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Finite element approximation of non-Fickian polymer diffusion
The problem of nonlinear non-Fickian polymer diffusion as modelled by a diffusion
equation with an adjoined spatially local evolution equation for a viscoelastic
stress is considered (see, for example, Cohen, White & Witelski, SIAM J. Appl. Math.
55, pp. 348–368, 1995). We present numerical schemes based, spatially, on the
Galerkin finite element method and, temporally, on the Crank-Nicolson method. Special
attention is paid to linearising the discrete equations by extrapolating the value
of the nonlinear term from previous time steps. Optimal a priori error estimates are
given, based on the assumption that the exact solution possesses certain regularity
properties, and numerical experiments are given to support these error estimates
Decoherence induced CPT violation and entangled neutral mesons
We discuss two classes of semi-microscopic theoretical models of stochastic
space-time foam in quantum gravity and the associated effects on entangled
states of neutral mesons, signalling an intrinsic breakdown of CPT invariance.
One class of models deals with a specific model of foam, initially constructed
in the context of non-critical (Liouville) string theory, but viewed here in
the more general context of effective quantum-gravity models. The relevant
Hamiltonian perturbation, describing the interaction of the meson with the foam
medium, consists of off-diagonal stochastic metric fluctuations, connecting
distinct mass eigenstates (or the appropriate generalisation thereof in the
case of K-mesons), and it is proportional to the relevant momentum transfer
(along the direction of motion of the meson pair). There are two kinds of
CPT-violating effects in this case, which can be experimentally disentangled:
one (termed ``omega-effect'') is associated with the failure of the
indistinguishability between the neutral meson and its antiparticle, and
affects certain symmetry properties of the initial state of the two-meson
system; the second effect is generated by the time evolution of the system in
the medium of the space-time foam, and can result in time-dependent
contributions of the $omega-effect type in the time profile of the two meson
state. Estimates of both effects are given, which show that, at least in
certain models, such effects are not far from the sensitivity of experimental
facilities available currently or in the near future. The other class of
quantum gravity models involves a medium of gravitational fluctuations which
behaves like a ``thermal bath''. In this model both of the above-mentioned
intrinsic CPT violation effects are not valid.Comment: 16 pages revtex, no figure
Inhibitory control as a mediator of bidirectional effects between early oppositional behavior and maternal depression.
Maternal depression is an established risk factor for child conduct problems, but relatively few studies have tested whether children's behavioral problems exacerbate mothers' depression or whether other child behavioral characteristics (e.g., self-regulation) may mediate bidirectional effects between maternal depression and child disruptive behavior. This longitudinal study examined the parallel growth of maternal depressive symptoms and child oppositional behavior from ages 2 to 5; the magnitude and timing of their bidirectional effects; and whether child inhibitory control, a temperament-based self-regulatory mechanism, mediated effects between maternal depression and child oppositionality. A randomized control trial of 731 at-risk families assessed children annually from ages 2 to 5. Transactional models demonstrated positive and bidirectional associations between mothers' depressive symptoms and children's oppositional behavior from ages 2 to 3, with a less consistent pattern of reciprocal relations up to age 5. Mediation of indirect mother-child effects and child evocative effects depended on the rater of children's inhibitory control. Findings are discussed in regard to how child evocative effects and self-regulatory mechanisms may clarify the transmission of psychopathology within families
The Complex Time WKB Approximation And Particle Production
The complex time WKB (CWKB) approximation has been an effective technique to
understand particle production in curved as well as in flat spacetime. Earlier
we obtained the standard results on particle production in time dependent gauge
in various curved spacetime. In the present work we generalize the technique of
CWKB to the equivalent problems in space dependent gauge. Using CWKB, we first
obtain the gauge invariant result for particle production in Minkowski
spacetime in strong electric field. We then carry out particle production in
de-Sitter spacetime in space dependent gauge and obtain the same result that we
obtained earlier in time dependent gauge. The results obtained for de-Sitter
spacetime has a obvious extension to particle production in black hole
spacetime. It is found that the origin of Planckian spectrum is due to repeated
reflections between the turning points. As mentioned earlier, it is now
explicitly shown that particle production is accompanied by rotation of
currents.Comment: 12 pages, Revte
Epidemic spreading in evolving networks
A model for epidemic spreading on rewiring networks is introduced and
analyzed for the case of scale free steady state networks. It is found that
contrary to what one would have naively expected, the rewiring process
typically tends to suppress epidemic spreading. In particular it is found that
as in static networks, rewiring networks with degree distribution exponent
exhibit a threshold in the infection rate below which epidemics die
out in the steady state. However the threshold is higher in the rewiring case.
For no such threshold exists, but for small infection rate
the steady state density of infected nodes (prevalence) is smaller for rewiring
networks.Comment: 7 pages, 7 figure
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