52,820 research outputs found
Self-dual Hopfions
We construct static and time-dependent exact soliton solutions with
non-trivial Hopf topological charge for a field theory in 3+1 dimensions with
the target space being the two dimensional sphere S**2. The model considered is
a reduction of the so-called extended Skyrme-Faddeev theory by the removal of
the quadratic term in derivatives of the fields. The solutions are constructed
using an ansatz based on the conformal and target space symmetries. The
solutions are said self-dual because they solve first order differential
equations which together with some conditions on the coupling constants, imply
the second order equations of motion. The solutions belong to a sub-sector of
the theory with an infinite number of local conserved currents. The equation
for the profile function of the ansatz corresponds to the Bogomolny equation
for the sine-Gordon model.Comment: plain latex, no figures, 23 page
Arbitrary beam control using passive lossless metasurfaces enabled by orthogonally-polarized custom surface waves
For passive, lossless impenetrable metasurfaces, a design technique for
arbitrary beam control of receiving, guiding, and launching is presented.
Arbitrary control is enabled by a custom surface wave in an orthogonal
polarization such that its addition to the incident (input) and the desired
scattered (output) fields is supported by a reactive surface impedance
everywhere on the reflecting surface. Such a custom surface wave (SW) takes the
form of an evanescent wave propagating along the surface with a spatially
varying envelope. A growing SW appears when an illuminating beam is received.
The SW amplitude stays constant when power is guided along the surface. The
amplitude diminishes as a propagating wave (PW) is launched from the surface as
a leaky wave. The resulting reactive tensor impedance profile may be realized
as an array of anisotropic metallic resonators printed on a grounded dielectric
substrate. Illustrative design examples of a Gaussian beam
translator-reflector, a probe-fed beam launcher, and a near-field focusing lens
are provided
A highly miniaturized electron and ion energy spectrometer prototype for the rapid analysis of space plasmas.
MEMS (Micro Electro-Mechanical Systems) plasma analyzers are a promising possibility for future space missions but conventional instrument designs are not necessarily well suited to micro-fabrication. Here, a candidate design for a MEMS-based instrument has been prototyped using electron-discharge machining. The device features 10 electrostatic analyzers that, with a single voltage applied to it, allow five different energies of electron and five different energies of positive ion to be simultaneously sampled. It has been simulated using SIMION and the electron response characteristics tested in an instrument calibration chamber. Small deviations found in the electrode spacing of the as-built prototype were found to have some effect on the electron response characteristics but do not significantly impede its performance
Variation-norm and fluctuation estimates for ergodic bilinear averages
For any dynamical system, we show that higher variation-norms for the
sequence of ergodic bilinear averages of two functions satisfy a large range of
bilinear Lp estimates. It follows that, with probability one, the number of
fluctuations along this sequence may grow at most polynomially with respect to
(the growth of) the underlying scale. These results strengthen previous works
of Lacey and Bourgain where almost surely convergence of the sequence was
proved (which is equivalent to the qualitative statement that the number of
fluctuations is finite at each scale). Via transference, the proof reduces to
establishing new bilinear Lp bounds for variation-norms of truncated bilinear
operators on R, and the main ingredient of the proof of these bounds is a
variation-norm extension of maximal Bessel inequalities of Lacey and
Demeter--Tao--Thiele.Comment: 37 pages, new version fixed some references not displaying correctl
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