9,793 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
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
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
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
Numerical simulations on the motion of atoms travelling through a standing-wave light field
The motion of metastable helium atoms travelling through a standing light
wave is investigated with a semi-classical numerical model. The results of a
calculation including the velocity dependence of the dipole force are compared
with those of the commonly used approach, which assumes a conservative dipole
force. The comparison is made for two atom guiding regimes that can be used for
the production of nanostructure arrays; a low power regime, where the atoms are
focused in a standing wave by the dipole force, and a higher power regime, in
which the atoms channel along the potential minima of the light field. In the
low power regime the differences between the two models are negligible and both
models show that, for lithography purposes, pattern widths of 150 nm can be
achieved. In the high power channelling regime the conservative force model,
predicting 100 nm features, is shown to break down. The model that incorporates
velocity dependence, resulting in a structure size of 40 nm, remains valid, as
demonstrated by a comparison with quantum Monte-Carlo wavefunction
calculations.Comment: 9 pages, 4 figure
Somatisation and functional impairment in adolescents: longitudinal link with mothers' reactions
Adolescents' somatisation (i.e., the psychological tendency to experience and report multiple physical complaints for which no definite medical cause can be found; SOM) and functional impairment (i.e., all bothersome aftermath of somatisation; FI) were studied in relation to mothers' protection, encouraging/monitoring, and minimisation of physical functional complaints. Besides main effects, interaction effects with other child and parenting characteristics were examined. A total of 990 adolescents and their mothers filled out questionnaires when the adolescents were respectively 12-13 (T1) and 13-14 (T2) years old. At T1, there was a significant relation between mothers' higher amounts of minimisation and adolescents' higher levels of SOM. Further, the link between mothers' higher levels of T1 minimisation and adolescents' higher amounts of T1 FI was significant, but not for adolescents with high levels of depressive mood. Longitudinal analyses revealed that mothers' reactions did not significantly predict adolescents' SOM/FI, nor did adolescents' SOM/FI significantly predict mothers' reactions. Practical implications are discussed
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