54,773 research outputs found
Small-amplitude perturbations of shape for a nearly spherical bubble in an inviscid straining flow (steady shapes and oscillatory motion)
The method of domain perturbations is used to study the problem of a nearly spherical bubble in an inviscid, axisymmetric straining flow. Steady-state shapes and axisymmetric oscillatory motions are considered. The steady-state solutions suggest the existence of a limit point at a critical Weber number, beyond which no solution exists on the steady-state solution branch which includes the spherical equilibrium state in the absence of flow (e.g. the critical value of 1.73 is estimated from the third-order solution). In addition, the first-order steady-state shape exhibits a maximum radius at θ = 1/6π which clearly indicates the barrel-like shape that was found earlier via numerical finite-deformation theories for higher Weber numbers. The oscillatory motion of a nearly spherical bubble is considered in two different ways. First, a small perturbation to a spherical base state is studied with the ad hoc assumption that the steady-state shape is spherical for the complete Weber-number range of interest. This analysis shows that the frequency of oscillation decreases as Weber number increases, and that a spherical bubble shape is unstable if Weber number is larger than 4.62. Secondly, the correct steady-state shape up to O(W) is included to obtain a rigorous asymptotic formula for the frequency change at small Weber number. This asymptotic analysis also shows that the frequency decreases as Weber number increases; for example, in the case of the principal mode (n = 2), ω^2 = ω_0^0(1−0.31W), where ω_0 is the oscillation frequency of a bubble in a quiescent fluid
Bubble dynamics in time-periodic straining flows
The dynamics and breakup of a bubble in an axisymmetric, time-periodic straining flow has been investigated via analysis of an approximate dynamic model and also by time-dependent numerical solutions of the full fluid mechanics problem. The analyses reveal that in the neighbourhood of a stable steady solution, an O(ϵ1/3) time-dependent change of bubble shape can be obtained from an O(ε) resonant forcing. Furthermore, the probability of bubble breakup at subcritical Weber numbers can be maximized by choosing an optimal forcing frequency for a fixed forcing amplitude
Quasiparticle and Optical Properties of Rutile and Anatase TiO
Quasiparticle excitation energies and optical properties of TiO in the
rutile and anatase structures are calculated using many-body perturbation
theory methods. Calculations are performed for a frozen crystal lattice;
electron-phonon coupling is not explicitly considered. In the GW method,
several approximations are compared and it is found that inclusion of the full
frequency dependence as well as explicit treatment of the Ti semicore states
are essential for accurate calculation of the quasiparticle energy band gap.
The calculated quasiparticle energies are in good agreement with available
photoemission and inverse photoemission experiments. The results of the GW
calculations, together with the calculated static screened Coulomb interaction,
are utilized in the Bethe-Salpeter equation to calculate the dielectric
function for both the rutile and anatase structures. The
results are in good agreement with experimental observations, particularly the
onset of the main absorption features around 4 eV. For comparison to low
temperature optical absorption measurements that resolve individual excitonic
transitions in rutile, the low-lying discrete excitonic energy levels are
calculated with electronic screening only. The lowest energy exciton found in
the energy gap of rutile has a binding energy of 0.13 eV. In agreement with
experiment, it is not dipole allowed, but the calculated exciton energy exceeds
that measured in absorption experiments by about 0.22 eV and the scale of the
exciton binding energy is also too large. The quasiparticle energy alignment of
rutile is calculated for non-polar (110) surfaces. In the GW approximation, the
valence band maximum is 7.8 eV below the vacuum level, showing a small shift
from density functional theory results.Comment: Submitted to Physical Review
Neutrino Oscillations and Lepton Flavor Mixing
In view of the recent announcement on non-zero neutrino mass from
Super-Kamiokande experiment, it would be very timely to investigate all the
possible scenarios on masses and mixings of light neutrinos. Recently suggested
mass matrix texture for the quark CKM mixing, which can be originated from the
family permutation symmetry and its suitable breakings, is assumed for the
neutrino mass matrix and determined by the four combinations of solar,
atmospheric and LSND neutrino data and cosmological hot dark matter bound as
input constraints. The charged-lepton mass matrix is assumed to be diagonal so
that the neutrino mixing matrix can be identified directly as the lepton flavor
mixing matrix and no CP invariance violation originates from the leptonic
sector. The results favor hierarchical patterns for the neutrino masses, which
follow from the case when either solar-atmospheric data or solar-HDM
constraints are used.Comment: Latex, 9 page
Diffusive propagation of wave packets in a fluctuating periodic potential
We consider the evolution of a tight binding wave packet propagating in a
fluctuating periodic potential. If the fluctuations stem from a stationary
Markov process satisfying certain technical criteria, we show that the square
amplitude of the wave packet after diffusive rescaling converges to a
superposition of solutions of a heat equation.Comment: 13 pages (v2: added a paragraph on the history of the problem, added
some references, correct a few typos; v3 minor corrections, added keywords
and subject classes
Neutrino masses along with fermion mass hierarchy
Recently a new mechanism has been proposed to cure the problem of fermion
mass hierarchy in the Standard Model (SM) model. In this scenario, all SM
charged fermions other than top quark arise from higher dimensional operators
involving the SM Higgs field. This model also predicted some interesting
phenomenology of the Higgs boson. We generalize this model to accommodate
neutrino masses (Dirac & Majorana) and also obtain the mixing pattern in the
leptonic sector. To generate neutrino masses, we add extra three right handed
neutrinos in this model.Comment: 20 pages, the content on results and phenomenology have been
expanded, a new section on UV completion of the model has been added and also
some new references, this version has been accepted by Physical Review
Is the Number of Giant Arcs in LCDM Consistent With Observations?
We use high-resolution N-body simulations to study the galaxy-cluster
cross-sections and the abundance of giant arcs in the CDM model.
Clusters are selected from the simulations using the friends-of-friends method,
and their cross-sections for forming giant arcs are analyzed. The background
sources are assumed to follow a uniform ellipticity distribution from 0 to 0.5
and to have an area identical to a circular source with diameter 1\arcsec. We
find that the optical depth scales as the source redshift approximately as
\tau_{1''} = 2.25 \times 10^{-6}/[1+(\zs/3.14)^{-3.42}] (0.6<\zs<7). The
amplitude is about 50% higher for an effective source diameter of 0.5\arcsec.
The optimal lens redshift for giant arcs with the length-to-width ratio ()
larger than 10 increases from 0.3 for \zs=1, to 0.5 for \zs=2, and to
0.7-0.8 for \zs>3. The optical depth is sensitive to the source redshift, in
qualitative agreement with Wambsganss et al. (2004). However, our overall
optical depth appears to be only 10% to 70% of those from previous
studies. The differences can be mostly explained by different power spectrum
normalizations () used and different ways of determining the
ratio. Finite source size and ellipticity have modest effects on the optical
depth. We also found that the number of highly magnified (with magnification
) and ``undistorted'' images (with ) is comparable to the
number of giant arcs with and . We conclude that our
predicted rate of giant arcs may be lower than the observed rate, although the
precise `discrepancy' is still unclear due to uncertainties both in theory and
observations.Comment: Revised version after the referee's reports (32 pages,13figures). The
paper has been significantly revised with many additions. The new version
includes more detailed comparisons with previous studies, including the
effects of source size and ellipticity. New discussions about the redshift
distribution of lensing clusters and the width of giant arcs have been adde
A simple strategy for identifying a single complementing clone in a 96-well microtiter dish.
A simple strategy for identifying a single complementing clone in a 96-well microtiter dish
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