A general procedure for constructing action principles for continuum models via a generalization of Hamilton's principle of mechanics is described. Through the procedure, an action principle for a gyroviscous magnetohydrodynamics (MHD) model is constructed. The model is shown to agree with a reduced version of Braginskii's fluid equations. The construction reveals the origin of the gyromap, a device used to derive previous gyrofluid models. Also, a systematic reduction procedure is presented for obtaining the Hamiltonian structure in terms of the noncanonical Poisson bracket. The construction procedure yields a class of Casimir invariants, which are then used to variational principles for equilibrium equations with flow and gyroviscosity. The procedure for obtaining reduced fluid models with gyroviscosity is also described.

Surface-enhanced Raman optical activity (SEROA) is investigated theoretically for molecules near a metal nanoshell. For this purpose, induced molecular electric dipole, magnetic dipole, and electric quadrupole moments must all be included. The incident field and the induced multipole fields all scatter from the nanoshell, and the scattered waves can be calculated via extended Mie theory. It is straightforward in this framework to calculate the incident frequency dependence of SEROA intensities, i.e., SEROA excitation profiles. The differential Raman scattering is examined in detail for a simple chiroptical model that provides analytical forms for the relevant dynamical molecular response tensors. This allows a detailed investigation into circumstances that simultaneously provide strong enhancement of differential intensities and remain selective for molecules with chirality.

Abstract.In this paper, we analyze a mixed form of a time-dependent eddy current problem formulated in terms of the electric field E. We show that this formulation admits a well-posed saddle point structure when the constraints satisfied by the primary unknown in the dielectric material are handled by means of a Lagrange multiplier. We use Nédélec edge elements and standard nodal finite elements to define a semi-discrete Galerkin scheme. Furthermore, we introduce the corresponding backward-Euler fully-discrete formulation and prove error estimates.

Surface-enhanced Raman optical activity (SEROA) in molecules near a spherical metal nanoshell is examined for different experimental polarization schemes. This is accomplished within extended Mie theory, including both the nanoparticle surface plasmon modes and the radiating molecular multipole fields. Analytical simplification of the scattering expansion is accomplished through judicious use of the spherical harmonic addition theorem. Special attention is paid to the dependence of backscatter circular polarization difference signals on molecular direction from the spherical nanoparticle and to the conditions that ensure the differences occur only for molecules of chiral character. Dual circular polarization strategies are determined to have special advantages in these circumstances, and the corresponding excitation profiles for a simple chiroptical model are analyzed in detail to suggest preferred excitation wavelengths.

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Orthogonal compact-support Daubechies wavelets are employed as bases for both space and time variables in the solution of the time-dependent Schrodinger equation. Initial value conditions are enforced using special early-time wavelets analogous to edge wavelets used in boundary-value problems. It is shown that the quantum equations may be solved directly and accurately in the discrete wavelet representation, an important finding for the eventual goal of highly adaptive multiresolution Schrodinger equation solvers. While the temporal part of the basis is not sharp in either time or frequency, the Chebyshev method used for pure time-domain propagations is adapted to use in the mixed domain and is able to take advantage of Hamiltonian matrix sparseness. The orthogonal separation into different time scales is determined theoretically to persist throughout the evolution and is demonstrated numerically in a partially adaptive treatment of scattering from an asymmetric Eckart barrier.

A means of evaluating the action of Hamiltonian operators on functions expanded in orthogonal compact support wavelet bases is developed, avoiding the direct construction and storage of operator matrices that complicate extension to coupled multidimensional quantum applications. Application of a potential energy operator is accomplished by simple multiplication of the two sets of expansion coefficients without any convolution. The errors of this coefficient product approximation are quantified and lead to use of particular generalized coiflet bases, derived here, that maximize the number of moment conditions satisfied by the scaling function. This is at the expense of the number of vanishing moments of the wavelet function (approximation order), which appears to be a disadvantage but is shown surmountable. In particular, application of the kinetic energy operator, which is accomplished through the use of one-dimensional (1D) [or at most two-dimensional (2D)] differentiation filters, then degrades in accuracy if the standard choice is made. However, it is determined that use of high-order finite-difference filters yields strongly reduced absolute errors. Eigensolvers that ordinarily use only matrix-vector multiplications, such as the Lanczos algorithm, can then be used with this more efficient procedure. Applications are made to anharmonic vibrational problems: a 1D Morse oscillator, a 2D model of proton transfer, and three-dimensional vibrations of nitrosyl chloride on a global potential energy surface.