410 research outputs found
A solvable non-conservative model of Self-Organized Criticality
We present the first solvable non-conservative sandpile-like critical model
of Self-Organized Criticality (SOC), and thereby substantiate the suggestion by
Vespignani and Zapperi [A. Vespignani and S. Zapperi, Phys. Rev. E 57, 6345
(1998)] that a lack of conservation in the microscopic dynamics of an SOC-model
can be compensated by introducing an external drive and thereby re-establishing
criticality. The model shown is critical for all values of the conservation
parameter. The analytical derivation follows the lines of Broeker and
Grassberger [H.-M. Broeker and P. Grassberger, Phys. Rev. E 56, 3944 (1997)]
and is supported by numerical simulation. In the limit of vanishing
conservation the Random Neighbor Forest Fire Model (R-FFM) is recovered.Comment: 4 pages in RevTeX format (2 Figures) submitted to PR
Broken scaling in the Forest Fire Model
We investigate the scaling behavior of the cluster size distribution in the
Drossel-Schwabl Forest Fire model (DS-FFM) by means of large scale numerical
simulations, partly on (massively) parallel machines. It turns out that simple
scaling is clearly violated, as already pointed out by Grassberger [P.
Grassberger, J. Phys. A: Math. Gen. 26, 2081 (1993)], but largely ignored in
the literature. Most surprisingly the statistics not seems to be described by a
universal scaling function, and the scale of the physically relevant region
seems to be a constant. Our results strongly suggest that the DS-FFM is not
critical in the sense of being free of characteristic scales.Comment: 9 pages in RevTEX4 format (9 figures), submitted to PR
Oxidation States of Graphene: Insights from Computational Spectroscopy
When it is oxidized, graphite can be easily exfoliated forming graphene oxide
(GO). GO is a critical intermediate for massive production of graphene, and it
is also an important material with various application potentials. With many
different oxidation species randomly distributed on the basal plane, GO has a
complicated nonstoichiometric atomic structure that is still not well
understood in spite of of intensive studies involving many experimental
techniques. Controversies often exist in experimental data interpretation. We
report here a first principles study on binding energy of carbon 1s orbital in
GO. The calculated results can be well used to interpret experimental X-ray
photoelectron spectroscopy (XPS) data and provide a unified spectral
assignment. Based on the first principles understanding of XPS, a GO structure
model containing new oxidation species epoxy pair and epoxy-hydroxy pair is
proposed. Our results demonstrate that first principles computational
spectroscopy provides a powerful means to investigate GO structure.Comment: accepted by J. Chem. Phy
Synchronization and Coarsening (without SOC) in a Forest-Fire Model
We study the long-time dynamics of a forest-fire model with deterministic
tree growth and instantaneous burning of entire forests by stochastic lightning
strikes. Asymptotically the system organizes into a coarsening self-similar
mosaic of synchronized patches within which trees regrow and burn
simultaneously. We show that the average patch length grows linearly with
time as t-->oo. The number density of patches of length L, N(L,t), scales as
^{-2}M(L/), and within a mean-field rate equation description we find
that this scaling function decays as e^{-1/x} for x-->0, and as e^{-x} for
x-->oo. In one dimension, we develop an event-driven cluster algorithm to study
the asymptotic behavior of large systems. Our numerical results are consistent
with mean-field predictions for patch coarsening.Comment: 5 pages, 4 figures, 2-column revtex format. To be submitted to PR
Universal Behavior of the Coefficients of the Continuous Equation in Competitive Growth Models
The competitive growth models involving only one kind of particles (CGM), are
a mixture of two processes one with probability and the other with
probability . The dependance produce crossovers between two different
regimes. We demonstrate that the coefficients of the continuous equation,
describing their universality classes, are quadratic in (or ). We show
that the origin of such dependance is the existence of two different average
time rates. Thus, the quadratic dependance is an universal behavior of all
the CGM. We derive analytically the continuous equations for two CGM, in 1+1
dimensions, from the microscopic rules using a regularization procedure. We
propose generalized scalings that reproduce the scaling behavior in each
regime. In order to verify the analytic results and the scalings, we perform
numerical integrations of the derived analytical equations. The results are in
excellent agreement with those of the microscopic CGM presented here and with
the proposed scalings.Comment: 9 pages, 3 figure
A Cellular Automaton Model for Diffusive and Dissipative Systems
We study a cellular automaton model, which allows diffusion of energy (or
equivalently any other physical quantities such as mass of a particular
compound) at every lattice site after each timestep. Unit amount of energy is
randomly added onto a site. Whenever the local energy content of a site reaches
a fixed threshold , energy will be dissipated. Dissipation of energy
propagates to the neighboring sites provided that the energy contents of those
sites are greater than or equal to another fixed threshold . Under such dynamics, the system evolves into three different types of
states depending on the values of and as reflected in their
dissipation size distributions, namely: localized peaks, power laws, or
exponential laws. This model is able to describe the behaviors of various
physical systems including the statistics of burst sizes and burst rates in
type-I X-ray bursters. Comparisons between our model and the famous forest-fire
model (FFM) are made.Comment: in REVTEX 3.0. Figures available on request. Extensively revised.
