11,914 research outputs found
Compact two-electron wave function for bond dissociation and Van der Waals interactions: A natural amplitude assessment
Electron correlations in molecules can be divided in short range dynamical
correlations, long range Van der Waals type interactions and near degeneracy
static correlations. In this work we analyze for a one-dimensional model of a
two-electron system how these three types of correlations can be incorporated
in a simple wave function of restricted functional form consisting of an
orbital product multiplied by a single correlation function
depending on the interelectronic distance . Since the three types of
correlations mentioned lead to different signatures in terms of the natural
orbital (NO) amplitudes in two-electron systems we make an analysis of the wave
function in terms of the NO amplitudes for a model system of a diatomic
molecule. In our numerical implementation we fully optimize the orbitals and
the correlation function on a spatial grid without restrictions on their
functional form. Due to this particular form of the wave function, we can prove
that none of the amplitudes vanishes and moreover that it displays a distinct
sign pattern and a series of avoided crossings as a function of the bond
distance in agreement with the exact solution. This shows that the wave
function Ansatz correctly incorporates the long range Van der Waals
interactions. We further show that the approximate wave function gives an
excellent binding curve and is able to describe static correlations. We show
that in order to do this the correlation function needs to diverge
for large at large internuclear distances while for shorter bond
distances it increases as a function of to a maximum value after which
it decays exponentially. We further give a physical interpretation of this
behavior.Comment: 16 pages, 13 figure
Tumbling of a rigid rod in a shear flow
The tumbling of a rigid rod in a shear flow is analyzed in the high viscosity
limit. Following Burgers, the Master Equation is derived for the probability
distribution of the orientation of the rod. The equation contains one
dimensionless number, the Weissenberg number, which is the ratio of the shear
rate and the orientational diffusion constant. The equation is solved for the
stationary state distribution for arbitrary Weissenberg numbers, in particular
for the limit of high Weissenberg numbers. The stationary state gives an
interesting flow pattern for the orientation of the rod, showing the interplay
between flow due to the driving shear force and diffusion due to the random
thermal forces of the fluid. The average tumbling time and tumbling frequency
are calculated as a function of the Weissenberg number. A simple cross-over
function is proposed which covers the whole regime from small to large
Weissenberg numbers.Comment: 22 pages, 9 figure
Free energies in the presence of electric and magnetic fields
We discuss different free energies for materials in static electric and
magnetic fields. We explain what the corresponding Hamiltonians are, and
describe which choice gives rise to which result for the free energy change,
dF, in the thermodynamic identity. We also discuss which Hamiltonian is the
most appropriate for calculations using statistical mechanics, as well as the
relationship between the various free energies and the "Landau function", which
has to be minimized to determine the equilibrium polarization or magnetization,
and is central to Landau's theory of second order phase transitions
Many-body Green's function theory for electron-phonon interactions: ground state properties of the Holstein dimer
We study ground-state properties of a two-site, two-electron Holstein model
describing two molecules coupled indirectly via electron-phonon interaction by
using both exact diagonalization and self-consistent diagrammatic many-body
perturbation theory. The Hartree and self-consistent Born approximations used
in the present work are studied at different levels of self-consistency. The
governing equations are shown to exhibit multiple solutions when the
electron-phonon interaction is sufficiently strong whereas at smaller
interactions only a single solution is found. The additional solutions at
larger electron-phonon couplings correspond to symmetry-broken states with
inhomogeneous electron densities. A comparison to exact results indicates that
this symmetry breaking is strongly correlated with the formation of a bipolaron
state in which the two electrons prefer to reside on the same molecule. The
results further show that the Hartree and partially self-consistent Born
solutions obtained by enforcing symmetry do not compare well with exact
energetics, while the fully self-consistent Born approximation improves the
qualitative and quantitative agreement with exact results in the same symmetric
case. This together with a presented natural occupation number analysis
supports the conclusion that the fully self-consistent approximation describes
partially the bipolaron crossover. These results contribute to better
understanding how these approximations cope with the strong localizing effect
of the electron-phonon interaction.Comment: 9 figures, corrected typo
Strongly coupled modes in a weakly driven micromechanical resonator
We demonstrate strong coupling between the flexural vibration modes of a
clamped-clamped micromechanical resonator vibrating at low amplitudes. This
coupling enables the direct measurement of the frequency response via
amplitude- and phase modulation schemes using the fundamental mode as a
mechanical detector. In the linear regime, a frequency shift of
is observed for a mode with a line width of
in vacuum. The measured response is well-described by the
analytical model based on the Euler-Bernoulli beam including tension.
