544 research outputs found
On the Spinning Motion of the Hovering Magnetic Top
In this paper we analyze the spinning motion of the hovering magnetic top. We
have observed that its motion looks different from that of a classical top. A
classical top rotates about its own axis which precesses around a vertical
fixed external axis. The hovering magnetic top, on the other hand, has its axis
slightly tilted and moves rigidly as a whole about the vertical axis. We call
this motion synchronous, because in a stroboscopic experiment we see that a
point at the rim of the top moves synchronously with the top axis. We show that
the synchronous motion may be attributed to a small deviation of the magnetic
moment from the symmetry axis of the top. We calculate the minimum angular
velocity required for stability in terms of the moments of inertia and magnetic
field and show that it is different from that of a classical top. We also give
experimental results that were taken with a top whose moment of inertia can be
changed. These results show very good agreement with our calculations.Comment: 19 pages (including 3 figures named fig1.eps-fig3.eps), uses amssymb,
epsf and amsbsy (AMSLaTeX
Magnetic trapping of neutral particles: Classical and Quantum-mechanical study of a Ioffe-Pritchard type trap
Recently, we developed a method for calculating the lifetime of a particle
inside a magnetic trap with respect to spin flips, as a first step in our
efforts to understand the quantum-mechanics of magnetic traps. The 1D toy model
that was used in this study was physically unrealistic because the magnetic
field was not curl-free. Here, we study, both classically and
quantum-mechanically, the problem of a neutral particle with spin S, mass m and
magnetic moment mu, moving in 3D in an inhomogeneous magnetic field
corresponding to traps of the Ioffe-Pritchard, `clover-leaf' and `baseball'
type. Defining by omega_p, omega_z and omega_r the precessional, the axial and
the lateral vibrational frequencies, respectively, of the particle in the
adiabatic potential, we find classically the region in the $(\omega_{r}%
(omega_r -- omega_z) plane where the particle is trapped.
Quantum-mechanically, we study the problem of a spin-one particle in the same
field. Treating omega_r / omega_p and omega_z / omega_p as small parameters for
the perturbation from the adiabatic Hamiltonian, we derive a closed-form
expression for the transition rate 1/T_{esc} of the particle from its trapped
ground-state. We find that in the extreme cases, the expression for 1/T_{esc}
is dominated by the largest of the two frequencies omega_r and omega_z.Comment: 25 pages + 1 EPS figur
Packing defects and the width of biopolymer bundles
The formation of bundles composed of actin filaments and cross-linking
proteins is an essential process in the maintenance of the cells' cytoskeleton.
It has also been recreated by in-vitro experiments, where actin networks are
routinely produced to mimic and study the cellular structures. It has long been
observed that these bundles seem to have a well defined width distribution,
which has not been adequately described theoretically. We propose here that
packing defects of the filaments, quenched and random, contribute an effective
repulsion that counters the cross-linking adhesion energy and leads to a well
defined bundle width. This is a two-dimensional strain-field version of the
classic Rayleigh instability of charged droplets
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