3,240 research outputs found
Algebraic treatment of the confluent Natanzon potentials
Using the so(2,1) Lie algebra and the Baker, Campbell and Hausdorff formulas,
the Green's function for the class of the confluent Natanzon potentials is
constructed straightforwardly. The bound-state energy spectrum is then
determined. Eventually, the three-dimensional harmonic potential, the
three-dimensional Coulomb potential and the Morse potential may all be
considered as particular cases.Comment: 9 page
Probing ferroelectricity in highly conducting materials through their elastic response: persistence of ferroelectricity in metallic BaTiO3-d
The question whether ferroelectricity (FE) may coexist with a metallic or
highly conducting state, or rather it must be suppressed by the screening from
the free charges, is the focus of a rapidly increasing number of theoretical
studies and is finally receiving positive experimental responses. The issue is
closely related to the thermoelectric and multiferroic (also magnetic)
applications of FE materials, where the electrical conductivity is required or
spurious. In these circumstances, the traditional methods for probing
ferroelectricity are hampered or made totally ineffective by the free charges,
which screen the polar response to an external electric field. This fact may
explain why more than 40 years passed between the first proposals of FE metals
and the present experimental and theoretical activity. The measurement of the
elastic moduli, Young's modulus in the present case, versus temperature is an
effective method for studying the influence of doping on a FE transition
because the elastic properties are unaffected by electrical conductivity. In
this manner, it is shown that the FE transitions of BaTiO3-d are not suppressed
by electron doping through O vacancies; only the onset temperatures are
depressed, but the magnitudes of the softenings, and hence of the piezoelectric
activity, are initially even increased
Quantitative analysis of the dripping and jetting regimes in co-flowing capillary jets
We study a liquid jet that breaks up into drops in an external co-flowing
liquid inside a confining microfluidic geometry. The jet breakup can occur
right after the nozzle in a phenomenon named dripping or through the generation
of a liquid jet that breaks up a long distance from the nozzle, which is called
jetting. Traditionally, these two regimes have been considered to reflect the
existence of two kinds of spatiotemporal instabilities of a fluid jet, the
dripping regime corresponding to an absolutely unstable jet and the jetting
regime to a convectively unstable jet. Here, we present quantitative
measurements of the dripping and jetting regimes, both in an unforced and a
forced state, and compare these measurements with recent theoretical studies of
spatiotemporal instability of a confined liquid jet in a co-flowing liquid. In
the unforced state, the frequency of oscillation and breakup of the liquid jet
is measured and compared to the theoretical predictions. The dominant frequency
of the jet oscillations as a function of the inner flow rate agrees
qualitatively with the theoretical predictions in the jetting regime but not in
the dripping regime. In the forced state, achieved with periodic laser heating,
the dripping regime is found to be insensitive to the perturbation and the
frequency of drop formation remains unaltered. The jetting regime, on the
contrary, amplifies the externally imposed frequency, which translates in the
formation of drops at the frequency imposed by the external forcing. In
conclusion, the dripping and jetting regimes are found to exhibit the main
features of absolutely and convectively unstable flows respectively, but the
frequency selection in the dripping regime is not ruled by the absolute
frequency predicted by the stability analysis.Comment: 10 pages, 12 figures, to appear in Physics of Fluid
Homogeneous geodesics of non-unimodular Lorentzian Lie groups and naturally reductive Lorentzian spaces in dimension three
We determine, for all three-dimensional non-unimodular Lie groups equipped
with a Lorentzian metric, the set of homogeneous geodesics through a point.
