254,037 research outputs found
Scale disparities and magnetohydrodynamics in the Earth’s core
Fluid motions driven by convection in the Earth’s fluid core sustain geomagnetic
fields by magnetohydrodynamic dynamo processes. The dynamics of the core is critically
influenced by the combined effects of rotation and magnetic fields. This paper
attempts to illustrate the scale-related difficulties in modelling a convection-driven
geodynamo by studying both linear and nonlinear convection in the presence of
imposed toroidal and poloidal fields. We show that there exist three extremely large
disparities, as a direct consequence of small viscosity and rapid rotation of the Earth’s
fluid core, in the spatial, temporal and amplitude scales of a convection-driven geodynamo.
We also show that the structure and strength of convective motions, and,
hence, the relevant dynamo action, are extremely sensitive to the intricate dynamical
balance between the viscous, Coriolis and Lorentz forces; similarly, the structure and
strength of the magnetic field generated by the dynamo process can depend very
sensitively on the fluid flow. We suggest, therefore, that the zero Ekman number
limit is strongly singular and that a stable convection-driven strong-field geodynamo
satisfying Taylor’s constraint may not exist. Instead, the geodynamo may vacillate
between a strong field state, as at present, and a weak field state, which is also
unstable because it fails to convect sufficient heat
On the complete classification of extremal log Enriques surfaces
We show that there are exactly, up to isomorphisms, seven extremal log
Enriques surfaces Z and construct all of them; among them types D_{19} and
A_{19} have been shown of certain uniqueness by M. Reid. We also prove that the
(degree 3 or 2) canonical covering of each of these seven Z has either X_3 or
X_4 as its minimal resolution. Here X_3 (resp. X_4) is the unique K3 surface
with Picard number 20 and discriminant 3 (resp. 4), which are called the most
algebraic K3 surfaces by Vinberg and have infinite automorphism groups (by
Shioda-Inose and Vinberg).Comment: 22 pages. Math. Z. to appea
Exact two-qubit universal quantum circuit
We provide an analytic way to implement any arbitrary two-qubit unitary
operation, given an entangling two-qubit gate together with local gates. This
is shown to provide explicit construction of a universal quantum circuit that
exactly simulates arbitrary two-qubit operations in SU(4). Each block in this
circuit is given in a closed form solution. We also provide a uniform upper
bound of the applications of the given entangling gates, and find that exactly
half of all the Controlled-Unitary gates satisfy the same upper bound as the
CNOT gate. These results allow for the efficient implementation of operations
in SU(4) required for both quantum computation and quantum simulation.Comment: 5 page
Interacting Individuals Leading to Zipf's Law
We present a general approach to explain the Zipf's law of city distribution.
If the simplest interaction (pairwise) is assumed, individuals tend to form
cities in agreement with the well-known statisticsComment: 4 pages 2 figure
Early Results on Radioactive Background Characterization for Sanford Laboratory and DUSEL Experiments
Measuring external sources of background for a deep underground laboratory at
the Homestake Mine is an important step for the planned low-background
experiments. The naturally occurring -ray fluxes at different levels in
the Homestake Mine are studied using NaI detectors and Monte Carlo simulations.
A simple algorithm is developed to convert the measured -ray rates into
-ray fluxes. A good agreement between the measured and simulated
-ray fluxes is achieved with the knowledge of the chemical composition
and radioactivity levels in the rock. The neutron fluxes and -ray
fluxes are predicted by Monte Carlo simulations for different levels including
inaccessible levels that are under construction for the planned low background
experiments.Comment: 16 pages, 2 figures, and 9 table
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