576 research outputs found
Coupled skinny baker's maps and the Kaplan-Yorke conjecture
The Kaplan-Yorke conjecture states that for "typical" dynamical systems with
a physical measure, the information dimension and the Lyapunov dimension
coincide. We explore this conjecture in a neighborhood of a system for which
the two dimensions do not coincide because the system consists of two uncoupled
subsystems. We are interested in whether coupling "typically" restores the
equality of the dimensions. The particular subsystems we consider are skinny
baker's maps, and we consider uni-directional coupling. For coupling in one of
the possible directions, we prove that the dimensions coincide for a prevalent
set of coupling functions, but for coupling in the other direction we show that
the dimensions remain unequal for all coupling functions. We conjecture that
the dimensions prevalently coincide for bi-directional coupling. On the other
hand, we conjecture that the phenomenon we observe for a particular class of
systems with uni-directional coupling, where the information and Lyapunov
dimensions differ robustly, occurs more generally for many classes of
uni-directionally coupled systems (also called skew-product systems) in higher
dimensions.Comment: 33 pages, 3 figure
Explanation of the discrepancy between the measured and atomistically calculated yield stresses in body-centered cubic metals
We propose a mesoscopic model that explains the factor of two to three
discrepancy between experimentally measured yield stresses of BCC metals at low
temperatures and typical Peierls stresses determined by atomistic simulations
of isolated screw dislocations. The model involves a Frank-Read type source
emitting dislocations that become pure screws at a certain distance from the
source and, owing to their high Peierls stress, control its operation. However,
due to the mutual interaction between emitted dislocations the group consisting
of both non-screw and screw dislocations can move at an applied stress that is
about a factor of two to three lower than the stress needed for the glide of
individual screw dislocations.Comment: 4 pages, 2 figures; RevTex4; submitted to PR
Atomistic studies of transformation pathways and energetics in plutonium
One of the most challenging problems in understanding the structural phase
transformations in Pu is to determine the energetically favored, continuous
atomic pathways from one crystal symmetry to another. This problem involves
enumerating candidate pathways and studying their energetics to garner insight
into instabilities and energy barriers. The purpose of this work is to
investigate the energetics of two transformation pathways for the delta to
alpha' transformation in Pu that were recently proposed [Lookman et al., Phys.
Rev. Lett. 100:145504, 2008] on the basis of symmetry. These pathways require
the presence of either an intermediate hexagonal closed-packed (hcp) structure
or a simple hexagonal (sh) structure. A subgroup of the parent fcc and the
intermediate hexagonal structure, which has trigonal symmetry, facilitates the
transformation to the intermediate hcp or sh structure. Phonons then break the
translational symmetry from the intermediate hcp or sh structure to the final
monoclinic symmetry of the alpha' structure. We perform simulations using the
modified embedded atom method (MEAM) for Pu to investigate these candidate
pathways. Our main conclusion is that the path via hcp is energetically favored
and the volume change for both pathways essentially occurs in the second step
of the transformation, i.e. from the intermediate sh or hcp to the monoclinic
structure. Our work also highlights the deficiency of the current
state-of-the-art MEAM potential in capturing the anisotropy associated with the
lower symmetry monoclinic structure.Comment: 12 pages, 5 figures, accepted for publication in Philos. Ma
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