5,214 research outputs found
Approximation and geometric modeling with simplex B-splines associated with irregular triangles
Bivariate quadratic simplical B-splines defined by their corresponding set of knots derived from a (suboptimal) constrained Delaunay triangulation of the domain are employed to obtain a C1-smooth surface. The generation of triangle vertices is adjusted to the areal distribution of the data in the domain. We emphasize here that the vertices of the triangles initially define the knots of the B-splines and do generally not coincide with the abscissae of the data. Thus, this approach is well suited to process scattered data.\ud
\ud
With each vertex of a given triangle we associate two additional points which give rise to six configurations of five knots defining six linearly independent bivariate quadratic B-splines supported on the convex hull of the corresponding five knots.\ud
\ud
If we consider the vertices of the triangulation as threefold knots, the bivariate quadratic B-splines turn into the well known bivariate quadratic Bernstein-Bézier-form polynomials on triangles. Thus we might be led to think of B-splines as of smoothed versions of Bernstein-Bézier polynomials with respect to the entire domain. From the degenerate Bernstein-Bézier situation we deduce rules how to locate the additional points associated with each vertex to establish knot configurations that allow the modeling of discontinuities of the function itself or any of its directional derivatives. We find that four collinear knots out of the set of five defining an individual quadratic B-spline generate a discontinuity in the surface along the line they constitute, and that analogously three collinear knots generate a discontinuity in a first derivative.\ud
Finally, the coefficients of the linear combinations of normalized simplicial B-splines are visualized as geometric control points satisfying the convex hull property.\ud
Thus, bivariate quadratic B-splines associated with irregular triangles provide a great flexibility to approximate and model fast changing or even functions with any given discontinuities from scattered data.\ud
An example for least squares approximation with simplex splines is presented
Chern number spins of Mn acceptor magnets in GaAs
We determine the effective total spin of local moments formed from
acceptor states bound to Mn ions in GaAs by evaluating their magnetic Chern
numbers. We find that when individual Mn atoms are close to the sample surface,
the total spin changes from to , due to quenching of the
acceptor orbital moment. For Mn pairs in bulk, the total depends on the
pair orientation in the GaAs lattice and on the separation between the Mn
atoms. We point out that Berry curvature variation as a function of local
moment orientation can profoundly influence the quantum spin dynamics of these
magnetic entities.Comment: 4 pages, 3 figure
Controlling Spin Exchange Interactions of Ultracold Atoms in Optical Lattices
We describe a general technique that allows to induce and control strong
interaction between spin states of neighboring atoms in an optical lattice. We
show that the properties of spin exchange interactions, such as magnitude,
sign, and anisotropy can be designed by adjusting the optical potentials. We
illustrate how this technique can be used to efficiently ``engineer'' quantum
spin systems with desired properties, for specific examples ranging from
scalable quantum computation to probing a model with non-trivial topological
orders that supports exotic non-abelian anyonic excitations.Comment: 5 pages, 2 figures, revte
Floquet Spectrum and Transport Through an Irradiated Graphene Ribbon
Graphene subject to a spatially uniform, circularly-polarized electric field
supports a Floquet spectrum with properties akin to those of a topological
insulator, including non-vanishing Chern numbers associated with bulk bands and
current-carrying edge states. Transport properties of this system however are
complicated by the non-equilibrium occupations of the Floquet states. We
address this by considering transport in a two-terminal ribbon geometry for
which the leads have well-defined chemical potentials, with an irradiated
central scattering region. We demonstrate the presence of edge states, which
for infinite mass boundary conditions may be associated with only one of the
two valleys. At low frequencies, the bulk DC conductivity near zero energy is
shown to be dominated by a series of states with very narrow anticrossings,
leading to super-diffusive behavior. For very long ribbons, a ballistic regime
emerges in which edge state transport dominates.Comment: 4.2 pages, 3 figure
Widths of Isobaric Analog Resonances: a microscopic approach
A self-consistent particle-phonon coupling model is used to investigate the
properties of the isobaric analog resonance in Bi. It is shown that
quantitative agreement with experimental data for the energy and the width can
be obtained if the effects of isospin-breaking nuclear forces are included, in
addition to the Coulomb force effects. A connection between microscopic model
predictions and doorway state approaches which make use of the isovector
monopole resonance, is established via a phenomenological ansatz for the
optical potential.Comment: 18 pages, 1 figure. To appear on Phys. Rev. C (tentatively scheduled
for June 1998
Addendum to: Capillary floating and the billiard ball problem
We compare the results of our earlier paper on the floating in neutral
equilibrium at arbitrary orientation in the sense of Finn-Young with the
literature on its counterpart in the sense of Archimedes. We add a few remarks
of personal and social-historical character.Comment: This is an addendum to my article Capillary floating and the billiard
ball problem, Journal of Mathematical Fluid Mechanics 14 (2012), 363 -- 38
Atomic Bose-Fermi mixtures in an optical lattice
A mixture of ultracold bosons and fermions placed in an optical lattice
constitutes a novel kind of quantum gas, and leads to phenomena, which so far
have been discussed neither in atomic physics, nor in condensed matter physics.
