Moment asymptotic stability of stochastic hybrid delay systems

in this paper we investigate the moment asymptotic stability for the nonlinear stochastic hybrid delay systems. Sufficient criteria on the stabilization and robust stability are also established for linear stochastic hybrid delay systems. Copyright © 2005 IFAC.

Nonlinear phenomena in thermoacoustics: A comparison between single-mode and multi-mode methods

Nonlinear analysis of thermoacoustic instability is essential for prediction of frequencies and amplitudes of limit cycles. In frequency domain analyses, a quasi-linear transfer function between acoustic velocity and heat release rate perturbations, called the flame describing function (FDF), is obtained from a flame model or experiments. The FDF is a function of the frequency and amplitude of velocity perturbations but only contains the heat release response at the forcing frequency. While the gain and phase of the FDF provide insight into the nonlinear dynamics of the system, the accuracy of its predictions remains to be verified for different types of nonlinearity. In time domain analyses, the governing equations of the fully coupled problem are solved to find the time evolution of the system. One method is to discretize the governing equations using a suitable basis, such as the natural acoustic modes of the system. The number of modes used in the discretization alters the accuracy of the solution. In our previous work we have shown that predictions using the FDF are almost exactly the same as those obtained from the time-domain using only one mode for the discretization. We call this the single-mode method. In this paper we compare results from the single-mode and multi-mode methods, applied to a thermoacoustic system of a premixed flame in a tube. For some cases, the results differ greatly in both amplitude as well as frequency content. This study shows that the contribution from higher and subharmonics to the nonlinear dynamics can be significant and must be considered for an accurate and comprehensive analysis of thermoacoustic systems. Hence multi-mode simulations are necessary, and the single-mode method or the FDF may be insufficient to capture some of the complex nonlinear behaviour in fhermoacoustics.

Nonlinear drillstring dynamics analysis

This paper studies the dynamical response of a rotary drilling system with a drag bit, using a lumped parameter model that takes into consideration the axial and torsional vibration modes of the bit. These vibrations are coupled through a bit-rock interaction law. At the bit-rock interface, the cutting process introduces a state-dependent delay, while the frictional process is responsible for discontinuous right-hand sides in the equations governing the motion of the bit. This complex system is characterized by a fast axial dynamics compared to the slow torsional dynamics. A dimensionless formulation exhibits a large parameter in the axial equation, enabling a two-time-scales analysis that uses a combination of averaging methods and a singular perturbation approach. An approximate model of the decoupled axial dynamics permits us to derive a pseudoanalytical expression of the solution of the axial equation. Its averaged behavior influences the slow torsional dynamics by generating an apparent velocity weakening friction law that has been proposed empirically in earlier work. The analytical expression of the solution of the axial dynamics is used to derive an approximate analytical expression of the velocity weakening friction law related to the physical parameters of the system. This expression can be used to provide recommendations on the operating parameters and the drillstring or the bit design in order to reduce the amplitude of the torsional vibrations. Moreover, it is an appropriate candidate model to replace empirical friction laws encountered in torsional models used for control. © 2009 Society for Industrial and Applied Mathematics.

Stability margins of nonlinear receding-horizon control via inverse optimality

Using the nonlinear analog of the Fake Riccati equation developed for linear systems, we derive an inverse optimality result for several receding-horizon control schemes. This inverse optimality result unifies stability proofs and shows that receding-horizon control possesses the stability margins of optimal control laws. © 1997 Elsevier Science B.V.

APSK coded modulation schemes for nonlinear satellite channels with high power and spectral efficiency

A new class of 16-ary Amplitude Phase Shift Keying (APSK) coded modulations deemed double-ring PSK modulations best suited for (satellite) nonlinear channels is proposed. Constellation parameters optimization has been based on geometric and information-theoretic considerations. Furthermore, pre- and post-compensation techniques to reduce the nonlinearity impact have been examined. Digital timing clock and carrier phase have been derived and analyzed for a Turbo coded version of the same new modulation scheme. Finally, the performance of state-of the art Turbo coded modulation for this new 16-ary digital modulation has been investigated and compared to the known TCM schemes. It is shown that for the same coding scheme, double-ring APSK modulation outperforms classical 16-QAM and 16-PSK over a typical satellite nonlinear channel due to its intrinsic robustness against the High Power Amplifier (HPA) nonlinear characteristics. The new modulation is shown to be power- and spectrally-efficient, with interesting applications to satellite communications. © 2002 by the American Institute of Aeronautics and Astronautics, Inc.

Nonlinear Rashba model and spin relaxation in quantum wells

We find that the Rashba spin splitting is intrinsically a nonlinear function of the momentum, and the linear Rashba model may overestimate it significantly, especially in narrow-gap semiconductors. A nonlinear Rashba model is proposed, which is in good agreement with the numerical results from the eight-band k center dot p theory. Using this model, we find pronounced suppression of the D'yakonov-Perel' spin relaxation rate at large electron densities, and a nonmonotonic dependence of the resonance peak position of the electron spin lifetime on the electron density in [111]-oriented quantum wells, both in qualitative disagreement with the predictions of the linear Rashba model.

