22 research outputs found
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Electron heat transport in improved confinement discharges in DIII-D
In DIII-D tokamak plasmas with an internal transport barrier (ITB), the comparison of gyrokinetic linear stability (GKS) predictions with experiments in both low and strong negative magnetic shear plasmas provide improved understanding for electron thermal transport within the plasma. Within a limited region just inside the ITB, the electron temperature gradient (ETG) modes appear to control the electron temperature gradient and, consequently, the electron thermal transport. The increase in the electron temperature gradient with more strongly negative magnetic shear is consistent with the increase in the ETG mode marginal gradient. Closer to the magnetic axis the T{sub e} profile flattens and the ETG modes are predicted to be stable. With additional core electron heating, FIR scattering measurements near the axis show the presence of high k fluctuations (12 cm{sup {minus}1}), rotating in the electron diamagnetic drift direction. This turbulence could impact electron transport and possibly also ion transport. Thermal diffusivities for electrons, and to a lesser degree ions, increase. The ETG mode can exist at this wavenumber, but it is computed to be robustly stable near the axis. Consequently, in the plasmas the authors have examined, calculations of drift wave linear stability do not explain the observed transport near the axis in plasmas with or without additional electron heating, and there are probably other processes controlling transport in this region
A sharp growth condition for a fast escaping spider's web
We show that the fast escaping set of a transcendental entire function
has a structure known as a spider's web whenever the maximum modulus of
grows below a certain rate. We give examples of entire functions for which the
fast escaping set is not a spider's web which show that this growth rate is
best possible. By our earlier results, these are the first examples for which
the escaping set has a spider's web structure but the fast escaping set does
not. These results give new insight into a conjecture of Baker and a conjecture
of Eremenko
Entire functions with Julia sets of positive measure
Let f be a transcendental entire function for which the set of critical and
asymptotic values is bounded. The Denjoy-Carleman-Ahlfors theorem implies that
if the set of all z for which |f(z)|>R has N components for some R>0, then the
order of f is at least N/2. More precisely, we have log log M(r,f) > (N/2) log
r - O(1), where M(r,f) denotes the maximum modulus of f. We show that if f does
not grow much faster than this, then the escaping set and the Julia set of f
have positive Lebesgue measure. However, as soon as the order of f exceeds N/2,
this need not be true. The proof requires a sharpened form of an estimate of
Tsuji related to the Denjoy-Carleman-Ahlfors theorem.Comment: 17 page
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Dimensions of Julia sets of meromorphic functions with finitely many poles
Let be a transcendental meromorphic function with finitely many poles such that the finite singularities of lie in a bounded set. We show that the Julia set of has Hausdorff dimension strictly greater than one and packing dimension equal to two. The proof for Hausdorff dimension simplifies the earlier argument given for transcendental entire functions
Dimensions of Julia sets of meromorphic functions
We show that for any meromorphic function the Julia set has constant local upper and lower box dimensions, and , respectively, near all points of with at most two
exceptions. Further, the packing dimension of the Julia set is equal to . Using this result we show that, for any transcendental entire function in the class (that is, the class of functions such that the singularities of the inverse function are bounded), both the local upper box dimension and packing dimension of are equal to 2. Our approach is to show that the subset of the Julia set containing those points that escape to infinity as quickly as possible has local upper box dimension equal to 2
Determination of predevelopment denudation rates of an agricultural watershed (Cayaguas River, Puerto Rico) using in-situ-produced 10Be in river-borne quartz
cited By 69International audienceno abstrac
Escaping points of entire functions of small growth
Let f be a transcendental entire function and let I(f) denote the set of points that escape to infinity under iteration. We give conditions which ensure that, for certain functions, I(f) is connected. In particular, we show that I(f) is connected if f has order zero and sufficiently small growth or has order less than 1/2 and regular growth. This shows that, for these functions, Eremenko’s conjecture that I(f) has no bounded components is true. We also give a new criterion related to I(f) which is sufficient to ensure that f has no unbounded Fatou components