64 research outputs found
Calculation of the energy levels of Ge, Sn, Pb and their ions in the approximation
Energy levels of germanium, tin and lead together with their single, double
and triple ionized positive ions have been calculated using the
approximation suggested in the previous work (Dzuba, physics/0501032) (M=4 -
number of valence electrons). Initial Hartree-Fock calculations are done for
the quadruply ionized ions with all valence electrons removed. The core-valence
correlations are included beyond the second-order of the many-body perturbation
theory. Interaction between valence electrons is treated by means of the
configuration interaction technique. It is demonstrated that accurate treatment
of the core-valence correlations lead to systematic improvement of the accuracy
of calculations for all ions and neutral atoms.Comment: 7 pages, 3 figures, 3 tables; submitted to Phys. Rev.
Generalised fractional diffusion equations for subdiffusion on arbitrarily growing domains
Many physical phenomena occur on domains that grow in time. When the
timescales of the phenomena and domain growth are comparable, models must
include the dynamics of the domain. A widespread intrinsically slow transport
process is subdiffusion. Many models of subdiffusion include a history
dependence. This greatly confounds efforts to incorporate domain growth. Here
we derive the fractional partial differential equations that govern
subdiffusion on a growing domain, based on a Continuous Time Random Walk. This
requires the introduction of a new, comoving, fractional derivative.Comment: 12 pages, 1 figur
Precision isotope shift measurements in Ca using highly sensitive detection schemes
We demonstrate an efficient high-precision optical spectroscopy technique for
single trapped ions with non-closed transitions. In a double-shelving
technique, the absorption of a single photon is first amplified to several
phonons of a normal motional mode shared with a co-trapped cooling ion of a
different species, before being further amplified to thousands of fluorescence
photons emitted by the cooling ion using the standard electron shelving
technique. We employ this extension of the photon recoil spectroscopy technique
to perform the first high precision absolute frequency measurement of the
D P transition in Ca,
resulting in a transition frequency of kHz.
Furthermore, we determine the isotope shift of this transition and the
S P transition for Ca,
Ca and Ca ions relative to Ca with an
accuracy below 100 kHz. Improved field and mass shift constants of these
transitions as well as changes in mean square nuclear charge radii are
extracted from this high resolution data
An analytic approximation to the Diffusion Coefficient for the periodic Lorentz Gas
An approximate stochastic model for the topological dynamics of the periodic
triangular Lorentz gas is constructed. The model, together with an extremum
principle, is used to find a closed form approximation to the diffusion
coefficient as a function of the lattice spacing. This approximation is
superior to the popular Machta and Zwanzig result and agrees well with a range
of numerical estimates.Comment: 13 pages, 4 figure
Reaction-diffusion and reaction-subdiffusion equations on arbitrarily evolving domains
Reaction-diffusion equations are widely used as the governing evolution
equations for modeling many physical, chemical, and biological processes. Here
we derive reaction-diffusion equations to model transport with reactions on a
one-dimensional domain that is evolving. The model equations, which have been
derived from generalized continuous time random walks, can incorporate
complexities such as subdiffusive transport and inhomogeneous domain stretching
and shrinking. A method for constructing analytic expressions for short time
moments of the position of the particles is developed and moments calculated
from this approach are shown to compare favourably with results from random
walk simulations and numerical integration of the reaction transport equation.
The results show the important role played by the initial condition. In
particular, it strongly affects the time dependence of the moments in the short
time regime by introducing additional drift and diffusion terms. We also
discuss how our reaction transport equation could be applied to study the
spreading of a population on an evolving interface.Comment: 38 pages, 10 figure
Microstructural asymmetry of the corticospinal tracts predicts right-left differences in circle drawing skill in right-handed adolescents
Most humans show a strong preference to use their right hand, but strong preference for the right hand does not necessarily imply a strong rightâleft asymmetry in manual proficiency (i.e., dexterity). Here we tested the hypothesis that intra-individual asymmetry of manual proficiency would be reflected in microstructural differences between the right and left corticospinal tract (CST) in a cohort of 52 right-handed typically-developing adolescents (11â16Â years). Participants were asked to fluently draw superimposed circles with their right dominant and left non-dominant hand. Temporal regularity of circle drawing movements was assessed for each hand using a digitizing tablet. Although all participants were right-handed, there was substantial inter-individual variation regarding the relative right-hand advantage for fluent circle drawing. All subjects underwent whole-brain diffusion tensor imaging at 3 Tesla. The right and left CST were defined as regions-of-interest and mean fractional anisotropy (FA) and diffusivity values were calculated for right and left CST. On average, mean FA values were higher in the left CST relative to right CST. The degree of rightâleft FA asymmetry showed a linear relationship with rightâleft asymmetry in fluent circle drawing after correction for age and gender. The higher the mean FA values were in the left dominant CST relative to the right non-dominant CST, the stronger was the relative right-hand advantage for regular circle drawing. These findings show that rightâleft differences in manual proficiency are highly variable in right-handed adolescents and that this variation is associated with a right-left microstructural asymmetry of the CST
A New Option for a Search for Alpha Variation: Narrow Transitions with Enhanced Sensitivity
We consider several transitions between narrow lines that have an enhanced
sensitivity to a possible variation of the fine structure constant, alpha. This
enhancement may allow a search to be performed with an effective suppression of
the systematic sources of uncertainty that are unavoidable in conventional
high-resolution spectroscopic measurements. In the future this may provide the
strongest laboratory constraints on alpha variation
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