Effect of the electrostatic interactions of chromophores on the macroscopic second-order nonlinear optical properties of the polymer films

The polyetherketone (PEK-c) guest-host system thin films doped with 3-(1,1-dicyanothenyl)-1-phenyl-4,5-dihydro-1H-pryazole (DCNP) were prepared. Their second-order nonlinear optical (NLO) coefficients chi(33)((2)) were measured by using Maker fringe method for the polymer films doped with different weight percents of DCNP. Experimental results indicate that the second-order NLO properties of the poled polymer films could decrease with the chromophore loading increasing when the chromophore loading reaches a fairly high level. In this paper, the relationship between the macroscopic second-order NLO coefficient and the chromophore number density was modified under considering the role of the electrostatic interactions of chromophores in the polymer film. According to the modified relationship, the macroscopic second-order NLO coefficient is no longer in direct proportion with the chromophore number density in the polymer film. The effect of the electrostatic interactions of chromophores on second-order NLO properties was discussed. The attenuation of the macroscopic second-order NLO activity can be demonstrated by the role of the chromophore electrostatic interactions at high loading of chromophore in the polymer systems.

CHARACTERISTICS OF THE MAGNETIC DEPOPULATION OF SUBBANDS IN VERY NARROW SYSTEMS

We present a model for electrons confined in narrow conducting channels by a parabolic well under moderate to high magnetic fields which takes into account a cutoff in the filling of the subbands. Such a cutoff gives rise to energy-separated subbands and a two-dimensional (2D) like subband depopulation, resulting in a relation between sublevel index n and inverse magnetic field B-1 such that in the high-field regime it changes over to the well-known 2D form as expected, and in the moderate field regime it shows pronounced deviation from linearity. This agrees well with the experimental results. The linear region of the n-B-1 experimental plot is believed to arise from the two dimensionality of the system. Calculations show that no resolvable 1D sublevel exists in the 0.5-mu-m-wide wire at very small magnetic fields (including zero field), which agrees qualitatively with the experimental results found in other wires that the Hall resistance, R(H), approaches its classical value B/n(e)e in this region and R(H) = 0 at B = 0, where n(e) is the electron concentration. In this model the linear and nonlinear regions in the experimental n-B-1 plot are used to extract the characteristic frequency omega-0, and the effective 2D electron concentration N(e)2D, respectively.

Block and parallel modelling of broad domain nonlinear continuous mapping based on NN

The necessity of the use of the block and parallel modeling of the nonlinear continuous mappings with NN is firstly expounded quantitatively. Then, a practical approach for the block and parallel modeling of the nonlinear continuous mappings with NN is proposed. Finally, an example indicating that the method raised in this paper can be realized by suitable existed software is given. The results of the experiment of the model discussed on the 3-D Mexican straw hat indicate that the block and parallel modeling based on NN is more precise and faster in computation than the direct ones and it is obviously a concrete example and the development of the large-scale general model established by Tu Xuyan.

Simulations of X and Y Retinal Ganglion Cell Behavior with a Nonlinear Push-pull Model of Spatiotemporal Retinal Processing

This article describes a nonlinear model of neural processing in the vertebrate retina, comprising model photoreceptors, model push-pull bipolar cells, and model ganglion cells. Previous analyses and simulations have shown that with a choice of parameters that mimics beta cells, the model exhibits X-like linear spatial summation (null response to contrast-reversed gratings) in spite of photoreceptor nonlinearities; on the other hand, a choice of parameters that mimics alpha cells leads to Y-like frequency doubling. This article extends the previous work by showing that the model can replicate qualitatively many of the original findings on X and Y cells with a fixed choice of parameters. The results generally support the hypothesis that X and Y cells can be seen as functional variants of a single neural circuit. The model also suggests that both depolarizing and hyperpolarizing bipolar cells converge onto both ON and OFF ganglion cell types. The push-pull connectivity enables ganglion cells to remain sensitive to deviations about the mean output level of nonlinear photoreceptors. These and other properties of the push-pull model are discussed in the general context of retinal processing of spatiotemporal luminance patterns.

High speed nonlinear optical components for next-generation optical communications

