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Model Example (model + example)

Distribution by Scientific Domains

Chemistry	60%

Selected Abstracts

Quantitative structure retrieval using scanning transmission electron microscopy

ACTA CRYSTALLOGRAPHICA SECTION A, Issue 4 2005
S. D. Findlay
A method is described that reconstructs the projected object potential using data recorded in the coherent imaging mode of a scanning transmission electron microscope. The technique is applicable in the presence of multiple scattering. It is not required that the thickness is known. Model examples exploring the nature of the data set required, the stability of the algorithm and the limitations on resolution are provided. [source]

Combination of Jacobi,Davidson and conjugate gradients for the partial symmetric eigenproblem

NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS, Issue 1 2002
Y. Notay
Abstract To compute the smallest eigenvalues and associated eigenvectors of a real symmetric matrix, we consider the Jacobi,Davidson method with inner preconditioned conjugate gradient iterations for the arising linear systems. We show that the coefficient matrix of these systems is indeed positive definite with the smallest eigenvalue bounded away from zero. We also establish a relation between the residual norm reduction in these inner linear systems and the convergence of the outer process towards the desired eigenpair. From a theoretical point of view, this allows to prove the optimality of the method, in the sense that solving the eigenproblem implies only a moderate overhead compared with solving a linear system. From a practical point of view, this allows to set up a stopping strategy for the inner iterations that minimizes this overhead by exiting precisely at the moment where further progress would be useless with respect to the convergence of the outer process. These results are numerically illustrated on some model example. Direct comparison with some other eigensolvers is also provided. Copyright © 2001 John Wiley & Sons, Ltd. [source]

Maleimide-Modified Phosphonium Ionic Liquids: A Template Towards (Multi)Task-Specific Ionic Liquids

CHEMISTRY - A EUROPEAN JOURNAL, Issue 30 2010
Jocelyn
Abstract The synthesis and characterization of several compounds representing a new class of multitask-specific phosphonium ionic liquids that contain a maleimide functionality is reported. The maleimide moiety of the ionic liquid (IL) is shown to undergo Michael-type additions with substrates containing either a thiol or amine moiety, thus, serving as a template to introduce wide structural diversity into the IL. Multitask-specific ILs are accessible by reaction of the maleimide with Michael donors that are capable of serving some function. As a model example to illustrate this concept, a redox active ferrocenyl thiol was incorporated and examined by cyclic voltammetry. Because the maleimide moiety is highly reactive to additions, the task-specific ionic liquids (TSILs) are prepared as the furan-protected Diels,Alder maleimide. The maleimide moiety can then be liberated when required by simple heating. [source]

An arbitrary Lagrangian,Eulerian finite element method for finite strain plasticity

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 4 2003
Francisco Armero
Abstract This paper presents a new arbitrary Lagrangian,Eulerian (ALE) finite element formulation for finite strain plasticity in non-linear solid mechanics. We consider the models of finite strain plasticity defined by the multiplicative decomposition of the deformation gradient in an elastic and a plastic part (F = FeFp), with the stresses given by a hyperelastic relation. In contrast with more classical ALE approaches based on plastic models of the hypoelastic type, the ALE formulation presented herein considers the direct interpolation of the motion of the material with respect to the reference mesh together with the motion of the spatial mesh with respect to this same reference mesh. This aspect is shown to be crucial for a simple treatment of the advection of the plastic internal variables and dynamic variables. In fact, this advection is carried out exactly through a particle tracking in the reference mesh, a calculation that can be accomplished very efficiently with the use of the connectivity graph of the fixed reference mesh. A staggered scheme defined by three steps (the smoothing, the advection and the Lagrangian steps) leads to an efficient method for the solution of the resulting equations. We present several representative numerical simulations that illustrate the performance of the newly proposed methods. Both quasi-static and dynamic conditions are considered in these model examples. Copyright © 2003 John Wiley & Sons, Ltd. [source]

Comparison of the numerical stability of methods for anharmonic calculations of vibrational molecular energies

JOURNAL OF COMPUTATIONAL CHEMISTRY, Issue 10 2007
Petr Dan
Abstract On model examples, we compare the performance of the vibrational self-consistent field, variational, and four perturbational schemes used for computations of vibrational energies of semi-rigid molecules, with emphasis on the numerical stability. Although the accuracy of the energies is primarily dependent on the quality of the potential energy surface, approximate approaches to the anharmonic vibrational problem often do not converge to the same results due to the approximations involved. For furan, the sensitivity to variations of the anharmonic potential was systematically investigated by adding random noise to the cubic and quartic constants. The self-consistent field methods proved to be the most resistant to the potential variations. The second order perturbational techniques are sensitive to random degeneracies and provided the least stable results. However, their stability could be significantly improved by a simple generalization of the perturbational formula. The variational configuration interaction is practically limited by the size of the matrix that can be diagonalized for larger molecules; however, relatively fewer states need to be involved than for smaller ones, in favor of the computing. © 2007 Wiley Periodicals, Inc. J Comput Chem, 2007 [source]