9,068 research outputs found
Near mean-field behavior in the generalized Burridge-Knopoff earthquake model with variable range stress transfer
Simple models of earthquake faults are important for understanding the
mechanisms for their observed behavior in nature, such as Gutenberg-Richter
scaling. Because of the importance of long-range interactions in an elastic
medium, we generalize the Burridge-Knopoff slider-block model to include
variable range stress transfer. We find that the Burridge-Knopoff model with
long-range stress transfer exhibits qualitatively different behavior than the
corresponding long-range cellular automata models and the usual
Burridge-Knopoff model with nearest-neighbor stress transfer, depending on how
quickly the friction force weakens with increasing velocity. Extensive
simulations of quasiperiodic characteristic events, mode-switching phenomena,
ergodicity, and waiting-time distributions are also discussed. Our results are
consistent with the existence of a mean-field critical point and have important
implications for our understanding of earthquakes and other driven dissipative
systems.Comment: 24 pages 12 figures, revised version for Phys. Rev.
Quantum Hall effect in narrow graphene ribbons
The edge states in the integer quantum Hall effect are known to be
significantly affected by electrostatic interactions leading to the formation
of compressible and incompressible strips at the boundaries of Hall bars. We
show here, in a combined experimental and theoretical analysis, that this does
not hold for the quantum Hall effect in narrow graphene ribbons. In our
graphene Hall bar, which is only 60 nm wide, we observe the quantum Hall effect
up to Landau level index k=2 and show within a zero free-parameter model that
the spatial extent of the compressible and incompressible strips is of a
similar magnitude as the magnetic length. We conclude that in narrow graphene
ribbons the single-particle picture is a more appropriate description of the
quantum Hall effect and that electrostatic effects are of minor importance.Comment: RevTex, 5 pages, 4 figures (matches published version
Simulation of the Burridge-Knopoff Model of Earthquakes with Variable Range Stress Transfer
Simple models of earthquake faults are important for understanding the
mechanisms for their observed behavior, such as Gutenberg-Richter scaling and
the relation between large and small events, which is the basis for various
forecasting methods. Although cellular automaton models have been studied
extensively in the long-range stress transfer limit, this limit has not been
studied for the Burridge-Knopoff model, which includes more realistic friction
forces and inertia. We find that the latter model with long-range stress
transfer exhibits qualitatively different behavior than both the long-range
cellular automaton models and the usual Burridge-Knopoff model with nearest
neighbor springs, depending on the nature of the velocity-weakening friction
force. This result has important implications for our understanding of
earthquakes and other driven dissipative systems.Comment: 4 pages, 5 figures, published on Phys. Rev. Let
Exact equqations and scaling relations for f-avalanche in the Bak-Sneppen evolution model
Infinite hierarchy of exact equations are derived for the newly-observed
f-avalanche in the Bak-Sneppen evolution model. By solving the first order
exact equation, we found that the critical exponent which governs the
divergence of the average avalanche size, is exactly 1 (for all dimensions),
confirmed by the simulations. Solution of the gap equation yields another
universal exponent, denoting the the relaxation to the attractor, is exactly 1.
We also establish some scaling relations among the critical exponents of the
new avalanche.Comment: 5 pages, 1 figur
Simulations of Spinodal Nucleation in Systems with Elastic Interactions
Systems with long-range interactions quenched into a metastable state near
the pseudospinodal exhibit nucleation that is qualitatively different than the
classical nucleation observed near the coexistence curve. We have observed
nucleation droplets in our Langevin simulations of a two-dimensional model of
martensitic transformations and have determined that the structure of the
nucleating droplet differs from the stable martensite structure. Our results,
together with experimental measurements of the phonon dispersion curve, allow
us to predict the nature of the droplet. These results have implications for
nucleation in many solid-solid transitions and the structure of the final
state
Minutes 1873
https://place.asburyseminary.edu/freemethodistminutesyearbooks/1011/thumbnail.jp
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