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41.
Many recent algorithmic approaches involve the construction of a differential equation model for computational purposes, typically
by introducing an artificial time variable. The actual computational model involves a discretization of the now time-dependent differential system, usually
employing forward Euler. The resulting dynamics of such an algorithm is then a discrete dynamics, and it is expected to be
“close enough” to the dynamics of the continuous system (which is typically easier to analyze) provided that small – hence
many – time steps, or iterations, are taken. Indeed, recent papers in inverse problems and image processing routinely report
results requiring thousands of iterations to converge. This makes one wonder if and how the computational modeling process
can be improved to better reflect the actual properties sought.
In this article we elaborate on several problem instances that illustrate the above observations. Algorithms may often lend
themselves to a dual interpretation, in terms of a simply discretized differential equation with artificial time and in terms
of a simple optimization algorithm; such a dual interpretation can be advantageous. We show how a broader computational modeling
approach may possibly lead to algorithms with improved efficiency.
AMS subject classification (2000) 65L05, 65M32, 65N21, 65N22, 65D18 相似文献
42.
An infinite row of periodically spaced, identical rigid circularcylinders is excited by an acoustic line source which is parallelto the generators of the cylinders. A method for calculatingthe scattered field accurately and efficiently is presented.When the cylinders are sufficiently close together, Rayleigh–Blochsurface waves that propagate energy to infinity along the arrayare excited. An expression is derived which enables the amplitudesof these surface waves to be computed without requiring thesolution to the full scattering problem. 相似文献
43.
T. Bernhard 《Surface science》2006,600(9):1877-1883
The structure and magnetism of thin epitaxial Fe layers grown on Cu(0 0 1) is investigated by grazing scattering of fast H and He atoms. Information on the atomic structure of the film and substrate surfaces is obtained by making use of ion beam triangulation with protons. The magnetic behavior is studied via the polarization of light emitted after capture of spin-polarized electrons into excited atomic terms during scattering of He atoms. For the formation of bcc(1 1 0)-like Fe films at higher coverages, we detect differences in structural and magnetic properties for room and low temperature growth. We suggest that the crystalline structure depends on the film morphology and that Cu impurities affect the magnetic properties. 相似文献
44.
N.-K. Lee T.A. Vilgis 《The European Physical Journal B - Condensed Matter and Complex Systems》2002,28(4):451-465
We study the elastic properties of single A/B random copolymer chains, with a specific sequence and use them as theoretical
model for so called HP proteins. HP proteins carry hydrophilic (P) and hydrophobic (H) monomers. We predict a rich structure
in the force-extension relations which can be attributed to the information in the sequence. The variational method is used
to probe local minima on the path of stretching and releasing for the chain molecules. At a given force, we find multiple
configurations which are separated by energy barriers. A collapsed globular configuration consists of several domains which
unravel cooperatively. Upon stretching, the unfolding path shows a stepwise pattern corresponding to the unfolding of each
domain. While releasing, several cores can be created simultaneously in the middle of the chain, resulting in a different
path of collapse. The long-range interactions and stiffness of the chain simplify the potential landscape given by the disorder
in sequence.
Received 5 March 2002 / Received in final form 16 May 2002 Published online 13 August 2002 相似文献
45.
Adhesion of zein to solid substrates has been studied using surface energy profiles as indices and by adhesion mapping using
atomic force microscopy (AFM). Different plasticizers like glycerol and sorbitol have been used to form mixed films with zein
and properties of these films are studied using surface energy profiles. Comparison of the results from the different mixed
samples with those from the pure zein films showed that force mapping could identify areas rich in protein. The adhesion maps
produced were deconvoluted from sample topography and contrasted with the data obtained from contact angle measurements. A
comparison of the two methods shows that the extent of contact angle hysteresis is indicative of both hydrophobicity of the
surface as well as the force of adhesion. Mechanical properties and microstructure of zein films prepared by casting from
solutions and using Langmuir-Blodgett film technique have been investigated. Pure zein seemed brittle and exhibited an essentially
linear relationship between stress and strain. Films with plasticizer were tougher than these films. In general, mixed films
showed better mechanical properties than pure films and had higher ultimate tensile strength and increased per cent elongation.
Further, the mixed films of zein showed a higher force of adhesion compared to the pure films. 相似文献
46.
Juan Gonzá lez-Meneses Luis Paris 《Transactions of the American Mathematical Society》2004,356(1):219-243
We show that Vassiliev invariants separate braids on a closed oriented surface, and we exhibit a universal Vassiliev invariant for these braids in terms of chord diagrams labeled by elements of the fundamental group of the surface.
47.
A mathematical model of laser beam treatment of double layer alloys (Ni/Fe, Al/Fe and Cr/Fe systems) describing the effect of laser beam on different physical and geometrical parameters of coated layer system has been adapted. The numerical solutions of the non-homogeneous heat-transport differential equation could estimate the temperature of the treated region.The suggested model allows investigation of the temperature distribution as a function of treated surface and laser parameters. The physical parameters of the treated materials were taken as functions of temperature due to the change in the temperature of the treated double layer materials. 相似文献
48.
An m‐covering of a graph G is a spanning subgraph of G with maximum degree at most m. In this paper, we shall show that every 3‐connected graph on a surface with Euler genus k ≥ 2 with sufficiently large representativity has a 2‐connected 7‐covering with at most 6k ? 12 vertices of degree 7. We also construct, for every surface F2 with Euler genus k ≥ 2, a 3‐connected graph G on F2 with arbitrarily large representativity each of whose 2‐connected 7‐coverings contains at least 6k ? 12 vertices of degree 7. © 2003 Wiley Periodicals, Inc. J Graph Theory 43: 26–36, 2003 相似文献
49.
Andrzej Dabrowski Erich Robens Peter Klobes Klaus Meyer Przemyslaw Podkocielny 《Particle & Particle Systems Characterization》2003,20(5):311-322
Since a comprehensive survey published in 1999 [1] much work was done in standardizing measuring methods to characterize the surface geometry of dispersed and/or porous solids and to certify reference materials. The present paper is an extension of a short communication [2]. It gives a survey on existing standards and reports on new drafts and proposals. 相似文献
50.
Maria G. Semenova Larisa E. Belyakova Anna S. Antipova Yu. N. Polikarpov Lida Klouda Anna Markovic Michael M. Il'in 《Colloids and surfaces. B, Biointerfaces》2003,31(1-4):47-54
We report on the effect of commercially important polysaccharides (maltodextrins with variable dextrose equivalent (Paselli SA-2, MD-6 and MD-10) on the surface activity at the air–water interface of small-molecule surfactants (sms), possessing different hydrophobic–lipophilic balance ((SSL (Na+), the main component is a sodium salt of stearol–lactoyl lactic acid, and PGE (080), polyglycerol ester of C18 fatty acid), and widely used in food products. A marked change of the surface activity of sms was found in the presence of maltodextrins by tensiometry. The combined data of laser multiangle light scattering and mixing calorimetry have suggested that this result is governed by specific complex formation between maltodextrins and sms in aqueous medium. Measurements have been made of the molar mass, the second virial coefficient and the enthalpy of intermolecular interactions in aqueous solutions. The implication of a degree of polymerization of maltodextrins in this phenomenon was shown. The interrelation between the molecular parameters of the formed complexes and their surface activity at the air–water interface has been revealed and discussed. 相似文献