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91.
92.
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
93.
94.
S. Neukirch G.H.M. van der HeijdenJ.M.T. Thompson 《Journal of the mechanics and physics of solids》2002,50(6):1175-1191
We use three different approaches to describe the static spatial configurations of a twisted rod as well as its stability during rigid loading experiments. The first approach considers the rod as infinite in length and predicts an instability causing a jump to self-contact at a certain point of the experiment. Semi-finite corrections, taken into account as a second approach, reveal some possible experiments in which the configuration of a very long rod will be stable through out. Finally, in a third approach, we consider a rod of real finite length and we show that another type of instability may occur, leading to possible hysteresis behavior. As we go from infinite to finite length, we compare the different information given by the three approaches on the possible equilibrium configurations of the rod and their stability. These finite size effects studied here in a 1D elasticity problem could help us guess what are the stability features of other more complicated (2D elastic shells for example) problems for which only the infinite length approach is understood. 相似文献
95.
In an earlier paper on a malignant cell invasion model (Marchantet al., SIAM J. Appl. Math, 60, 2000) we introduced a novelform of discontinuous travelling wave solution. These solutionscould be studied easily by combining behaviour within a phaseplane with the RankineHugoniot shock conditions, whichdescribe properties (such as the ratio of the jump discontinuitiesto the speed of propagation) that solutions may possess. Theseresults were new for several reasons. The shock conditions relateto hyperbolic equations (which the model is) but were appliedin a travelling wave ordinary differential equation phase planeusing techniques that usually apply to parabolic reactiondiffusionsystems. In addition the solutions possess singular behaviournear several points in the phase plane but in spite of thisthere exists a robust and stable family of physically interestingsolutions. In this paper we discuss two previously studied models, oneof detonation theory and one of angiogenesis. We show that eachof these models also possesses a family of discontinuous travellingwave solutions which was not previously discovered. Of particularinterest is the solution which has a blunt interface at thefront of the invading profile. In all three models it is thissolution that is seen to stably evolve from physically relevantinitial data, and for physically relevant parameter values. This work confirms the robustness of these novel travellingwave solutions and their applicability to a wider range of mathematicalmodelling situations. 相似文献
96.
Apurba Bhattacharya Nitin C. Patel Michael Peddicord Luca Parlanti John A. Grosso 《Tetrahedron letters》2006,47(30):5341-5343
An efficient, one-pot, phase transfer N-amination technology was developed. The protocol utilizes chloramine, an inexpensive and safe electrophilic aminating agent potentially viable for commercial manufacturing. 相似文献
97.
John T. Herron 《国际化学动力学杂志》1987,19(2):129-142
The gas phase chemical kinetics of SF4, SF5, and S2F10 are reviewed with particular emphasis on relevance to the general problem of the dielectric breakdown of SF6. Specific reaction systems treated are SF4 + F2, SF5 + SF5, and the pyrolysis of S2F10. Computer modeling calculations were carried out to arrive at the best estimates of rate parameters. Based on the results of these calculations, sets of recommended rate parameters are provided. The major discrepancies and problems in establishing the kinetic data base are described. Thermochemical consequences of different model calculations are given. 相似文献
98.
John A. Ryan 《Discrete Applied Mathematics》2006,154(2):399-412
We consider irreducible Goppa codes over Fq of length qn defined by polynomials of degree r, where q is a prime power and n,r are arbitrary positive integers. We obtain an upper bound on the number of such codes. 相似文献
99.
100.
R. Eric Berson John S. Young Thomas R. Hanley 《Applied biochemistry and biotechnology》2006,130(1-3):612-620
Following detoxification of the liquid hydrolysate produced in a corn stover pretreatment process, inhibitor levels are seen
to increase with the re-addition of solids for the ensuing hydrolysis and fermentation processes. The solids that were separated
from the slurry before detoxification of the liquor contain approx 60% (w/w) moisture, and contamination occurs owing to the
diffusion of inhibitors from the moisture entrained in the porous structure of the corn stover solids into the bulk fluid.
This evidence suggests the need for additional separation and detoxification steps to purge residual inhibitors entrained
in the moisture in the solids. An overliming process to remove furans from the hydrolysate failed to reduce total organic
acids concentration, so acids were removed by treatment with an activated carbon powder. Smaller carbon doses proved more
efficient in removing organic acids in terms of grams of acid removed per gram of carbon powder. Sugar adsorption by the activated
carbon powder was minimal. 相似文献