Accepted by Phys.Rev.
A large-scale correlated study of linear optical absorption and low-lying excited states of polyacenes: Pariser-Parr-Pople Hamiltonian
In this paper we present large-scale correlated calculations of linear
optical absorption spectrum of oligo-acenes containing up to seven benzene
rings. For the calculations we used the Pariser-Parr-Pople (P-P-P) Hamiltonian,
along with the configuration interaction (CI) technique at various levels such
as the full CI (FCI), the quadruple CI (QCI) and multi-reference
singles-doubles CI (MRSDCI). The role of Coulomb parameters used in the P-P-P
Hamiltonian was examined by considering standard Ohno parameters, as well as a
screened set of parameters. A detailed analysis of the many-body character of
the important excited states contributing to the linear absorption has also
been performed. The results of our calculations have been compared extensively
with the theoretical work of other authors, as well as with the experiments.Comment: 45 pages, 9 figure
The radical character of the acenes: A density matrix renormalization group study
We present a detailed investigation of the acene series using high-level
wavefunction theory. Our ab-initio Density Matrix Renormalization Group
algorithm has enabled us to carry out Complete Active Space calculations on the
acenes from napthalene to dodecacene correlating the full pi-valence space.
While we find that the ground-state is a singlet for all chain-lengths,
examination of several measures of radical character, including the natural
orbitals, effective number of unpaired electrons, and various correlation
functions, suggests that the longer acene ground-states are polyradical in
nature.Comment: 10 pages, 8 figures, supplementary material, to be published in J.
Chem. Phys. 127, 200
Dehydrogenated polycyclic aromatic hydrocarbons and UV bump
Recent calculations have shown that the UV bump at about 217.5 nm in the
extinction curve can be explained by a complex mixture of PAHs in several
charge states. Other studies proposed that the carriers are a restricted
population made of neutral and singly-ionised dehydrogenated coronene molecules
(C24Hn, n less than 3), in line with models of the hydrogenation state of
interstellar PAHs predicting that medium-sized species are highly
dehydrogenated. To assess the observational consequences of the latter
hypothesis we have undertaken a systematic study of the electronic spectra of
dehydrogenated PAHs. We use our first results to see whether such spectra show
strong general trends upon dehydrogenation. We used state-of-the-art techniques
in the framework of the density functional theory (DFT) to obtain the
electronic ground-state geometries, and of the time- dependent DFT to evaluate
the electronic excited-state properties. We computed the absorption
cross-section of the species C24Hn (n=12,10,8,6,4,2,0) in their neutral and
cationic charge-states. Similar calculations were performed for other PAHs and
their fullydehydrogenated counterparts. pi electron energies are always found
to be strongly affected by dehydrogenation. In all cases we examined,
progressive dehydrogenation translates into a correspondingly progressive blue
shift of the main electronic transitions. In particular, the pi-pi* collective
resonance becomes broader and bluer with dehydrogenation. Its calculated energy
position is therefore predicted to fall in the gap between the UV bump and the
far-UV rise of the extinction curve. Since this effect appears to be
systematic, it poses a tight observational limit on the column density of
strongly dehydrogenated medium-sized PAHs.Comment: 5 pages, 7 figures, Astronomy & Astrophysics, in pres
Clar Sextet Analysis of Triangular, Rectangular and Honeycomb Graphene Antidot Lattices
Pristine graphene is a semimetal and thus does not have a band gap. By making
a nanometer scale periodic array of holes in the graphene sheet a band gap may
form; the size of the gap is controllable by adjusting the parameters of the
lattice. The hole diameter, hole geometry, lattice geometry and the separation
of the holes are parameters that all play an important role in determining the
size of the band gap, which, for technological applications, should be at least
of the order of tenths of an eV. We investigate four different hole
configurations: the rectangular, the triangular, the rotated triangular and the
honeycomb lattice. It is found that the lattice geometry plays a crucial role
for size of the band gap: the triangular arrangement displays always a sizable
gap, while for the other types only particular hole separations lead to a large
gap. This observation is explained using Clar sextet theory, and we find that a
sufficient condition for a large gap is that the number of sextets exceeds one
third of the total number of hexagons in the unit cell. Furthermore, we
investigate non-isosceles triangular structures to probe the sensitivity of the
gap in triangular lattices to small changes in geometry
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