2,420 research outputs found
Bivariate spline interpolation with optimal approximation order
Let be a triangulation of some polygonal domain f c R2 and let S9 (A) denote the space of all bivariate polynomial splines of smoothness r and degree q with respect to A. We develop the first Hermite-type interpolation scheme for S9 (A), q >_ 3r + 2, whose approximation error is bounded above by Kh4+i, where h is the maximal diameter of the triangles in A, and the constant K only depends on the smallest angle of the triangulation and is independent of near-degenerate edges and nearsingular vertices. Moreover, the fundamental functions of our scheme are minimally supported and form a locally linearly independent basis for a superspline subspace of Sr, (A). This shows that the optimal approximation order can be achieved by using minimally supported splines. Our method of proof is completely different from the quasi-interpolation techniques for the study of the approximation power of bivariate splines developed in [71 and [181
Order statistics and heavy-tail distributions for planetary perturbations on Oort cloud comets
This paper tackles important aspects of comets dynamics from a statistical
point of view. Existing methodology uses numerical integration for computing
planetary perturbations for simulating such dynamics. This operation is highly
computational. It is reasonable to wonder whenever statistical simulation of
the perturbations can be much more easy to handle. The first step for answering
such a question is to provide a statistical study of these perturbations in
order to catch their main features. The statistical tools used are order
statistics and heavy tail distributions. The study carried out indicated a
general pattern exhibited by the perturbations around the orbits of the
important planet. These characteristics were validated through statistical
testing and a theoretical study based on Opik theory.Comment: 9 pages, 12 figures, submitted for publication in Astronomy and
Astrophysic
Quadrupole transitions near interface: general theory and application to atom inside a planar cavity
Quadrupole radiation of an atom in an arbitrary environment is investigated
within classical as well as quantum electrodynamical approaches. Analytical
expressions for decay rates are obtained in terms of Green function of Maxwell
equations. The equivalence of both approaches is shown. General expressions are
applied to analyze the quadrupole decay rate of an atom placed between two half
spaces with arbitrary dielectric constant. It is shown that in the case when
the atom is close to the surface, the total decay rate is inversely
proportional to the fifth power of distance between an atom and a plane
interface.Comment: 18 pages, 7 figure
Calculation of the energy spectrum of a two-electron spherical quantum dot
We study the energy spectrum of the two-electron spherical parabolic quantum
dot using the exact Schroedinger, the Hartree-Fock, and the Kohn-Sham
equations. The results obtained by applying the shifted-1/N method are compared
with those obtained by using an accurate numerical technique, showing that the
relative error is reasonably small, although the first method consistently
underestimates the correct values. The approximate ground-state Hartree-Fock
and local-density Kohn-Sham energies, estimated using the shifted-1/N method,
are compared with accurate numerical self-consistent solutions. We make some
perturbative analyses of the exact energy in terms of the confinement strength,
and we propose some interpolation formulae. Similar analysis is made for both
mean-field approximations and interpolation formulae are also proposed for
these exchange-only ground-state cases.Comment: 18 pages, LaTeX, 2 figures-ep
Proton Wires in an Electric Field: the Impact of Grotthuss Mechanism on Charge Translocation
We present the results of the modeling of proton translocation in finite
H-bonded chains in the framework of two-stage proton transport model. We
explore the influence of reorientation motion of protons, as well as the effect
of electric field and proton correlations on system dynamics. An increase of
the reorientation energy results in the transition of proton charge from the
surrounding to the inner water molecules in the chain. Proton migration along
the chain in an external electric field has a step-like character, proceeding
with the occurrence of electric field threshold-type effects and drastic
redistribution of proton charge. Electric field applied to correlated chains
induces first a formation of ordered dipole structures for lower field
strength, and than, with a further field strength increase, a stabilization of
states with Bjerrum D-defects. We analyze the main factors responsible for the
formation/annihilation of Bjerrum defects showing the strong influence of the
complex interplay between reorientation energy, electric field and temperature
in the dynamics of proton wire.Comment: 28 pages, 9 figure
Solitons in Yakushevich-like models of DNA dynamics with improved intrapair potential
The Yakushevich (Y) model provides a very simple pictures of DNA torsion
dynamics, yet yields remarkably correct predictions on certain physical
characteristics of the dynamics. In the standard Y model, the interaction
between bases of a pair is modelled by a harmonic potential, which becomes
anharmonic when described in terms of the rotation angles; here we substitute
to this different types of improved potentials, providing a more physical
description of the H-bond mediated interactions between the bases. We focus in
particular on soliton solutions; the Y model predicts the correct size of the
nonlinear excitations supposed to model the ``transcription bubbles'', and this
is essentially unchanged with the improved potential. Other features of soliton
dynamics, in particular curvature of soliton field configurations and the
Peierls-Nabarro barrier, are instead significantly changed
Cylindrically symmetric solitons in Einstein-Yang-Mills theory
Recently new Einstein-Yang-Mills (EYM) soliton solutions were presented which
describe superconducting strings with Kasner asymptotic (hep-th/0610183). Here
we study the static cylindrically symmetric SU(2) EYM system in more detail.
The ansatz for the gauge field corresponds to superposition of the azimuthal
and the longitudinal components of the color magnetic field. We
derive sum rules relating data on the symmetry axis to asymptotic data and show
that generic asymptotic structure of regular solutions is Kasner. Solutions
starting with vacuum data on the axis generically are divergent. Regular
solutions correspond to some bifurcation manifold in the space of parameters
which has the low-energy limiting point corresponding to string solutions in
flat space (with the divergent total energy) and the high-curvature point where
gravity is crucial. Some analytical results are presented for the low energy
limit, and numerical bifurcation curves are constructed in the gravitating
case. Depending on the parameters, the solution looks like a straight string or
a pair of straight and circular strings. The existence of such non-linear
superposition of two strings becomes possible due to self-interaction terms in
the Yang-Mills action which suppress contribution of the circular string near
the polar axis.Comment: 21 pages, 11 figure
Quantum coherence and carriers mobility in organic semiconductors
We present a model of charge transport in organic molecular semiconductors
based on the effects of lattice fluctuations on the quantum coherence of the
electronic state of the charge carrier. Thermal intermolecular phonons and
librations tend to localize pure coherent states and to assist the motion of
less coherent ones. Decoherence is thus the primary mechanism by which
conduction occurs. It is driven by the coupling of the carrier to the molecular
lattice through polarization and transfer integral fluctuations as described by
the hamiltonian of Gosar and Choi. Localization effects in the quantum coherent
regime are modeled via the Anderson hamiltonian with correlated diagonal and
non-diagonal disorder leading to the determination of the carrier localization
length. This length defines the coherent extension of the ground state and
determines, in turn, the diffusion range in the incoherent regime and thus the
mobility. The transfer integral disorder of Troisi and Orlandi can also be
incorporated. This model, based on the idea of decoherence, allowed us to
predict the value and temperature dependence of the carrier mobility in
prototypical organic semiconductors that are in qualitative accord with
experiments
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