We discuss the phase diagram at low temperatures, and in the limit of strong
atom-atom interactions, and predict the existence of quantum phases that
involve pairing of fermions with one or more bosons, or, respectively, bosonic
holes. The resulting composite fermions may form, depending on the system
parameters, a normal Fermi liquid, a density wave, a superfluid liquid, or an
insulator with fermionic domains. We discuss the feasibility for observing such
phases in current experiments.Comment: 4 pages, 1 eps figure, misprints correcte
Neutrino-nucleus reactions on ^{12}C and ^{16}O
Exclusive and inclusive cross-sections and
-capture rates are calculated for ^{12}C and ^{16}O using the consistent
random phase approximation (RPA) and pairing model. After a pairing correction
is introduced to the RPA results the flux-averaged theoretical cross-sections and -capture rates in C are
in good agreement with experiment. In particular when one takes into account
the experimental error bars, the recently measured range of values for the
cross-section is in agreement with the present theoretical
results. Predictions of and cross-sections in
^{16}O are also presented.Comment: 13 pages, Revte
Theory of parity violation in compound nuclear states; one particle aspects
In this work we formulate the reaction theory of parity violation in compound
nuclear states using Feshbach's projection operator formalism. We derive in
this framework a complete set of terms that contribute to the longitudinal
asymmetry measured in experiments with polarized epithermal neutrons. We also
discuss the parity violating spreading width resulting from this formalism. We
then use the above formalism to derive expressions which hold in the case when
the doorway state approximation is introduced. In applying the theory we limit
ourselves in this work to the case when the parity violating potential and the
strong interaction are one-body. In this approximation, using as the doorway
the giant spin-dipole resonance and employing well known optical potentials and
a time-reversal even, parity odd one-body interaction we calculate or estimate
the terms we derived. In our calculations we explicitly orthogonalize the
continuum and bound wave functions. We find the effects of orthogonalization to
be very important. Our conclusion is that the present one-body theory cannot
explain the average longitudinal asymmetry found in the recent polarized
neutron experiments. We also confirm the discrepancy, first pointed out by
Auerbach and Bowman, that emerges, between the calculated average asymmetry and
the parity violating spreading width, when distant doorways are used in the
theory.Comment: 37 pages, REVTEX, 5 figures not included (Postscript, available from
the authors
Topological Classification of Gapped Spin Chains :Quantized Berry Phase as a Local Order Parameter
We characterize several phases of gapped spin systems by local order
parameters defined by quantized Berry phases. This characterization is
topologically stable against any small perturbation as long as the energy gap
remains finite. The models we pick up are dimerized Heisenberg chains
and S=2 Heisenberg chains with uniaxial single-ion-type anisotropy.
Analytically we also evaluate the topological local order parameters for the
generalized Affleck-Kennedy-Lieb-Tasaki (AKLT) model. The relation between the
present Berry phases and the fractionalization in the integer spin chains are
discussed as well.Comment: 6 pages, 4 figures, accepted for publication in Phys. Rev.
- …