9,947 research outputs found
Electron correlations in a C fullerene cluster: A lattice density-functional study of the Hubbard model
The ground-state properties of C fullerene clusters are determined in
the framework of the Hubbard model by using lattice density-functional theory
(LDFT) and scaling approximations to the interaction-energy functional. Results
are given for the ground-state energy, kinetic and Coulomb energies, local
magnetic moments, and charge-excitation gap, as a function of the Coulomb
repulsion and for electron or hole doping close half-band
filling (). The role of electron correlations is analyzed by
comparing the LDFT results with fully unrestricted Hartree-Fock (UHF)
calculations which take into account possible noncollinear arrangements of the
local spin-polarizations. The consequences of the spin-density-wave symmetry
breaking, often found in UHF, and the implications of this study for more
complex fullerene structures are discussed.Comment: 18 pages, 7 figures, Submitted to PR
A note on the 2D generalized Zakharov-Kuznetsov equation: local, global, and scattering results
We consider the generalized two-dimensional Zakharov-Kuznetsov equation
, where is an integer
number. For we prove local well-posedness in the -based Sobolev
spaces , where is greater than the critical scaling
index . For we also establish a sharp criteria to obtain
global solutions. A nonlinear scattering result in is
also established assuming the initial data is small and belongs to a suitable
Lebesgue space
Adsorption of Self-Assembled Rigid Rods on Two-Dimensional Lattices
Monte Carlo (MC) simulations have been carried out to study the adsorption on
square and triangular lattices of particles with two bonding sites that, by
decreasing temperature or increasing density, polymerize reversibly into chains
with a discrete number of allowed directions and, at the same time, undergo a
continuous isotropic-nematic (IN) transition. The process has been monitored by
following the behavior of the adsorption isotherms for different values of
lateral interaction energy/temperature. The numerical data were compared with
mean-field analytical predictions and exact functions for noninteracting and 1D
systems. The obtained results revealed the existence of three adsorption
regimes in temperature. (1) At high temperatures, above the critical one
characterizing the IN transition at full coverage Tc(\theta=1), the particles
are distributed at random on the surface and the adlayer behaves as a
noninteracting 2D system. (2) At very low temperatures, the asymmetric monomers
adsorb forming chains over almost the entire range of coverage, and the
adsorption process behaves as a 1D problem. (3) In the intermediate regime, the
system exhibits a mixed regime and the filling of the lattice proceeds
according to two different processes. In the first stage, the monomers adsorb
isotropically on the lattice until the IN transition occurs in the system and,
from this point, particles adsorb forming chains so that the adlayer behaves as
a 1D fluid. The two adsorption processes are present in the adsorption
isotherms, and a marked singularity can be observed that separates both
regimes. Thus, the adsorption isotherms appear as sensitive quantities with
respect to the IN phase transition, allowing us (i) to reproduce the phase
diagram of the system for square lattices and (ii) to obtain an accurate
determination of the phase diagram for triangular lattices.Comment: Langmuir, 201
Breaking a secure communication scheme based on the phase synchronization of chaotic systems
A security analysis of a recently proposed secure communication scheme based
on the phase synchronization of chaotic systems is presented. It is shown that
the system parameters directly determine the ciphertext waveform, hence it can
be readily broken by parameter estimation of the ciphertext signal.Comment: 4 pages, 6 figure
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