to obtain sufficient data to explain and predict experimental results. Mathematical details of this approach are demonstrated on an example with the response function being the (external) dynamic electrical conductivity of cold dense hydrogen-like plasmas. In particular, the exact values of the leading terms of asymptotic expansions of the conductivity are calculated. (© 2003 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] Reverse modelling for seismic event characterizationGEOPHYSICAL JOURNAL INTERNATIONAL, Issue 1 2005Dirk Gajewski SUMMARY The localization of seismic events is of utmost importance in seismology and exploration. Current techniques rely on the fact that the recorded event is detectable at most of the stations of a seismic network. Weak events, not visible in the individual seismogram of the network, are missed out. We present an approach, where no picking of events in the seismograms of the recording network is required. The observed wavefield of the network is reversed in time and then considered as the boundary value for the reverse modelling. Assuming the correct velocity model, the reversely modelled wavefield focuses on the hypocentre of the seismic event. The origin time of the event is given by the time where maximum focussing is observed. The spatial extent of the focus resembles the resolution power of the recorded wavefield and the acquisition. This automatically provides the uncertainty in the localization with respect to the bandwidth of the recorded data. The method is particularly useful for the upcoming large passive networks since no picking is required. It has great potential for localizing very weak events, not detectable in the individual seismogram, since the reverse modelling sums the energy of all recorded traces and, therefore, enhances the signal-to-noise ratio similar to stacking in seismic exploration. The method is demonstrated by 2-D and 3-D numerical case studies, which show the potential of the technique. Events with a S/N ratio smaller than 1 where the events cannot be identified in the individual seismogram of the network are localized very well by the method. [source] On generalized stochastic perturbation-based finite element methodINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 1 2006Marcin Kami Abstract Generalized nth order stochastic perturbation technique, that can be applied to solve some boundary value or boundary initial problems in computational physics and/or engineering with random parameters is proposed here. This technique is demonstrated in conjunction with the finite element method (FEM) to model 1D linear elastostatics problem with a single random variable. The symbolic computer program is employed to perform computational studies on convergence of the first two probabilistic moments for simple unidirectional tension of a bar. These numerical studies verify the influence of coefficient of variation of the random input and, at the same time, of the perturbation parameter on the first two probabilistic moments of the final solution vector. Copyright © 2005 John Wiley & Sons, Ltd. [source] Application of second-order adjoint technique for conduit flow problemINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 11 2007T. Kurahashi Abstract This paper presents the way to obtain the Newton gradient by using a traction given by the perturbation for the Lagrange multiplier. Conventionally, the second-order adjoint model using the Hessian/vector products expressed by the product of the Hessian matrix and the perturbation of the design variables has been researched (Comput. Optim. Appl. 1995; 4:241,262). However, in case that the boundary value would like to be obtained, this model cannot be applied directly. Therefore, the conventional second-order adjoint technique is extended to the boundary value determination problem and the second-order adjoint technique is applied to the conduit flow problem in this paper. As the minimization technique, the Newton-based method is employed. The Broyden,Fletcher,Goldfarb,Shanno (BFGS) method is applied to calculate the Hessian matrix which is used in the Newton-based method and a traction given by the perturbation for the Lagrange multiplier is used in the BFGS method. Copyright © 2007 John Wiley & Sons, Ltd. [source] The restricted likelihood ratio test at the boundary in autoregressive seriesJOURNAL OF TIME SERIES ANALYSIS, Issue 6 2009Willa W. Chen Abstract., The restricted likelihood ratio test, RLRT, for the autoregressive coefficient in autoregressive models has recently been shown to be second-order pivotal when the autoregressive coefficient is in the interior of the parameter space and so is very well approximated by the distribution. In this article, the non-standard asymptotic distribution of the RLRT for the unit root boundary value is obtained and is found to be almost identical to that of the in the right tail. Together, these two results imply that the distribution approximates the RLRT distribution very well even for near unit root series and transitions smoothly to the unit root distribution. [source] Fast direct solver for Poisson equation in a 2D elliptical domainNUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, Issue 1 2004Ming-Chih Lai Abstract In this article, we extend our previous work M.