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 $Q(\tau)$, where $\tau^3+\tau^2-2\tau-1=0$. 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 $\epsilon^a$ and an isotropic dielectric fluid of relative permittivity $\epsilon^b$, it was found that the sensitivity was maximized when there was a large contrast between $\epsilon^a$ and $\epsilon^b$; the maximum sensitivity was achieved at mid-range values of porosity. Especially high sensitivities may be achieved for $\epsilon^b$ close to unity when $\epsilon^a >> 1$, 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