90,537 research outputs found
The bounded proper forcing axiom and well orderings of the reals
We show that the bounded proper forcing axiom BPFA implies that there is a well-ordering of P(ω_1) which is Δ_1 definable with parameter a subset of ω_1. Our proof shows that if BPFA holds then any inner model of the universe of sets that correctly computes N_2 and also satisfies BPFA must contain all subsets of ω_1. We show as applications how to build minimal models of BPFA and that BPFA implies that the decision problem for the Härtig quantifier is not lightface projective
Microscopic theory for the glass transition in a system without static correlations
We study the orientational dynamics of infinitely thin hard rods of length L,
with the centers-of-mass fixed on a simple cubic lattice with lattice constant
a.We approximate the influence of the surrounding rods onto dynamics of a pair
of rods by introducing an effective rotational diffusion constant D(l),l=L/a.
We get D(l) ~ [1-v(l)], where v(l) is given through an integral of a
time-dependent torque-torque correlator of an isolated pair of rods. A glass
transition occurs at l_c, if v(l_c)=1. We present a variational and a
numerically exact evaluation of v(l).Close to l_c the diffusion constant
decreases as D(l) ~ (l_c-l)^\gamma, with \gamma=1. Our approach predicts a
glass transition in the absence of any static correlations, in contrast to
present form of mode coupling theory.Comment: 6 pages, 3 figure
A theoretical model of the variation of the meridional circulation with the solar cycle
Observations of the meridional circulation of the Sun, which plays a key role
in the operation of the solar dynamo, indicate that its speed varies with the
solar cycle, becoming faster during the solar minima and slower during the
solar maxima. To explain this variation of the meridional circulation with the
solar cycle, we construct a theoretical model by coupling the equation of the
meridional circulation (the component of the vorticity equation within
the solar convection zone) with the equations of the flux transport dynamo
model. We consider the back reaction due to the Lorentz force of the
dynamo-generated magnetic fields and study the perturbations produced in the
meridional circulation due to it. This enables us to model the variations of
the meridional circulation without developing a full theory of the meridional
circulation itself. We obtain results which reproduce the observational data of
solar cycle variations of the meridional circulation reasonably well. We get
the best results on assuming the turbulent viscosity acting on the velocity
field to be comparable to the magnetic diffusivity (i.e. on assuming the
magnetic Prandtl number to be close to unity). We have to assume an appropriate
bottom boundary condition to ensure that the Lorentz force cannot drive a flow
in the subadiabatic layers below the bottom of the tachocline. Our results are
sensitive to this bottom boundary condition. We also suggest a hypothesis how
the observed inward flow towards the active regions may be produced.Comment: 15 pages, 11 figures, accepted for publication in MNRA
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