-C. Lai and W.-C. Wang, Numer Methods Partial Differential Eq 18:56,68, 2002 for developing some fast Poisson solvers on 2D polar and spherical geometries to an elliptical domain. Instead of solving the equation in an irregular Cartesian geometry, we formulate the equation in elliptical coordinates. The solver relies on representing the solution as a truncated Fourier series, then solving the differential equations of Fourier coefficients by finite difference discretizations. Using a grid by shifting half mesh away from the pole and incorporating the derived numerical boundary value, the difficulty of coordinate singularity can be elevated easily. Unlike the case of 2D disk domain, the present difference equation for each Fourier mode is coupled with its conjugate mode through the numerical boundary value near the pole; thus, those two modes are solved simultaneously. Both second- and fourth-order accurate schemes for Dirichlet and Neumann problems are presented. In particular, the fourth-order accuracy can be achieved by a three-point compact stencil which is in contrast to a five-point long stencil for the disk case. © 2003 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 20: 72,81, 2004 [source] Optimal disturbance rejection control for singularly perturbed composite systems with time-delay,ASIAN JOURNAL OF CONTROL, Issue 3 2009Bao-Lin Zhang Abstract The optimal control problem for a class of singularly perturbed time-delay composite systems affected by external disturbances is investigated. The system is decomposed into a fast linear subsystem and a slow time-delay subsystem with disturbances. For the slow subsystem, the feedforward compensation technique is proposed to reject the disturbances, and the successive approximation approach (SAA) is applied to decompose it into decoupled subsystems and solve the two-point boundary value (TPBV) problem. By combining with the optimal control law of the fast subsystem, the feedforward and feedback composite control (FFCC) law of the original composite system is obtained. The FFCC law consists of analytic state feedback and feedforward terms and a compensation term which is the limit of the adjoint vector sequence. The compensation term can be obtained from an iteration formula of adjoint vectors. Simulation results are employed to test the validity of the proposed design algorithm. Copyright © 2009 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society [source] Sharp regularity results on second derivatives of solutions to the Monge-Ampère equation with VMO type dataCOMMUNICATIONS ON PURE & APPLIED MATHEMATICS, Issue 5 2009Qingbo Huang We establish interior estimates for Lp -norms, Orlicz norms, and mean oscillation of second derivatives of solutions to the Monge-Ampère equation det D2u = f(x) with zero boundary value, where f(x) is strictly positive, bounded, and satisfies a VMO-type condition. These estimates develop the regularity theory of the Monge-Ampère equation in VMO-type spaces. Our Orlicz estimates also sharpen Caffarelli's celebrated W2, p -estimates. © 2008 Wiley Periodicals, Inc. [source] Least-square-based radial basis collocation method for solving inverse problems of Laplace equation from noisy dataINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 1 2010Xian-Zhong Mao Abstract The inverse problem of 2D Laplace equation involves an estimation of unknown boundary values or the locations of boundary shape from noisy observations on over-specified boundary or internal data points. The application of radial basis collocation method (RBCM), one of meshless and non-iterative numerical schemes, directly induces this inverse boundary value problem (IBVP) to a single-step solution of a system of linear algebraic equations in which the coefficients matrix is inherently ill-conditioned. In order to solve the unstable problem observed in the conventional RBCM, an effective procedure that builds an over-determined linear system and combines with least-square technique is proposed to restore the stability of the solution in this paper. The present work investigates three examples of IBVPs using over-specified boundary conditions or internal data with simulated noise and obtains stable and accurate results. It underlies that least-square-based radial basis collocation method (LS-RBCM) poses a significant advantage of good stability against large noise levels compared with the conventional RBCM. Copyright © 2010 John Wiley & Sons, Ltd. [source] Direct solution of ill-posed boundary value problems by radial basis function collocation methodINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 1 2005A. H.