Search results for "APPROXIMATION"

On the accuracy of the fast hierarchical DBEM for the analysis of static and dynamic crack problems

2010

In this paper the main features of a fast dual boundary element method based on the use of hierarchical matrices and iterative solvers are described and its effectiveness for fracture mechanics problems, both in the static and dynamic case, is demonstrated. The fast solver is built by representing the collocation matrix in hierarchical format and by using a preconditioned GMRES for the solution of the algebraic system. The preconditioner is computed in hierarchical format by LU decomposition of a coarse hierarchical representation of the collocation matrix. The method is applied to elastostatic problems and to elastodynamic cases represented in the Laplace transform domain. The application …

Limits of Sobolev homeomorphisms

2017

Let X; Y subset of R-2 be topologically equivalent bounded Lipschitz domains. We prove that weak and strong limits of homeomorphisms h: X (onto)-> Y in the Sobolev space W-1,W-p (X, R-2), p >= 2; are the same. As an application, we establish the existence of 2D-traction free minimal deformations for fairly general energy integrals. Peer reviewed

Slow-roll corrections in multi-field inflation: a separate universes approach

2018

In view of cosmological parameters being measured to ever higher precision, theoretical predictions must also be computed to an equally high level of precision. In this work we investigate the impact on such predictions of relaxing some of the simplifying assumptions often used in these computations. In particular, we investigate the importance of slow-roll corrections in the computation of multi-field inflation observables, such as the amplitude of the scalar spectrum $P_\zeta$, its spectral tilt $n_s$, the tensor-to-scalar ratio $r$ and the non-Gaussianity parameter $f_{NL}$. To this end we use the separate universes approach and $\delta N$ formalism, which allows us to consider slow-roll…

Time propagation of the Kadanoff–Baym equations for inhomogeneous systems

2009

We have developed a time propagation scheme for the Kadanoff-Baym equations for general inhomogeneous systems. These equations describe the time evolution of the nonequilibrium Green function for interacting many-body systems in the presence of time-dependent external fields. The external fields are treated nonperturbatively whereas the many-body interactions are incorporated perturbatively using Phi-derivable self-energy approximations that guarantee the satisfaction of the macroscopic conservation laws of the system. These approximations are discussed in detail for the time-dependent Hartree-Fock, the second Born and the GW approximation.

Sequential Learning with LS-SVM for Large-Scale Data Sets

2006

We present a subspace-based variant of LS-SVMs (i.e. regularization networks) that sequentially processes the data and is hence especially suited for online learning tasks. The algorithm works by selecting from the data set a small subset of basis functions that is subsequently used to approximate the full kernel on arbitrary points. This subset is identified online from the data stream. We improve upon existing approaches (esp. the kernel recursive least squares algorithm) by proposing a new, supervised criterion for the selection of the relevant basis functions that takes into account the approximation error incurred from approximating the kernel as well as the reduction of the cost in th…

B-parameters for ΔS=2 supersymmetric operators

1998

We present a calculation of the matrix elements of the most general set of DeltaS=2 dimension-six four-fermion operators. The values of the matrix elements are given in terms of the corresponding B-parameters. Our results can be used in many phenomenological applications, since the operators considered here give important contributions to K^0--K^0bar mixing in several extensions of the Standard Model (supersymmetry, left-right symmetric models, multi-Higgs models etc.). The determination of the matrix elements improves the accuracy of the phenomenological analyses intended to put bounds on basic parameters of the different models, as for example the pattern of the sfermion mass matrices. Th…

Structural and Luminescent Properties of Homoleptic Silver(I), Gold(I), and Palladium(II) Complexes with nNHC-tzNHC Heteroditopic Carbene Ligands

2019

Novel silver(I), gold(I), and palladium(II) complexes were synthesized with bidentate heteroditopic carbene ligands that combine an imidazol-2-ylidene (nNHC) with a 1,2,3-triazol-5-ylidene (tzNHC) connected by a propylene bridge. The silver(I) and gold(I) complexes were dinuclear species, [M-2(nNHC-tzNHC)(2)](PF6)(2) (M = Ag or Au), with the two bidentate ligands bridging the metal centers, whereas in the palladium(II) complex [Pd(nNHC-tzNHC)(2)]-(PF6)(2), the two ligands were chelated on the same metal center. Because of the presence of two different carbene units, isomers were observed for the gold(I) and palladium(II) complexes. The molecular structures of the head-to-tail isomer for gol…

Matemātika

1994

Accurate expansion of cylindrical paraxial waves for its straightforward implementation in electromagnetic scattering

2017

Abstract The evaluation of vector wave fields can be accurately performed by means of diffraction integrals, differential equations and also series expansions. In this paper, a Bessel series expansion which basis relies on the exact solution of the Helmholtz equation in cylindrical coordinates is theoretically developed for the straightforward yet accurate description of low-numerical-aperture focal waves. The validity of this approach is confirmed by explicit application to Gaussian beams and apertured focused fields in the paraxial regime. Finally we discuss how our procedure can be favorably implemented in scattering problems.

Isotropic compensation of diffraction-driven angular dispersion

2007

We report on an optical arrangement capable of compensating angular dispersion of paraxial wave fields developed by diffractive optical elements (DOEs). Schematically, the system is a beam expander in which two phase-only zone plates have been inserted, remaining afocal the coupled system. The DOE, which induces a continuous set of dispersive tilted plane waves, is placed at a specific position within the proposed setup providing an output spectrum with achromatic angular deviation. A directional matching between phase fronts and pulse fronts of output wave packets is demonstrated.