53,773 research outputs found
Approximate renormalization for the break-up of invariant tori with three frequencies
We construct an approximate renormalization transformation for Hamiltonian
systems with three degrees of freedom in order to study the break-up of
invariant tori with three incommensurate frequencies which belong to the cubic
field , where . This renormalization has two
fixed points~: a stable one and a hyperbolic one with a codimension one stable
manifold. We compute the associated critical exponents that characterize the
universality class for the break-up of the invariant tori we consider.Comment: 5 pages, REVTe
Lattice quantization of Yangian charges
By placing theories with Yangian charges on the lattice in the analogue of
the St Petersburg school's approach to the sine-Gordon system, we exhibit the
Yangian structure of the auxiliary algebra, and explain how the two Yangians
are related.Comment: 9 pages, LaTeX. v2 has minor changes, including correction of a
propagating sign erro
On chemiluminescent emission from an infiltrated chiral sculptured thin film
The theory describing the far-field emission from a dipole source embedded
inside a chiral sculptured thin film (CSTF), based on a spectral Green function
formalism, was further developed to allow for infiltration of the void regions
of the CSTF by a fluid. In doing so, the extended Bruggeman homogenization
formalism--which accommodates constituent particles that are small compared to
wavelength but not vanishingly small--was used to estimate the relative
permittivity parameters of the infiltrated CSTF. For a numerical example, we
found that left circularly polarized (LCP) light was preferentially emitted
through one face of the CSTF while right circularly polarized (RCP) light was
preferentially emitted through the opposite face, at wavelengths within the
Bragg regime. The centre wavelength for the preferential emission of LCP/RCP
light was red shifted as the refractive index of the infiltrating fluid
increased from unity, and this red shift was accentuated when the size of the
constituent particles in our homogenization model was increased. Also, the
bandwidth of the preferential LCP/RCP emission regime decreased as the
refractive index of the infiltrating fluid increased from unity
On the sensitivity of generic porous optical sensors
A porous material was considered as a platform for optical sensing. It was
envisaged that the porous material was infiltrated by a fluid which contains an
agent to be sensed. Changes in the optical properties of the infiltrated porous
material provide the basis for detection of the agent to be sensed. Using a
homogenization approach based on the Bruggeman formalism, wherein the
infiltrated porous material was regarded as a homogenized composite material,
the sensitivity of such a sensor was investigated. For the case of an isotropic
dielectric porous material of relative permittivity and an
isotropic dielectric fluid of relative permittivity , it was found
that the sensitivity was maximized when there was a large contrast between
and ; the maximum sensitivity was achieved at
mid-range values of porosity. Especially high sensitivities may be achieved for
close to unity when , for example. Furthermore,
higher sensitivities may be achieved by incorporating pores which have
elongated spheroidal shapes
Invitation to the Twentieth Annual John F. Sonnett Memorial Lecture Series: The Advocate: Should He Speak or Write?
Invitation to The Advocate: Should He Speak or Write? by Lord Chancellor James Mackay of Great Britain (1987-1997).https://ir.lawnet.fordham.edu/events_programs_sonnett_miscellaneous/1006/thumbnail.jp
John F. Sonnett Memorial Lecture Series: The Advocate: Should He Speak or Write?
Lecture by Lord Chancellor James Mackay of Great Britain (1987-1997) regarding advocacy skills. Document includes a speaker introduction and handwritten notes.https://ir.lawnet.fordham.edu/events_programs_sonnet_lectures/1006/thumbnail.jp
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