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Mathematics Institute

Nonlinear Engineering Problems and Challenges

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Monday 29 November 2010
Organisers: Igor Khovanov (Warwick Engineering) and Nigel Stocks (Warwick Engineering)

 

All talks will be in Room B3.02 Mathematics Institute, Zeeman Building

Programme pdf(PDF Document)
  • 12:30 Buffet Lunch in the Mathematics Institute common room
  • 13:45-14:00 Introduction
  • 14:00-14:50 Stefano Beri (Dept. Applied Physics & Photonics, Vrije Universiteit Brussel) The Stochastic and Nonlinear Dynamics of Semiconductor Ring Lasers
  • 14:50-15:40 Neil Evans (School of Engineering, University of Warwick) Quantification of antibody binding kinetics using surface plasmon resonance
  • 15:45-16:15 Tea in the Mathematics Institute Common Room
  • 16:15-16:35 Hin Kwan Wong (School of Engineering, University of Warwick) The Jump Resonance Phenomenon in Nonlinear Feedback Systems
  • 16:35-17:25 Petr Denissenko (Fluid Dynamics Group, University of Warwick) Engineering vs. mathematical approaches illustrated with the example of runup statistics and the non-linear wave dynamics
  • 17:30 Wine and snacks in the Mathematics Institute Common Room

Abstracts:

Stefano Beri (Dept. Applied Physics & Photonics, Vrije Universiteit Brussel)

The Stochastic and Nonlinear Dynamics of Semiconductor Ring Lasers

Semiconductor Ring Lasers (SRL) are a modern class of lasers whose active cavity is characterized by a circular geometry. SRLs have attracted attention due to their potential in applications such as all-optical memories and data treatment.
This talk will address the stochastic and nonlinear dynamics of SRL, putting emphasis on the experimentally observable effects that are a consequence of the ring symmetry and that can be theoretically addressed in a device-independent way by investigating the invariant manifolds of the system.
We will show how to experimentally control the internal parameter of the SRL such as the mode-coupling and how to break the ring symmetry in a controllable and reversible way. In particular, we will discuss non-Arrhenius features appearing in the residence time distribution in the symmetric SRL as well as the anatomy of a mode-hopping event. Multistability between three coexisting operating states will be disclosed.
Finally, when the symmetry of the system is broken in a controlled way, excitability will be revealed, suggesting that SRL are possible candidates for scalable optical excitable units which could be in principle integrated on chip with densities exceeding 100000/cm2.

Neil Evans (School of Engineering, University of Warwick)

Quantification of antibody binding kinetics using surface plasmon resonance

In order to characterise antibody binding characteristics it is necessary to determine reaction constants from quantitative measurements of the underlying biological process. Surface plasmon resonance (SPR) provides convenient real-time measurement of the reaction that enables subsequent estimation of the reaction constants. Two models are considered that represent the binding reaction in the presence of transport effects. One of these models, the effective rate constant approximation, can be derived from the other applying a quasi-steady state assumption. Uniqueness of the reaction constants with respect to SPR measurements is considered via a structural identifiability analysis. It is shown that the effective rate constant model is unidentifiable, unless the analyte concentration is known, while the full model is structurally globally identifiable provided association and dissociation phases are considered. Both models provide comparable estimates for the unknown rate constants for a commercial anti-A monoclonal IgM experiment. The analysis is then extended to account for the heterogeneity of the analyte, and the resulting complexity is discussed.

Hin Kwan Wong (School of Engineering, University of Warwick)

The Jump Resonance Phenomenon in Nonlinear Feedback Systems

The jump phenomenon is an abrupt change of frequency response of a nonlinear feedback system even when subjected to only a infinitesimal change in input amplitude or frequency, and when the input is periodic and sinusoidal. This phenomenon can only occur in moderately nonlinear systems with feedback. For example, in aircraft control, the pilot induced oscillation (PIO) in military aircrafts; in microelectromechanical systems (MEMS) there are surface acoustic wave (SAW) resonators. This talk focuses on the method of predicting the phenomenon using Describing Function (DF) theory.

 

Petr Denissenko (Fluid Dynamics Group, University of Warwick)

Engineering vs. mathematical approaches illustrated with the example of runup statistics and the non-linear wave dynamics

Statistical characteristics of the wave runup (vertical displacement of the moving shoreline and its velocity) are important parameters affecting the near-shore sediment transport. The rigorous mathematical methods can be applied to calculate the statistics of runup in the framework of shallow water theory. Currently, experiments are running at the School of Engineering to test the solutions. Relation between idealisations of rigorous modelling and the restrictions of a real experiment will be discussed.