1,313 research outputs found
Wavelet treatment of the intra-chain correlation functions of homopolymers in dilute solutions
Discrete wavelets are applied to parametrization of the intra-chain two-point
correlation functions of homopolymers in dilute solutions obtained from Monte
Carlo simulation. Several orthogonal and biorthogonal basis sets have been
investigated for use in the truncated wavelet approximation. Quality of the
approximation has been assessed by calculation of the scaling exponents
obtained from des Cloizeaux ansatz for the correlation functions of
homopolymers with different connectivities in a good solvent. The resulting
exponents are in a better agreement with those from the recent renormalisation
group calculations as compared to the data without the wavelet denoising. We
also discuss how the wavelet treatment improves the quality of data for
correlation functions from simulations of homopolymers at varied solvent
conditions and of heteropolymers.Comment: RevTeX, 19 pages, 7 PS figures. Accepted for publication in PR
Construction of Hilbert Transform Pairs of Wavelet Bases and Gabor-like Transforms
We propose a novel method for constructing Hilbert transform (HT) pairs of
wavelet bases based on a fundamental approximation-theoretic characterization
of scaling functions--the B-spline factorization theorem. In particular,
starting from well-localized scaling functions, we construct HT pairs of
biorthogonal wavelet bases of L^2(R) by relating the corresponding wavelet
filters via a discrete form of the continuous HT filter. As a concrete
application of this methodology, we identify HT pairs of spline wavelets of a
specific flavor, which are then combined to realize a family of complex
wavelets that resemble the optimally-localized Gabor function for sufficiently
large orders.
Analytic wavelets, derived from the complexification of HT wavelet pairs,
exhibit a one-sided spectrum. Based on the tensor-product of such analytic
wavelets, and, in effect, by appropriately combining four separable
biorthogonal wavelet bases of L^2(R^2), we then discuss a methodology for
constructing 2D directional-selective complex wavelets. In particular,
analogous to the HT correspondence between the components of the 1D
counterpart, we relate the real and imaginary components of these complex
wavelets using a multi-dimensional extension of the HT--the directional HT.
Next, we construct a family of complex spline wavelets that resemble the
directional Gabor functions proposed by Daugman. Finally, we present an
efficient FFT-based filterbank algorithm for implementing the associated
complex wavelet transform.Comment: 36 pages, 8 figure
Wavelet-Fourier CORSING techniques for multi-dimensional advection-diffusion-reaction equations
We present and analyze a novel wavelet-Fourier technique for the numerical
treatment of multidimensional advection-diffusion-reaction equations based on
the CORSING (COmpRessed SolvING) paradigm. Combining the Petrov-Galerkin
technique with the compressed sensing approach, the proposed method is able to
approximate the largest coefficients of the solution with respect to a
biorthogonal wavelet basis. Namely, we assemble a compressed discretization
based on randomized subsampling of the Fourier test space and we employ sparse
recovery techniques to approximate the solution to the PDE. In this paper, we
provide the first rigorous recovery error bounds and effective recipes for the
implementation of the CORSING technique in the multi-dimensional setting. Our
theoretical analysis relies on new estimates for the local a-coherence, which
measures interferences between wavelet and Fourier basis functions with respect
to the metric induced by the PDE operator. The stability and robustness of the
proposed scheme is shown by numerical illustrations in the one-, two-, and
three-dimensional case
Almost diagonal matrices and Besov-type spaces based on wavelet expansions
This paper is concerned with problems in the context of the theoretical
foundation of adaptive (wavelet) algorithms for the numerical treatment of
operator equations. It is well-known that the analysis of such schemes
naturally leads to function spaces of Besov type. But, especially when dealing
with equations on non-smooth manifolds, the definition of these spaces is not
straightforward. Nevertheless, motivated by applications, recently Besov-type
spaces on certain two-dimensional, patchwise
smooth surfaces were defined and employed successfully. In the present paper,
we extend this definition (based on wavelet expansions) to a quite general
class of -dimensional manifolds and investigate some analytical properties
(such as, e.g., embeddings and best -term approximation rates) of the
resulting quasi-Banach spaces. In particular, we prove that different prominent
constructions of biorthogonal wavelet systems on domains or manifolds
which admit a decomposition into smooth patches actually generate the
same Besov-type function spaces , provided that
their univariate ingredients possess a sufficiently large order of cancellation
and regularity (compared to the smoothness parameter of the space).
For this purpose, a theory of almost diagonal matrices on related sequence
spaces of Besov type is developed.
Keywords: Besov spaces, wavelets, localization, sequence spaces, adaptive
methods, non-linear approximation, manifolds, domain decomposition.Comment: 38 pages, 2 figure
Variational Approach in Wavelet Framework to Polynomial Approximations of Nonlinear Accelerator Problems
In this paper we present applications of methods from wavelet analysis to
polynomial approximations for a number of accelerator physics problems.
According to variational approach in the general case we have the solution as a
multiresolution (multiscales) expansion in the base of compactly supported
wavelet basis. We give extension of our results to the cases of periodic
orbital particle motion and arbitrary variable coefficients. Then we consider
more flexible variational method which is based on biorthogonal wavelet
approach. Also we consider different variational approach, which is applied to
each scale.Comment: LaTeX2e, aipproc.sty, 21 Page
Variational-Wavelet Approach to RMS Envelope Equations
We present applications of variational-wavelet approach to nonlinear
(rational) rms envelope equations. We have the solution as a multiresolution
(multiscales) expansion in the base of compactly supported wavelet basis. We
give extension of our results to the cases of periodic beam motion and
arbitrary variable coefficients. Also we consider more flexible variational
method which is based on biorthogonal wavelet approach.Comment: 21 pages, 8 figures, LaTeX2e, presented at Second ICFA Advanced
Accelerator Workshop, UCLA, November, 199
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