851,592 research outputs found
Cross talk for angle- and wavelength-multiiplexed image plane holograms
The cross talk for image plane holograms is calculated and compared with previously derived results for Fourier plane holograms. Image plane storage is found to have significantly smaller cross talk
Point Charge Dynamics Near a Grounded Conducting Plane
The classic image problem in electromagnetism involves a grounded infinite
conducting plane and a point charge. The force of attraction between the point
charge and the plane is identified using an equivalent-field picture of an
image charge with opposite sign equidistant behind the plane resulting in a
1/{\it r} force of attraction between the original charge and the
plane. If the point charge is released from rest it will reach the plane in a
time . This time has not been calculated correctly up to now.
Clarification of the inconsistency is presented along with a correct solution
to the classic image problem. Other electromagnetism problems are mentioned
with attractive 1/{\it r} forces (where {\it n} 1). Such
situations arise between a point charge and a line charge (1/{\it r}), between
a line charge and a point dipole (1/{\it r}), between a point charge and
a point dipole (1/{\it r}, and between a point dipole and a second point
dipole (1/{\it r}).Comment: 6 pages, 4 figure
Tropical Quadrics Through Three Points
We tropicalize the rational map that takes triples of points in the
projective plane to the plane of quadrics passing through these points. The
image of its tropicalization is contained in the tropicalization of its image.
We identify these objects inside the tropical Grassmannian of planes in
projective 5-space, and we explore a small tropical Hilbert scheme.Comment: 9 pages, 3 figure
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