Calculations predict an upper limit for the room-temperature Q-factor of
for our top-down fabricated micromechanical beam
resonators.Comment: 9 pages, 2 figure
The photochemistry and photophysics of a series of alpha octa(alkyl-substituted) silicon, zinc and palladium phthalocyanines
Photophysical and photochemical measurements have been made on a series of novel alpha octa(alkyl-substituted) silicon, zinc and palladium phthalocyanines for which the synthesis is outlined. Fluorescence quantum yields and lifetimes, triplet quantum yields and lifetimes and singlet delta oxygen quantum yields were measured in 1% v/v pyridine in toluene. The effects of varying central atom and addition of alkyl substituents relative to unsubstituted parent molecules, zinc phthalocyanine (ZnPc) and silicon phthalocyanine (SiPc), are discussed. All phthalocyanines studied exhibit absorption and emission maxima in the region of 680–750 nm with molar absorptivity of the Q-band 105 M−1 cm−1. The series of compounds also exhibited triplet quantum yields of 0.65–0.95 and singlet oxygen quantum yields of 0.49–0.93
Intermittent nulls in PSR B0818-13, and the subpulse-drift alias mode
We show that all long nulls in PSR B0818-13 are trains of rapidly alternating
nulls and pulses (each shorter than one pulse period). Sometimes only the nulls
coincide with our pulse window, resulting in one of the apparently long nulls
seen occasionally. We show these are seen as often as expected if during such a
train the probability for nulls is 1.2 times less than for pulses.
During nulls, the subpulse drift-speed appears to increase. We assume that
the carousel of sparks that possibly underlies the subpulses actually slows
down, as it does in similar pulsars like PSR B0809+74, and conclude that the
subpulse-drift in this pulsar must be aliased. The carousel must then rotate in
30 seconds or less, making it the fastest found to date.Comment: Accepted for A&A. 7 pages with low-resolution images; high-resolution
versions are available at
http://www.astro.uu.nl/~jleeuwen/preprints/0818-nulls
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Measuring the impact of observations on the predictability of the Kuroshio Extension in a shallow-water model
In this paper sequential importance sampling is used to assess the impact of observations on a ensemble prediction for the decadal path transitions of the Kuroshio Extension (KE). This particle filtering approach gives access to the probability density of the state vector, which allows us to determine the predictive power — an entropy based measure — of the ensemble prediction. The proposed set-up makes use of an ensemble that, at each time, samples the climatological probability distribution. Then, in a post-processing step, the impact of different sets of observations is measured by the increase in predictive power of the ensemble over the climatological signal during one-year. The method is applied in an identical-twin
experiment for the Kuroshio Extension using a reduced-gravity shallow water model. We investigate the impact of assimilating velocity observations from different locations during the elongated and the contracted meandering state of the KE. Optimal observations location correspond to regions with strong potential vorticity gradients. For the elongated state the optimal location is in the first meander of the KE. During the contracted state of the KE it is located south of Japan, where the Kuroshio separates from the coast
Architectural design-by-features
Design tasks, in particular architectural design tasks, have been found hard to support by means of computers. The main reason for this is that design is a problem solving process, which requires a dynamic way of handling information involved in the design process. The research presented in this paper focuses on this aspect of CAAD: the support of design tasks with dynamic, flexible information modelling techniques. The basic concepts for the developed approach is taken from the field of Feature-based modelling. We briefly review these concepts and then interpret and transport them to the context of architectural design. In defining types of Features, a distinction is made between domain-specific Features and generic Features for which we propose a classification. A framework for the definition and modelling of Features is discussed as well as a prototype Feature-based Modelling Shell based on this framework
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