5,943 research outputs found
Tearing of free-standing graphene
We examine the fracture mechanics of tearing graphene. We present a molecular dynamics simulation of the propagation of cracks in clamped, free-standing graphene as a function of the out-of-plane force. The geometry is motivated by experimental configurations that expose graphene sheets to out-of-plane forces, such as back-gate voltage. We establish the geometry and basic energetics of failure and obtain approximate analytical expressions for critical crack lengths and forces. We also propose a method to obtain graphene's toughness. We observe that the cracks' path and the edge structure produced are dependent on the initial crack length. This work may help avoid the tearing of graphene sheets and aid the production of samples with specific edge structures.CAPESNational Science Foundation DMR 1002428Physic
Energy in an Expanding Universe in the Teleparallel Geometry
The main purpose of this paper is to explicitly verify the consistency of the
energy-momentum and angular momentum tensor of the gravitational field
established in the Hamiltonian structure of the Teleparallel Equivalent of
General Relativity (TEGR). In order to reach these objectives, we obtained the
total energy and angular momentum (matter plus gravitational field) of the
closed universe of the Friedmann-Lemaitre-Robertson-Walker (FLRW). The result
is compared with those obtained from the pseudotensors of Einstein and
Landau-Lifshitz. We also applied the field equations (TEGR) in an expanding
FLRW universe. Considering the stress energy-momentum tensor for a perfect
fluid, we found a teleparallel equivalent of Friedmann equations of General
Relativity (GR).Comment: 19 pages, no figures. Revised in view of Referee's comments. Version
to appear in the Brazilian Journal of Physic
Zipf Law for Brazilian Cities
This work studies the Zipf Law for cities in Brazil. Data from censuses of
1970, 1980, 1991 and 2000 were used to select a sample containing only cities
with 30,000 inhabitants or more. The results show that the population
distribution in Brazilian cities does follow a power law similar to the ones
found in other countries. Estimates of the power law exponent were found to be
2.22 +/- 0.34 for the 1970 and 1980 censuses, and 2.26 +/- 0.11 for censuses of
1991 and 2000. More accurate results were obtained with the maximum likelihood
estimator, showing an exponent equal to 2.41 for 1970 and 2.36 for the other
three years.Comment: 12 pages, 6 figures, 3 tables, Elsevier LaTeX, accepted for
publication in "Physica A". Correction of minor mistyping (eq. 8
Behavioural Movement Strategies in Cyclic Models
The spatial segregation of species is fundamental to ecosystem formation and
stability. Behavioural strategies may determine where species are located and
how their interactions change the local environment arrangement. In response to
stimuli in the environment, individuals may move in a specific direction
instead of walking randomly. This behaviour can be innate or learned from
experience, and allow the individuals to conquer or the maintain territory,
foraging or taking refuge. We study a generalisation of the spatial
rock-paper-scissors model where individuals of one out of the species may
perform directional movement tactics. Running a series of stochastic
simulations, we investigate the effects of the behavioural tactics on the
spatial pattern formation and the maintenance of the species diversity. We also
explore a more realistic scenario, where not all individuals are conditioned to
perform the behavioural strategy or have different levels of neighbourhood
perception. Our outcomes show that self-preservation behaviour is more
profitable in terms of territorial dominance, with the best result being
achieved when all individuals are conditioned and have a long-range vicinity
perception. On the other hand, invading is more advantageous if part of
individuals is conditioned and if they have short-range neighbourhood
perception. Finally, our findings reveal that the self-defence strategy is the
least jeopardising to biodiversity which can help biologists to understand
population dynamics in a setting where individuals may move strategically.Comment: 11 pages, 8 figure
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