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

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

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

The Power of Journaling: A Dynamic Tool for Evaluating Student Teacher Adjustment in Cross-Cultural Contexts

Journaling is an acceptable pedagogical and assessment tool used to help leverage a university student teacher’s emotional and spiritual growth in a 10 week cross-cultural student teaching experience. The process requires students to document their life and learning experiences. Questions are designed for student response. Student teachers are encouraged to draw personal connections between their lives and new experiences. This article will show how journaling helped four student teachers process what Kelly and Meyers (1995) identify as the four components of cross-cultural adaptability: (1) emotional resilience, (2) flexibility/openness, (3) perceptual acuity and (4) personal autonomy. Excerpts from the personal journals of students are included for each of these four components. The journals are used to assess student preparation for cross-cultural living, weekly physical, emotional and spiritual health, the learning environment, and the learning process

Classically integrable boundary conditions for symmetric-space sigma models

We investigate boundary conditions for the nonlinear sigma model on the compact symmetric space $G/H$, where $H \subset G$ is the subgroup fixed by an involution $\sigma$ of $G$. The Poisson brackets and the classical local conserved charges necessary for integrability are preserved by boundary conditions in correspondence with involutions which commute with $\sigma$. Applied to $SO(3)/SO(2)$, the nonlinear sigma model on $S^2$, these yield the great circles as boundary submanifolds. Applied to $G \times G/G$, they reproduce known results for the principal chiral model.Comment: 8 pages. v2 has an introduction added and a few minor correction