Together with the results of [C] and [CM2], this leads to the full
classification of three-dimensional Lorentzian g.o. spaces and naturally
reductive spaces
Phase transitions and phase diagram of the ferroelectric perovskite NBT-BT by anelastic and dielectric measurements
The complex elastic compliance and dielectric susceptibility of
(Na_{0.5}Bi_{0.5})_{1-x}Ba_{x}TiO_{3} (NBT-BT) have been measured in the
composition range between pure NBT and the morphotropic phase boundary
included, 0 <= x <= 0.08. The compliance of NBT presents sharp peaks at the
rhombohedral/tetragonal and tetragonal/cubic transitions, allowing the
determination of the tetragonal region of the phase diagram, up to now
impossible due to the strong lattice disorder and small distortions and
polarizations involved. In spite of ample evidence of disorder and structural
heterogeneity, the R-T transition remains sharp up to x = 0.06, whereas the T-C
transition merges into the diffuse and relaxor-like transition associated with
broad maxima of the dielectric and elastic susceptibilities. An attempt is made
at relating the different features in the anelastic and dielectric curves to
different modes of octahedral rotations and polar cation shifts. The
possibility is also considered that the cation displacements locally have
monoclinic symmetry, as for PZT near the morphotropic phase boundary.Comment: 11 pages, 9 figures, submitted to Phys. Rev.
Identifying short motifs by means of extreme value analysis
The problem of detecting a binding site -- a substring of DNA where
transcription factors attach -- on a long DNA sequence requires the recognition
of a small pattern in a large background. For short binding sites, the matching
probability can display large fluctuations from one putative binding site to
another. Here we use a self-consistent statistical procedure that accounts
correctly for the large deviations of the matching probability to predict the
location of short binding sites. We apply it in two distinct situations: (a)
the detection of the binding sites for three specific transcription factors on
a set of 134 estrogen-regulated genes; (b) the identification, in a set of 138
possible transcription factors, of the ones binding a specific set of nine
genes. In both instances, experimental findings are reproduced (when available)
and the number of false positives is significantly reduced with respect to the
other methods commonly employed.Comment: 6 pages, 5 figure
A mutate-and-map protocol for inferring base pairs in structured RNA
Chemical mapping is a widespread technique for structural analysis of nucleic
acids in which a molecule's reactivity to different probes is quantified at
single-nucleotide resolution and used to constrain structural modeling. This
experimental framework has been extensively revisited in the past decade with
new strategies for high-throughput read-outs, chemical modification, and rapid
data analysis. Recently, we have coupled the technique to high-throughput
mutagenesis. Point mutations of a base-paired nucleotide can lead to exposure
of not only that nucleotide but also its interaction partner. Carrying out the
mutation and mapping for the entire system gives an experimental approximation
of the molecules contact map. Here, we give our in-house protocol for this
mutate-and-map strategy, based on 96-well capillary electrophoresis, and we
provide practical tips on interpreting the data to infer nucleic acid
structure.Comment: 22 pages, 5 figure
A Guide to Localized Frames and Applications to Galerkin-like Representations of Operators
This chapter offers a detailed survey on intrinsically localized frames and
the corresponding matrix representation of operators. We re-investigate the
properties of localized frames and the associated Banach spaces in full detail.
We investigate the representation of operators using localized frames in a
Galerkin-type scheme. We show how the boundedness and the invertibility of
matrices and operators are linked and give some sufficient and necessary
conditions for the boundedness of operators between the associated Banach
spaces.Comment: 32 page
Satellite potentials for hypergeometric Natanzon potentials
As a result of the so(2,1) of the hypergeometric Natanzon potential a set of
potentials related to the given one is determined. The set arises as a result
of the action of the so(2,1) generators.Comment: 9 page
Linear perturbations of the Wigner transform and the Weyl quantization
We study a class of quadratic time-frequency representations that, roughly
speaking, are obtained by linear perturbations of the Wigner transform. They
satisfy Moyal's formula by default and share many other properties with the
Wigner transform, but in general they do not belong to Cohen's class. We
provide a characterization of the intersection of the two classes. To any such
time-frequency representation, we associate a pseudodifferential calculus. We
investigate the related quantization procedure, study the properties of the
pseudodifferential operators, and compare the formalism with that of the Weyl
calculus.Comment: 38 pages. Contributed chapter for volume on the occasion of Luigi
Rodino's 70th birthda
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