5,452 research outputs found
Gradient Schemes for Linear and Non-linear Elasticity Equations
The Gradient Scheme framework provides a unified analysis setting for many
different families of numerical methods for diffusion equations. We show in
this paper that the Gradient Scheme framework can be adapted to elasticity
equations, and provides error estimates for linear elasticity and convergence
results for non-linear elasticity. We also establish that several classical and
modern numerical methods for elasticity are embedded in the Gradient Scheme
framework, which allows us to obtain convergence results for these methods in
cases where the solution does not satisfy the full -regularity or for
non-linear models
Application of projection algorithms to differential equations: boundary value problems
The Douglas-Rachford method has been employed successfully to solve many
kinds of non-convex feasibility problems. In particular, recent research has
shown surprising stability for the method when it is applied to finding the
intersections of hypersurfaces. Motivated by these discoveries, we reformulate
a second order boundary valued problem (BVP) as a feasibility problem where the
sets are hypersurfaces. We show that such a problem may always be reformulated
as a feasibility problem on no more than three sets and is well-suited to
parallelization. We explore the stability of the method by applying it to
several examples of BVPs, including cases where the traditional Newton's method
fails
Calculated Vibrational Properties of Ubisemiquinones
Density functional theory has been used to calculate harmonic normal mode vibrational frequencies for unlabeled and isotopelabeled ubisemiquinones in both the gas phase and in several solvents. It is shown that four methoxy group conformations are likely to be present in solution at room temperature. Boltzmann weighted infrared and Raman spectra for the four conformers were calculated, and composite spectra that are the sum of the Boltzmann weighted spectra were produced. These composite spectra were compared to experimental FTIR and resonance Raman spectra, and it is shown that the calculated band frequencies, relative band intensities, and 13C and 18O isotope-induced band shifts are in excellent agreement with experiment. The calculations show that the C=O and C=C modes of ubisemiquinone strongly mix with methoxy methyl CH bending vibrations, and that the degree of mixing is altered upon isotope labeling, resulting in complicated changes in mode frequencies, intensities, and composition upon isotope labeling. Upon consideration of the calculated potential energy distributions of the normal modes of ubisemiquinone, and how they change upon isotope labeling, an explanation of some puzzling features in previously published Raman spectra is provided
Calculated Vibrational Properties of Ubisemiquinones
Density functional theory has been used to calculate harmonic normal mode vibrational frequencies for unlabeled and isotopelabeled ubisemiquinones in both the gas phase and in several solvents. It is shown that four methoxy group conformations are likely to be present in solution at room temperature. Boltzmann weighted infrared and Raman spectra for the four conformers were calculated, and composite spectra that are the sum of the Boltzmann weighted spectra were produced. These composite spectra were compared to experimental FTIR and resonance Raman spectra, and it is shown that the calculated band frequencies, relative band intensities, and 13C and 18O isotope-induced band shifts are in excellent agreement with experiment. The calculations show that the C=O and C=C modes of ubisemiquinone strongly mix with methoxy methyl CH bending vibrations, and that the degree of mixing is altered upon isotope labeling, resulting in complicated changes in mode frequencies, intensities, and composition upon isotope labeling. Upon consideration of the calculated potential energy distributions of the normal modes of ubisemiquinone, and how they change upon isotope labeling, an explanation of some puzzling features in previously published Raman spectra is provided
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