5,841 research outputs found
Controlling Physical Systems with Symmetries
Symmetry properties of the evolution equation and the state to be controlled
are shown to determine the basic features of the linear control of unstable
orbits. In particular, the selection of control parameters and their minimal
number are determined by the irreducible representations of the symmetry group
of the linearization about the orbit to be controlled. We use the general
results to demonstrate the effect of symmetry on the control of two sample
physical systems: a coupled map lattice and a particle in a symmetric
potential.Comment: 6 page
The local electronic structure of alpha-Li3N
New theoretical and experimental investigation of the occupied and unoccupied
local electronic density of states (DOS) are reported for alpha-Li3N. Band
structure and density functional theory calculations confirm the absence of
covalent bonding character. However, real-space full-multiple-scattering
(RSFMS) calculations of the occupied local DOS finds less extreme nominal
valences than have previously been proposed. Nonresonant inelastic x-ray
scattering (NRIXS), RSFMS calculations, and calculations based on the
Bethe-Salpeter equation are used to characterize the unoccupied electronic
final states local to both the Li and N sites. There is good agreement between
experiment and theory. Throughout the Li 1s near-edge region, both experiment
and theory find strong similarities in the s- and p-type components of the
unoccupied local final density of states projected onto an orbital angular
momentum basis (l-DOS). An unexpected, significant correspondence exists
between the near-edge spectra for the Li 1s and N 1s initial states. We argue
that both spectra are sampling essentially the same final density of states due
to the combination of long core-hole lifetimes, long photoelectron lifetimes,
and the fact that orbital angular momentum is the same for all relevant initial
states. Such considerations may be generically applicable for low atomic number
compounds.Comment: 34 pages, 7 figures, 1 tabl
Change 1 to the History of the College of the Holy Cross Naval ROTC Unit
This document lists revisions made to the 2016 version of the History of the College of the Holy Cross Naval ROTC Unit. It is intended as a supplement for those who received print copies.
The revised version is available at http://crossworks.holycross.edu/nrotc75/1/
Change 2 to the History of the College of the Holy Cross Naval ROTC Unit
This document lists revisions made to the 2017 revision of the History of the College of the Holy Cross Naval ROTC Unit. It is intended as a supplement for those who received print copies.
The first printed version (2016) will need Change 1 and Change 2.; the second printed version (2017) will only need Change 2.
The revised version is available at http://crossworks.holycross.edu/nrotc75/1/
Square Patterns and Quasi-patterns in Weakly Damped Faraday Waves
Pattern formation in parametric surface waves is studied in the limit of weak
viscous dissipation. A set of quasi-potential equations (QPEs) is introduced
that admits a closed representation in terms of surface variables alone. A
multiscale expansion of the QPEs reveals the importance of triad resonant
interactions, and the saturating effect of the driving force leading to a
gradient amplitude equation. Minimization of the associated Lyapunov function
yields standing wave patterns of square symmetry for capillary waves, and
hexagonal patterns and a sequence of quasi-patterns for mixed capillary-gravity
waves. Numerical integration of the QPEs reveals a quasi-pattern of eight-fold
symmetry in the range of parameters predicted by the multiscale expansion.Comment: RevTeX, 11 pages, 8 figure
Exciton spectroscopy of hexagonal boron nitride using non-resonant x-ray Raman scattering
We report non-resonant x-ray Raman scattering (XRS) measurements from
hexagonal boron nitride for transferred momentum from 2 to 9
along directions both in and out of the basal plane. A
symmetry-based argument, together with real-space full multiple scattering
calculations of the projected density of states in the spherical harmonics
basis, reveals that a strong pre-edge feature is a dominantly -type
Frenkel exciton with no other \textit{s}-, \textit{p}-, or \textit{d}-
components. This conclusion is supported by a second, independent calculation
of the \textbf{q}-dependent XRS cross-section based on the Bethe-Salpeter
equation
PO-0690: Patient weight loss predicts worse overall survival for stage I lung cancer treated with SABR
Influence of the Dufour effect on convection in binary gas mixtures
Linear and nonlinear properties of convection in binary fluid layers heated
from below are investigated, in particular for gas parameters. A Galerkin
approximation for realistic boundary conditions that describes stationary and
oscillatory convection in the form of straight parallel rolls is used to
determine the influence of the Dufour effect on the bifurcation behaviour of
convective flow intensity, vertical heat current, and concentration mixing. The
Dufour--induced changes in the bifurcation topology and the existence regimes
of stationary and traveling wave convection are elucidated. To check the
validity of the Galerkin results we compare with finite--difference numerical
simulations of the full hydrodynamical field equations. Furthermore, we report
on the scaling behaviour of linear properties of the stationary instability.Comment: 14 pages and 10 figures as uuencoded Postscript file (using uufiles
Turing Instability in a Boundary-fed System
The formation of localized structures in the chlorine dioxide-idodine-malonic
acid (CDIMA) reaction-diffusion system is investigated numerically using a
realistic model of this system. We analyze the one-dimensional patterns formed
along the gradients imposed by boundary feeds, and study their linear stability
to symmetry-breaking perturbations (Turing instability) in the plane transverse
to these gradients. We establish that an often-invoked simple local linear
analysis which neglects longitudinal diffusion is inappropriate for predicting
the linear stability of these patterns. Using a fully nonuniform analysis, we
investigate the structure of the patterns formed along the gradients and their
stability to transverse Turing pattern formation as a function of the values of
two control parameters: the malonic acid feed concentration and the size of the
reactor in the dimension along the gradients. The results from this
investigation are compared with existing experiments.Comment: 41 pages, 18 figures, to be published in Physical Review
Orientation and solvatochromism of dyes in liquid crystals.
The orientation and solvatochromism of some dye molecules in a liquid crystal have been investigated. Interactions with the host and the structure of the dye molecule affect the macroscopic alignment of dichroic dye molecules in a liquid crystal: It was observed that some dye molecules show a large bathochromic shift of their absorption maxima in the liquid crystal host relative to the situation in isotropic solvents. It is suggested that this is due to the occurrence of a much weaker reaction field in the anisotropic, rigid host. These dye molecules show little or no apparent order in the anisotropic host despite the observation of a reduction in the electro optic switching time when the dye is present. The highest degree of macroscopic alignment was observed for a merocyanine compound, which showed the smallest solvatochromic shift in the liquid crystal host. These results are discussed in terms of the steric, dipolar and hydrogen bond interactions between the guest and the host
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