MODELED DIFFUSION-CONTROLLED RESPONSE AND RECOVERY BEHAVIOR OF A NAKED OPTICAL FILM SENSOR WITH A HYPERBOLIC-TYPE RESPONSE TO ANALYTE CONCENTRATION

The diffusion-controlled response and recovery behaviour of a naked optical film sensor (i.e., with no protective membrane) with a hyperbolic-type response [i.e., S0/S = (1 + Kc), where S is the measured value of the absorbance or luminescence intensity of one form of the sensor dye in the presence of the analyte, S0 is the observed value of S in the absence of analyte and K is a constant] to changes in analyte concentration, c, in a system under test is approximated using a simple model, and described more accurately using a numerical model; in both models it is assumed that the system under test represents an infinite reservoir. Each model predicts the variations in the response and recovery times of such an optical sensor, as a function of the final external analyte concentration, the film thickness (I) and the analyte diffusion coefficient (D). From an observed signal versus time profile for a naked optical film sensor it is shown how values for K and D/I2 can be extracted using the numerical model. Both models provide a qualitative description of the often cited asymmetric nature of the response and recovery for hyperbolic-type response naked optical film sensors. It is envisaged that the models will help in the interpretation of the response and recovery behaviour exhibited by many naked optical film sensors and might be especially apposite when the analyte is a gas.

Hyperbolic Polaritonic Crystals Based on Nanostructured Nanorod Metamaterials

Surface plasmon polaritons usually exist on a few suitable plasmonic materials; however, nanostructured plasmonic metamaterials allow a much broader range of optical properties to be designed. Here, bottom-up and top-down nanostructuring are combined, creating hyperbolic metamaterial-based photonic crystals termed hyperbolic polaritonic crystals, allowing free-space access to the high spatial frequency modes supported by these metamaterials.

Solving MPCC problem with the hyperbolic penalty function

The main goal of this work is to solve mathematical program with complementarity constraints (MPCC) using nonlinear programming techniques (NLP). An hyperbolic penalty function is used to solve MPCC problems by including the complementarity constraints in the penalty term. This penalty function [1] is twice continuously differentiable and combines features of both exterior and interior penalty methods. A set of AMPL problems from MacMPEC [2] are tested and a comparative study is performed.

Solving a signalized traffic intersection problem with an hyperbolic penalty function

Mathematical Program with Complementarity Constraints (MPCC) finds many applications in fields such as engineering design, economic equilibrium and mathematical programming theory itself. A queueing system model resulting from a single signalized intersection regulated by pre-timed control in traffic network is considered. The model is formulated as an MPCC problem. A MATLAB implementation based on an hyperbolic penalty function is used to solve this practical problem, computing the total average waiting time of the vehicles in all queues and the green split allocation. The problem was codified in AMPL.

Numerical optimization experiments using the hyperbolic smoothing strategy to solve MPCC

In this work we solve Mathematical Programs with Complementarity Constraints using the hyperbolic smoothing strategy. Under this approach, the complementarity condition is relaxed through the use of the hyperbolic smoothing function, involving a positive parameter that can be decreased to zero. An iterative algorithm is implemented in MATLAB language and a set of AMPL problems from MacMPEC database were tested.

Hausdorff dimension bounds for smoothness of holonomies for codimension 1 hyperbolic dynamics

We prove that the stable holonomies of a proper codimension 1 attractor Λ, for a Cr diffeomorphism f of a surface, are not C1+θ for θ greater than the Hausdorff dimension of the stable leaves of f intersected with Λ. To prove this result we show that there are no diffeomorphisms of surfaces, with a proper codimension 1 attractor, that are affine on a neighbourhood of the attractor and have affine stable holonomies on the attractor.

Hyperbolic Geometry

Exercises, exam questions and solutions for a fourth year hyperbolic geometry course. Diagrams for the questions are all together in the support.zip file, as .eps files

Branching random motions, nonlinear hyperbolic systems and traveling waves

A branching random motion on a line, with abrupt changes of direction, is studied. The branching mechanism, being independient of random motion, and intensities of reverses are defined by a particle's current direction. A soluton of a certain hyperbolic system of coupled non-linear equations (Kolmogorov type backward equation) have a so-called McKean representation via such processes. Commonly this system possesses traveling-wave solutions. The convergence of solutions with Heaviside terminal data to the travelling waves is discussed.This Paper realizes the McKean programme for the Kolmogorov-Petrovskii-Piskunov equation in this case. The Feynman-Kac formula plays a key role.