Electronic signal processing systems currently employed at core internet routers require huge amounts of power to operate and they may be unable to continue to satisfy consumer demand for more bandwidth without an inordinate increase in cost, size and/or energy consumption. Optical signal processing techniques may be deployed in next-generation optical networks for simple tasks such as wavelength conversion, demultiplexing and format conversion at high speed (≥100Gb.s-1) to alleviate the pressure on existing core router infrastructure. To implement optical signal processing functionalities, it is necessary to exploit the nonlinear optical properties of suitable materials such as III-V semiconductor compounds, silicon, periodically-poled lithium niobate (PPLN), highly nonlinear fibre (HNLF) or chalcogenide glasses. However, nonlinear optical (NLO) components such as semiconductor optical amplifiers (SOAs), electroabsorption modulators (EAMs) and silicon nanowires are the most promising candidates as all-optical switching elements vis-à-vis ease of integration, device footprint and energy consumption. This PhD thesis presents the amplitude and phase dynamics in a range of device configurations containing SOAs, EAMs and/or silicon nanowires to support the design of all optical switching elements for deployment in next-generation optical networks. Time-resolved pump-probe spectroscopy using pulses with a pulse width of 3ps from mode-locked laser sources was utilized to accurately measure the carrier dynamics in the device(s) under test. The research work into four main topics: (a) a long SOA, (b) the concatenated SOA-EAMSOA (CSES) configuration, (c) silicon nanowires embedded in SU8 polymer and (d) a custom epitaxy design EAM with fast carrier sweepout dynamics. The principal aim was to identify the optimum operation conditions for each of these NLO device configurations to enhance their switching capability and to assess their potential for various optical signal processing functionalities. All of the NLO device configurations investigated in this thesis are compact and suitable for monolithic and/or hybrid integration.

High speed optical communication systems: From modulation formats to radically new fibres

High volumes of data traffic along with bandwidth hungry applications, such as cloud computing and video on demand, is driving the core optical communication links closer and closer to their maximum capacity. The research community has clearly identifying the coming approach of the nonlinear Shannon limit for standard single mode fibre [1,2]. It is in this context that the work on modulation formats, contained in Chapter 3 of this thesis, was undertaken. The work investigates the proposed energy-efficient four-dimensional modulation formats. The work begins by studying a new visualisation technique for four dimensional modulation formats, akin to constellation diagrams. The work then carries out one of the first implementations of one such modulation format, polarisation-switched quadrature phase-shift keying (PS-QPSK). This thesis also studies two potential next-generation fibres, few-mode and hollow-core photonic band-gap fibre. Chapter 4 studies ways to experimentally quantify the nonlinearities in few-mode fibre and assess the potential benefits and limitations of such fibres. It carries out detailed experiments to measure the effects of stimulated Brillouin scattering, self-phase modulation and four-wave mixing and compares the results to numerical models, along with capacity limit calculations. Chapter 5 investigates hollow-core photonic band-gap fibre, where such fibres are predicted to have a low-loss minima at a wavelength of 2μm. To benefit from this potential low loss window requires the development of telecoms grade subsystems and components. The chapter will outline some of the development and characterisation of these components. The world's first wavelength division multiplexed (WDM) subsystem directly implemented at 2μm is presented along with WDM transmission over hollow-core photonic band-gap fibre at 2μm. References: [1]P. P. Mitra, J. B. Stark, Nature, 411, 1027-1030, 2001 [2] A. D. Ellis et al., JLT, 28, 423-433, 2010.

Control of the orientational order and nonlinear optical response of the "push-pull" chromophore RuPZn via specific incorporation into densely packed monolayer ensembles of an amphiphilic four-helix bundle peptide: characterization of the peptide-chromophore complexes.

"Push-pull" chromophores based on extended pi-electron systems have been designed to exhibit exceptionally large molecular hyperpolarizabilities. We have engineered an amphiphilic four-helix bundle peptide to vectorially incorporate such hyperpolarizable chromophores having a metalloporphyrin moiety, with high specificity into the interior core of the bundle. The amphiphilic exterior of the bundle facilitates the formation of densely packed monolayer ensembles of the vectorially oriented peptide-chromophore complexes at the liquid-gas interface. Chemical specificity designed into the ends of the bundle facilitates the subsequent covalent attachment of these monolayer ensembles onto the surface of an inorganic substrate. In this article, we describe the structural characterization of these monolayer ensembles at each stage of their fabrication for one such peptide-chromophore complex designated as AP0-RuPZn. In the accompanying article, we describe the characterization of their macroscopic nonlinear optical properties.

Efficient construction of nonorthogonal localized molecular orbitals in large systems.

Localized molecular orbitals (LMOs) are much more compact representations of electronic degrees of freedom than canonical molecular orbitals (CMOs). The most compact representation is provided by nonorthogonal localized molecular orbitals (NOLMOs), which are linearly independent but are not orthogonal. Both LMOs and NOLMOs are thus useful for linear-scaling calculations of electronic structures for large systems. Recently, NOLMOs have been successfully applied to linear-scaling calculations with density functional theory (DFT) and to reformulating time-dependent density functional theory (TDDFT) for calculations of excited states and spectroscopy. However, a challenge remains as NOLMO construction from CMOs is still inefficient for large systems. In this work, we develop an efficient method to accelerate the NOLMO construction by using predefined centroids of the NOLMO and thereby removing the nonlinear equality constraints in the original method ( J. Chem. Phys. 2004 , 120 , 9458 and J. Chem. Phys. 2000 , 112 , 4 ). Thus, NOLMO construction becomes an unconstrained optimization. Its efficiency is demonstrated for the selected saturated and conjugated molecules. Our method for fast NOLMO construction should lead to efficient DFT and NOLMO-TDDFT applications to large systems.