A differential lyapunov framework for contraction analysis

Lyapunov's second theorem is an essential tool for stability analysis of differential equations. The paper provides an analog theorem for incremental stability analysis by lifting the Lyapunov function to the tangent bundle. The Lyapunov function endows the state-space with a Finsler structure. Incremental stability is inferred from infinitesimal contraction of the Finsler metrics through integration along solutions curves. © 2013 IEEE.

Experimental demonstration of optical data links using a hybrid CAP/QAM modulation scheme.

The first known experimental demonstrations of a 10 Gb/s hybrid CAP-2/QAM-2 and a 20 Gb/s hybrid CAP-4/QAM-4 transmitter/receiver-based optical data link are performed. Successful transmission over 4.3 km of standard single-mode fiber (SMF) is achieved, with a link power penalty ∼0.4 dBo for CAP-2/QAM-2 and ∼1.5 dBo for CAP-4/QAM-4 at BER=10(-9).

Unified form language: A domain-specific language for weak formulations of partial differential equations

We present the Unified Form Language (UFL), which is a domain-specific language for representing weak formulations of partial differential equations with a view to numerical approximation. Features of UFL include support for variational forms and functionals, automatic differentiation of forms and expressions, arbitrary function space hierarchies formultifield problems, general differential operators and flexible tensor algebra. With these features, UFL has been used to effortlessly express finite element methods for complex systems of partial differential equations in near-mathematical notation, resulting in compact, intuitive and readable programs. We present in this work the language and its construction. An implementation of UFL is freely available as an open-source software library. The library generates abstract syntax tree representations of variational problems, which are used by other software libraries to generate concrete low-level implementations. Some application examples are presented and libraries that support UFL are highlighted. © 2014 ACM.

Novel passive launch scheme for ultimate bandwidth improvement of graded-index multimode fibers

We propose a new practical multimode fiber optical launch scheme, providing near single mode group excitation for >5 times transmission bandwidth improvement. Equalization-free transmission of a 10-Gb/s signal over 220-m fiber is achieved in experimental demonstrations. © 2010 Optical Society of America.

Differential equation based length scales to improve DES and RANS simulations

Surprisingly expensive to compute wall distances are still used in a range of key turbulence and peripheral physics models. Potentially economical, accuracy improving differential equation based distance algorithms are considered. These involve elliptic Poisson and hyperbolic natured Eikonal equation approaches. Numerical issues relating to non-orthogonal curvilinear grid solution of the latter are addressed. Eikonal extension to a Hamilton-Jacobi (HJ) equation is discussed. Use of this extension to improve turbulence model accuracy and, along with the Eikonal, enhance Detached Eddy Simulation (DES) techniques is considered. Application of the distance approaches is studied for various geometries. These include a plane channel flow with a wire at the centre, a wing-flap system, a jet with co-flow and a supersonic double-delta configuration. Although less accurate than the Eikonal, Poisson method based flow solutions are extremely close to those using a search procedure. For a moving grid case the Poisson method is found especially efficient. Results show the Eikonal equation can be solved on highly stretched, non-orthogonal, curvilinear grids. A key accuracy aspect is that metrics must be upwinded in the propagating front direction. The HJ equation is found to have qualitative turbulence model improving properties. © 2003 by P. G. Tucker.

Novel regrowth-free vertical active-passive integration scheme with improved fabrication tolerance

We present a novel vertically-coupled active-passive integration architecture that provides an order of magnitude reduction in coupling coefficient variation between misaligned waveguides when compared with a conventional vertically-coupled structure. © 2005 Optical Society of America.

Novel regrowth-free vertical active-passive integration scheme with improved fabrication tolerance

We present a novel vertically-coupled active-passive integration architecture that provides an order of magnitude reduction in coupling coefficient variation between misaligned waveguides when compared with a conventional vertically-coupled structure. © 2005 Optical Society of America.

Novel regrowth-free vertical active-passive integration scheme with improved fabrication tolerance

We present a novel vertically-coupled active-passive integration architecture that provides an order of magnitude reduction in coupling coefficient variation between misaligned waveguides when compared with a conventional vertically-coupled structure. © 2005 Optical Society of America.

Statistical study of a novel launch scheme for highperformance electronic-equalized multimode-fiber links

A novel launch scheme is proposed for multimode-fiber (MMF) links. Enhanced performance in 10 Gb/s MMF links using electronic equalization is demonstrated by statistical analysis of installed-base fiber and an experimental investigation. © 2007 Optical Society of America.

High performance optical data links using hybrid CAP/QAM transmitter/receiver scheme

We experimentally demonstrate the first optical data link at 20Gb/s using hybrid CAP- 4/QAM-4 with transmission over 4.3km SSMF and a power penalty ~1.5dBo at BER=10-9. The hybrid CAP-4/QAM-4 link significantly outperforms a reference PAM-4 link. © OSA 2013.