45 research outputs found
Wigner Crystalization in the Lowest Landau Level for
By means of exact diagonalization we study the low-energy states of seven
electrons in the lowest Landau level which are confined by a cylindric external
potential modelling the rest of a macroscopic system and thus controlling the
filling factor . Wigner crystal is found to be the ground state for
filling factors between and provided electrons
interact via the bare Coulomb potential. Even at the solid state has
lower energy than the Laughlin's one, although the two energies are rather
close. We also discuss the role of pseudopotential parameters in the lowest
Landau level and demonstrate that the earlier reported gapless state, appearing
when the short-range part of the interaction is suppressed, has nothing in
common with the Wigner crystalization in pure Coulomb case.Comment: 9 pages, LaTex, 8 figure
Minimax Current Density Coil Design
'Coil design' is an inverse problem in which arrangements of wire are
designed to generate a prescribed magnetic field when energized with electric
current. The design of gradient and shim coils for magnetic resonance imaging
(MRI) are important examples of coil design. The magnetic fields that these
coils generate are usually required to be both strong and accurate. Other
electromagnetic properties of the coils, such as inductance, may be considered
in the design process, which becomes an optimization problem. The maximum
current density is additionally optimized in this work and the resultant coils
are investigated for performance and practicality. Coils with minimax current
density were found to exhibit maximally spread wires and may help disperse
localized regions of Joule heating. They also produce the highest possible
magnetic field strength per unit current for any given surface and wire size.
Three different flavours of boundary element method that employ different basis
functions (triangular elements with uniform current, cylindrical elements with
sinusoidal current and conic section elements with sinusoidal-uniform current)
were used with this approach to illustrate its generality.Comment: 24 pages, 6 figures, 2 tables. To appear in Journal of Physics D:
Applied Physic
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