Invariant discrete flows

In this paper, we investigate the evolution of joint invariants under invariant geometric flows using the theory of equivariant moving frames and the induced invariant discrete variational complex. For certain arc length preserving planar curve flows invariant under the special Euclidean group , the special linear group , and the semidirect group , we find that the induced evolution of the discrete curvature satisfies the differential‐difference mKdV, KdV, and Burgers' equations, respectively. These three equations are completely integrable, and we show that a recursion operator can be constructed by precomposing the characteristic operator of the curvature by a certain invariant difference operator. Finally, we derive the constraint for the integrability of the discrete curvature evolution to lift to the evolution of the discrete curve itself.     

Solvent detection using porous silicon optical waveguides

Since the first report on the use of porous silicon as an optical waveguide medium in 1995, significant development has been made towards the understanding and applicability of such material. Here, the introduction of solvents (acetone, methanol, and propan-2-ol) into the pores is shown to dramatically reduce the loss of the waveguides, in a reversible manner. Both the magnitude and duration of this effect are sensitive to the solvent introduced. In some waveguides, for example, the measured loss (at 0.633 μm) falls by as much as 34 dB cm⁻¹ on the introduction of acetone. Theoretical estimates of the effect of solvents on the interfacial scattering loss confirm this as the origin of the observed reductions. These results, combined with the fact that a substantial portion of the guided-mode field interacts with the solvent, indicate an enhanced sensitivity for sensor applications may be achievable.     

A Popov-theory-based survey on digital control of infinite-dimensional systems with unboundedness

This paper represents a Popov-theory-based assessment of thecurrent status of the digital control of infinite–dimensionalsystems with certain unboundedness in control and/or observation,summarizing some results and indicating which, in the authors'opinion, would be the promising directions for future research.     

An adaptive control scheme for a continuous plant under Known output delay, unmodelled dynamics, and input saturation

This paper deals with robustness of adaptive control of continuoussystems subject to known output delay, input saturation, unmodelledlinear dynamics, and bounded disturbances. A simple gradient-typealgorithm with a relative deadzone is used. The relative deadzoneis built with an estimated contribution of the unmodelled dynamicsto the system output. The basic tool used for stability androbustness analysis is Gronwall's lemma.     

A bisection-extreme point search algorithm for optimizing over the efficient set in the linear dependence case

The algorithms and algorithmic ideas currently available for globally optimizing linear functions over the efficient sets of multiple objective linear programs either use nonstandard subroutines or cannot yet be implemented for lack of sufficient development. In this paper a Bisection-Extreme Point Search Algorithm is presented for globally solving a large class of such problems. The algorithm finds an exact, globally-optimal solution after a finite number of iterations. It can be implemented by using only well-known pivoting and optimization subroutines, and it is adaptable to large scale problems or to problems with many local optima.     

Time domain simulation in photonics: A comparison of nonlinear dispersive polarisation models

The paper investigates and compares a range of different models currently used for modelling nonlinear optical phenomena. The models are implemented in the numerical time domain Transmission Line Modelling (TLM) method and include a Kerr model and different formulations of the Duffing model. The models are used to simulate an all-optical limiter for a CW input and results compared with ones available in the literature. This enables a comparison to be made between the different models, from which it is concluded that the Duffing model has some advantages, when modelling materials and phenomena involving more than one frequency, arising from its ability to describe dispersive effects. These conclusions are further supported by the simulation results obtained for a pulse input.     

Advection and dispersion in time and space

Previous work showed how moving particles that rest along their trajectory lead to time-nonlocal advection–dispersion equations. If the waiting times have infinite mean, the model equation contains a fractional time derivative of order between 0 and 1. In this article, we develop a new advection–dispersion equation with an additional fractional time derivative of order between 1 and 2. Solutions to the equation are obtained by subordination. The form of the time derivative is related to the probability distribution of particle waiting times and the subordinator is given as the first passage time density of the waiting time process which is computed explicitly.     

Effective and flexible analysis for propagation in time varying waveguides

The equivalence between the propagation of dispersive modal fields in two-dimensional waveguides, and plane waves in a one-dimensional plasma is presented. Exploitation of this equivalence allows a time domain variant of the effective index approach to be used to model dispersive waveguides problems very efficiently. A time domain integral equation is developed for this important practical case and the stability of a computer algorithm based upon it is improved by means of both a semi-implicit formulation and the use of a modified space–time mesh.