35,398 research outputs found
Lagrangian submanifolds and dynamics on Lie affgebroids
We introduce the notion of a symplectic Lie affgebroid and their Lagrangian
submanifolds in order to describe the Lagrangian (Hamiltonian) dynamics on a
Lie affgebroid in terms of this type of structures. Several examples are
discussed.Comment: 50 pages. Several sections update
configuration of the system
We study the configuration of the system by
considering as a coupled channel. We solve the Faddeev equations
for these systems and find confirmation of the existence of a new
resonance around 1920 MeV with predicted in a single-channel
potential model and also found in a Faddeev calculation as an
state, with the generated in the ,
interaction.Comment: Published versio
A new multisymplectic unified formalism for second-order classical field theories
We present a new multisymplectic framework for second-order classical field
theories which is based on an extension of the unified Lagrangian-Hamiltonian
formalism to these kinds of systems. This model provides a straightforward and
simple way to define the Poincar\'e-Cartan form and clarifies the construction
of the Legendre map (univocally obtained as a consequence of the constraint
algorithm). Likewise, it removes the undesirable arbitrariness in the solutions
to the field equations, which are analyzed in-depth, and written in terms of
holonomic sections and multivector fields. Our treatment therefore completes
previous attempt to achieve this aim. The formulation is applied to describing
some physical examples; in particular, to giving another alternative
multisymplectic description of the Korteweg-de Vries equation.Comment: 52 pp. Revision of our previous paper. Minor corrections on the
statement of some results. A new example is added (Section 6.1). Conclusions
and bibliography have been enlarged, and some comments on the higher-order
case have been adde
Surface Percolation and Growth. An alternative scheme for breaking the diffraction limit in optical patterning
A nanopatterning scheme is presented by which the structure height can be
controlled in the tens of nanometers range and the lateral resolution is a
factor at least three times better than the point spread function of the
writing beam. The method relies on the initiation of the polymerization
mediated by a very inefficient energy transfer from a fluorescent dye molecule
after single photon absorption. The mechanism has the following distinctive
steps: the dye adsorbs on the substrate surface with a higher concentration
than in the bulk, upon illumination it triggers the polymerization, then
isolated islands develop and merge into a uniform structure (percolation),
which subsequently grows until the illumination is interrupted. This
percolation mechanism has a threshold that introduces the needed nonlinearity
for the fabrication of structures beyond the diffraction limit.Comment: 10 pages, 8 figure
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