6,211 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
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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
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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
Quantum phase transitions in the Fermi-Bose Hubbard model
We propose a multi-band Fermi-Bose Hubbard model with on-site fermion-boson
conversion and general filling factor in three dimensions. Such a Hamiltonian
models an atomic Fermi gas trapped in a lattice potential and subject to a
Feshbach resonance. We solve this model in the two state approximation for
paired fermions at zero temperature. The problem then maps onto a coupled
Heisenberg spin model. In the limit of large positive and negative detuning,
the quantum phase transitions in the Bose Hubbard and Paired-Fermi Hubbard
models are correctly reproduced. Near resonance, the Mott states are given by a
superposition of the paired-fermion and boson fields and the Mott-superfluid
borders go through an avoided crossing in the phase diagram.Comment: 4 pages, 3 figure
The fully self-consistent quasiparticle random phase approximation and its application to the isobaric analog resonances
A microscopic model aimed at the description of charge-exchange nuclear
excitations along isotopic chains which include open-shell systems, is
developed. It consists of quasiparticle random phase approximation (QRPA) made
on top of Hartree-Fock-Bardeen-Cooper-Schrieffer (HF-BCS). The calculations are
performed by using the Skyrme interaction in the particle-hole channel and a
zero-range, density-dependent pairing force in the particle-particle channel.
At variance with the (many) versions of QRPA which are available in literature,
in our work special emphasis is put on the full self-consistency. Its
importance, as well as the role played by the charge-breaking terms of the
nuclear Hamiltonian, like the Coulomb interaction, the charge symmetry and
charge independence breaking (CSB-CIB) forces and the electromagnetic
spin-orbit, are elucidated by means of numerical calculations of the isobaric
analog resonances (IAR). The theoretical energies of these states along the
chain of the Sn isotopes agree well with the experimental data in the stable
isotopes. Predictions for unstable systems are presented.Comment: 15 pages, 6 figure
Observability of Quantum Criticality and a Continuous Supersolid in Atomic Gases
We analyze the Bose-Hubbard model with a three-body hardcore constraint by
mapping the system to a theory of two coupled bosonic degrees of freedom. We
find striking features that could be observable in experiments, including a
quantum Ising critical point on the transition from atomic to dimer
superfluidity at unit filling, and a continuous supersolid phase for strongly
bound dimers.Comment: 4 pages, 2 figures, published version (Editor's suggestion
A magnetic analog of the isotope effect in cuprates
We present extensive magnetic measurements of the
(Ca_xLa_{1-x})(Ba_{1.75-x}La_{0.25+x})Cu_{3}O_{y} (CLBLCO) system with its four
different families (x) having a Tc^max(x) variation of 28% and minimal
structural changes. For each family we measured the Neel temperature, the
anisotropies of the magnetic interactions, and the spin glass temperature. Our
results exhibit a universal relation Tc=c*J*n_s for all families, where c~1, J
is the in plane Heisenberg exchange, and n_s is the carrier density. This
relates cuprate superconductivity to magnetism in the same sense that phonon
mediated superconductivity is related to atomic mass.Comment: With an additional inset in Fig.
Renormalization algorithm for the calculation of spectra of interacting quantum systems
We present an algorithm for the calculation of eigenstates with definite
linear momentum in quantum lattices. Our method is related to the Density
Matrix Renormalization Group, and makes use of the distribution of multipartite
entanglement to build variational wave--functions with translational symmetry.
Its virtues are shown in the study of bilinear--biquadratic S=1 chains.Comment: Corrected version. We have added an appendix with an extended
explanation of the implementation of our algorith
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
Spin and orbital valence bond solids in a one-dimensional spin-orbital system: Schwinger boson mean field theory
A generalized one-dimensional spin-orbital model is
studied by Schwinger boson mean-field theory (SBMFT). We explore mainly the
dimer phases and clarify how to capture properly the low temperature properties
of such a system by SBMFT. The phase diagrams are exemplified. The three dimer
phases, orbital valence bond solid (OVB) state, spin valence bond solid (SVB)
state and spin-orbital valence bond solid (SOVB) state, are found to be favored
in respectively proper parameter regions, and they can be characterized by the
static spin and pseudospin susceptibilities calculated in SBMFT scheme. The
result reveals that the spin-orbit coupling of type serves
as both the spin-Peierls and orbital-Peierles mechanisms that responsible for
the spin-singlet and orbital-singlet formations respectively.Comment: 6 pages, 3 figure
Modeling spontaneous formation of precursor nanoparticles in clear-solution zeolite synthesis
We present a lattice model describing the formation of silica nanoparticles in the early stages of the clear-solution templated synthesis of silicalite-1 zeolite. Silica condensation/hydrolysis is modeled by a nearest-neighbor attraction, while the electrostatics are represented by an orientation-dependent, short-range interaction. Using this simplified model, we show excellent qualitative agreement with published experimental observations. The nanoparticles are identified as a metastable state, stabilized by electrostatic interactions between the negatively charged silica surface and a layer of organic cations. Nanoparticle size is controlled mainly by the solution pH, through nanoparticle surface charge. The size and concentration of the charge-balancing cation are found to have a negligible effect on nanoparticle size. Increasing the temperature allows for further particle growth by Ostwald ripening. We suggest that this mechanism may play a role in the growth of zeolite crystals
A Path Intergal Approach to Current
Discontinuous initial wave functions or wave functions with discontintuous
derivative and with bounded support arise in a natural way in various
situations in physics, in particular in measurement theory. The propagation of
such initial wave functions is not well described by the Schr\"odinger current
which vanishes on the boundary of the support of the wave function. This
propagation gives rise to a uni-directional current at the boundary of the
support. We use path integrals to define current and uni-directional current
and give a direct derivation of the expression for current from the path
integral formulation for both diffusion and quantum mechanics. Furthermore, we
give an explicit asymptotic expression for the short time propagation of
initial wave function with compact support for both the cases of discontinuous
derivative and discontinuous wave function. We show that in the former case the
probability propagated across the boundary of the support in time is
and the initial uni-directional current is . This recovers the Zeno effect for continuous detection of a particle
in a given domain. For the latter case the probability propagated across the
boundary of the support in time is and the
initial uni-directional current is . This is an anti-Zeno
effect. However, the probability propagated across a point located at a finite
distance from the boundary of the support is . This gives a decay
law.Comment: 17 pages, Late
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