-D. Abstract Numerical solution of ill-posed boundary value problems normally requires iterative procedures. In a typical solution, the ill-posed problem is first converted to a well-posed one by assuming the missing boundary values. The new problem is solved by a conventional numerical technique and the solution is checked against the unused data. The problem is solved iteratively using optimization schemes until convergence is achieved. The present paper offers a different procedure. Using the radial basis function collocation method, we demonstrate that the solution of certain ill-posed problems can be accomplished without iteration. This method not only is efficient and accurate, but also circumvents the stability problem that can exist in the iterative method. Copyright © 2005 John Wiley & Sons, Ltd. [source] The Mediterranean intercalibration exercise on soft-bottom benthic invertebrates with special emphasis on the Italian situationMARINE ECOLOGY, Issue 4 2009Anna Occhipinti Ambrogi Abstract The intercalibration exercise is an important step in the building process of the surface water ecological quality assessment, which is required by the Water Framework Directive (WFD). Its aim is to apply the water quality classification in a uniform manner to all the Member States belonging to the same eco-region. Cyprus, France, Greece, Italy, Slovenia and Spain participated in the soft-bottom benthic invertebrate subgroup for the Mediterranean coastal region. The methodologies proposed by Member States were applied and tested; the results were compared and harmonized to establish agreed and comparable boundaries for the benthic invertebrate ecological status classes. The national methods used in the intercalibration process were: for Cyprus and Greece, the Bentix Index; for Slovenia, a combination of AZTI Marine Biotic Index (AMBI), richness and diversity with the use of factor and discriminant analysis (Multimetric AMBI); for Spain, a new index, named MEDOCC, which is an adaptation of the AMBI index to the Western Mediterranean area. Italy and France tested different methods, none of which have been officially adopted. Final class boundary values for the different official classification systems were obtained and compared. Besides describing methods and results obtained by the different countries, the Italian situation is examined in more detail. All the above methods have been applied to Italian data, but the results were not conclusive. Major causes for concern are related to insufficient sites and data, to the lack of real non-impacted reference sites, and to the difficulties in validating the ecological status classification in sites not showing a pollution gradient. [source] On the spectra of some integral operators related to the potential theory in the planeMATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 14 2010Oleg F. Gerus Abstract We study point spectra of the two integral operators that are generated by the boundary values of the simple-layer potential and of the integral tightly related to the double-layer potential; the operators act on the Hölder space Hµ(,), µ,(0,1), and on the Lebesgue space Lp(,), p>2, where , is a closed Lyapunov curve. Copyright © 2010 John Wiley & Sons, Ltd. [source] A solution method for the linear Chandrasekhar equationMATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 15 2006Elias Wegert Abstract The paper is devoted to the linearized H -equation of Chandrasekhar and Ambarzumyan. A Stieltjes-type transform reduces the equation to a boundary value problem for holomorphic functions in the upper half-plane which is solved in closed form. Additional conditions ensure that the solutions , extend holomorphically to the lower half-plane slit along a straight line segment. The solutions of the original problem are then determined from the boundary values of , on this slit. The approach gives necessary and sufficient conditions for Fredholmness and describes all Fredholm parameters in terms of zeros of two functions 1,K and G associated with the kernel and the right-hand side of the equation. Explicit formulas for the complete set of solutions are presented. Die Arbeit ist der linearisierten H -Gleichung von Chandrasekhar und Ambarzumyan gewidmet. Die Gleichung wird mit Hilfe einer modifizierten Stieltjes-Transformation auf ein Randwertproblem für holomorphe Funktionen in der oberen Halbebene zurückgeführt das in geschlossener Form gelöst wird. Unter zusätzlichen Bedingungen können die Lösungen holomorph in die längs einer Strecke aufgeschnittene untere Halbebene fortgesetzt werden. Die Lösungen , des Ausgangsproblems werden dann aus den Randwerten von , längs des Schlitzes bestimmt. Der Zugang liefert notwendige und hinreichende Bedingungen dafür, dass der Operator Fredholmsch ist und charakterisiert alle Fredholmparameter mit Hilfe der Nullstellen zweier Funktionen 1,K und G, die dem Kern und der rechten Seite der Gleichung zugeordnet sind. Es werden explizite Darstellungen für die vollständige Lösungsmenge angegeben. Copyright © 2006 John Wiley & Sons, Ltd. [source] Initial boundary value problem for the evolution system of MHD type describing geophysical flow in three-dimensional domainsMATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 9 2003Chunshan Zhao Abstract The initial boundary value problem for the evolution system describing geophysical flow in three-dimensional domains was considered. The existence and uniqueness of global strong solution to the evolution system were proved under assumption on smallness of data. Moreover, solvable compatibility conditions of initial data and boundary values which guarantee the existence and uniqueness of global strong solution were discussed. Copyright © 2003 John Wiley & Sons, Ltd. [source] The effect of a surface energy term on the distribution of phases in an elastic medium with a two-well elastic potentialMATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 2 2002Michael Bildhauer Abstract We consider the problem of minimizing among functions u:,d,,,,d, u,,,=0, and measurable subsets E of ,. Here fh+, f, denote quadratic potentials defined on ,¯×{symmetric d×d matrices}, h is the minimum energy of fh+ and ,(u) is the symmetric gradient of the displacement field u. An equilibrium state û, Ê of J(u,E) is called one-phase if E=, or E=,, two-phase otherwise. For two-phase states, ,,,E,,, measures the effect of the separating surface, and we investigate the way in which the distribution of phases is affected by the choice of the parameters h,,, ,>0. Additional results concern the smoothness of two-phase equilibrium states and the behaviour of inf J(u,E) in the limit ,,0. Moreover, we discuss the case of additional volume force potentials, and extend the previous results to non-zero boundary values. Copyright © 2002 John Wiley & Sons, Ltd. [source] Approximate identities in variable Lp spacesMATHEMATISCHE NACHRICHTEN, Issue 3 2007D. Cruz-Uribe SFO Abstract We give conditions for the convergence of approximate identities, both pointwise and in norm, in variable Lp spaces. We unify and extend results due to Diening [8], Samko [18] and Sharapudinov [19]. As applications, we give criteria for smooth functions to be dense in the variable Sobolev spaces, and we give solutions of the Laplace equation and the heat equation with boundary values in the variable Lp spaces. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] Finding initial costates in finite-horizon nonlinear-quadratic optimal control problemsOPTIMAL CONTROL APPLICATIONS AND METHODS, Issue 3 2008Vicente Costanza Abstract A procedure for obtaining the initial value of the costate in a regular, finite-horizon, nonlinear-quadratic problem is devised in dimension one. The optimal control can then be constructed from the solution to the Hamiltonian equations, integrated on-line. The initial costate is found by successively solving two first-order, quasi-linear, partial differential equations (PDEs), whose independent variables are the time-horizon duration T and the final-penalty coefficient S. These PDEs need to be integrated off-line, the solution rendering not only the initial condition for the costate sought in the particular (T, S)-situation but also additional information on the boundary values of the whole two-parameter family of control problems, that can be used for design purposes. Results are tested against exact solutions of the PDEs for linear systems and also compared with numerical solutions of the bilinear-quadratic problem obtained through a power-series' expansion approach. Bilinear systems are specially treated in their character of universal approximations of nonlinear systems with bounded controls during finite time-periods. Copyright © 2007 John Wiley & Sons, Ltd. [source] The generalized Dirichlet-to-Neumann map for certain nonlinear evolution PDEsCOMMUNICATIONS ON PURE & APPLIED MATHEMATICS, Issue 5 2005A. S. Fokas Let q(x,t) satisfy a nonlinear integrable evolution PDE whose highest spatial derivative is of order n. An initial boundary value problem on the half-line for such a PDE is at least linearly well-posed if one prescribes initial conditions, as well as N boundary conditions at x = 0, where for n even N equals n/2 and for n odd, depending on the sign of the highest derivative, N equals either n,1/2 or n+1/2. For example, for the nonlinear Schrödinger (NLS) and the sine-Gordon (sG), N = 1, while for the modified Korteweg-deVries (mKdV) N = 1 or N = 2 depending on the sign of the third derivative. Constructing the generalized Dirichlet-to-Neumann map means determining those boundary values at x = 0 that are not prescribed as boundary conditions in terms of the given initial and boundary conditions. A general methodology is presented that constructs this map in terms of the solution of a system of two nonlinear ODEs. This formulation implies that for the focusing NLS, for the sG, and for the two focusing versions of the mKdV, this map is global in time. It appears that this is the first time in the literature that such a characterization for nonlinear PDEs is explicitly described. It is also shown here that for particular choices of the boundary conditions the above map can be linearized. © 2005 Wiley Periodicals, Inc. [source] | ||||||||||||||||