Approximate and Exact Small Signal Analysis for Single-Mode Fiber Near Zero Dispersion Wavelength with Higher Order Dispersion

This article presents the comparison of approximate and exact small-signal theories for analyzing the influence of the higher-order dispersion terms on dispersive optical communication systems operating near zero dispersion wavelength for linear single-mode fiber. For the approximate theory, the generalized conversion matrix has been reported and gives the transfer function of intensity and phase from the fiber input to fiber output for a laser source including the influence of any higher-order dispersion term. In addition, expressions for the small-signal frequency response and the relative intensity noise (RIN) response of an ultrafast laser diode including noises are derived. However, it is observed that the approximation assumed for the second-order dispersion term for the approximate analysis is not valid. From the approximate theory, the exact generalized conversion matrix and exact expressions for small-signal frequency response and relative intensity noise (RIN) are obtained. We show that for the exact theory, the second-order dispersion term has no effect on intensity and frequency response even at large modulating frequencies and large propagation distances contrary to the approximate theory as reported by other authors. But we show that third-order dispersion term certainly has some minute impact on the frequency and RIN response for long distance links at high modulating frequencies.     

Unusual domain evolution in semiconducting ferroelectrics: A phase field study

The effect of electrical conductivity on the domain evolution of semiconducting ferroelectrics is investigated using a phase field model which includes the drift of space charges. Phase field simulations show that the tail-to-tail 90° charged domain wall appears during the domain formation in the semiconducting ferroelectrics at zero field, which is prohibited in common insulating ferroelectrics. Due to the screening of polarization charges, the domain switching takes place through the motion of head-to-head 180° charged domain wall in the semiconducting single-domain ferroelectrics subjected to an electric field. Comparing to the insulating ferroelectrics, the semiconducting ferroelectrics have a lower speed of domain evolution due to the decrease of mobility of charged domain walls. The response of semiconducting ferroelectrics to a mechanical load is also found different from that of insulating ferroelectrics.     

Thermal hysteresis and memory effects in TIInS2

The dielectric susceptibility of layered TlInS₂ was studied in the temperature range of successive phase transitions. Thermal hysteresis was observed in the incommensurate phase. It was shown that after annealing the crystal at a fixed temperature within the incommensurate phase, the existing temperature interval of this phase reveals noticeable broadening. The thermal memory effect is discussed using a defect density wave model.     

Pseudodifferential Operators on Prehomogeneous Vector Spaces

ABSTRACT

Let G be a connected, linear algebraic group defined over ?, acting regularly on a finite dimensional vector space V over ? with ?-structure V _?. Assume that V possesses a Zariski-dense orbit, so that (G, ?, V) becomes a prehomogeneous vector space over ?. We consider the left regular representation π of the group of ?-rational points G _? on the Banach space C₀(V _?) of continuous functions on V _? vanishing at infinity, and study the convolution operators π(f), where f is a rapidly decreasing function on the identity component of G _?. Denote the complement of the dense orbit by S, and put S _? = S ∩ V _?. It turns out that, on V _? ? S _?, π(f) is a smooth operator. If S _? = {0}, the restriction of the Schwartz kernel of π(f) to the diagonal defines a homogeneous distribution on V _? ? {0}. Its nonunique extension to V _? can then be regarded as a trace of π(f). If G is reductive, and S and S _? are irreducible hypersurfaces, π(f) corresponds, on each connected component of V _? ? S _?, to a totally characteristic pseudodifferential operator. In this case, the restriction of the Schwartz kernel of π(f) to the diagonal defines a distribution on V _? ? S _? given by some power |p(m)| ^s of a relative invariant p(m) of (G, ?, V) and, as a consequence of the Fundamental Theorem of Prehomogeneous Vector Spaces, its extension to V _?, and the complex s-plane, satisfies functional equations similar to those for local zeta functions. A trace of π(f) can then be defined by subtracting the singular contributions of the poles of the meromorphic extension.     

Using the Viable System Model (VSM) to structure information processing complexity in disaster response

Earthquakes, hurricanes, flooding and terrorist attacks continue to threaten our society and, when the worst happens, lives depend on different agencies to manage the response. The literature shows that there is significant potential for operational research (OR) to aid disaster management and that, whilst some of this potential has been delivered, there is more that OR can contribute. In particular, OR can provide detailed support to analysing the complexity of information processing – an essential topic as failure could cause response agencies to act on low quality information or act too slowly – putting responders and victims at risk. However, there is a gap in methods for analysing information processing whilst delivering rapid response. This paper explores how OR can fill this gap through taking a Viable System Model (VSM) approach to analyse information processing. It contributes to the OR literature by showing how VSM can support the analysis of information processing as well as how the OR modelling technique can be further strengthened to facilitate the task.     

On Conditional Independence,Mixing, and Association

Abstract

This is a follow-up to a recent article by Prakasa Rao [15 Prakasa Rao , B.L.S. 2008 . Conditional independence, conditional mixing and association . Annals of the Institute of Statistical Mathematics AISM , doi: 10.1007/S10463-007-0152-2 . [Google Scholar]] on conditional independence, conditional mixing and conditional association. The purpose of this article is to derive rigorously some results following from conditioning. To this end, a brief review is presented of the concepts of conditional independence of events, classes of events, and random variables, followed by a conditional version of a factorization theorem, as well as a first installment of some basic results. Next, the concepts of conditional covariance and variance are introduced, and a second installment of basic results follows. Furthermore, a certain representation of the covariance is established in detail, followed by a conditional version of it, as well as a generalization. The concept of the conditional characteristic function is also recalled, and a certain inequality is established. Finally, the concept of conditional positive (negative) quadrant dependence, as well as that of conditional positive (negative) association are introduced. The article concludes with the derivation of the conditional versions of some known results, regarding positive (negative) association. This is done anticipating that conditional association (and also conditional mixing) will prove to be of significant applicability.     

Frequency Domain Fluorescence Lifetime Study of Crude Petroleum Oils

Frequency domain (FD) fluorescence lifetime data was collected for a series of 20 crude petroleum oils using a 405 nm excitation source and over a spectral range of ~426 to ~650 nm. Average fluorescence lifetimes were calculated using three different models: discrete multi-exponential, Gaussian distribution, and Lorentzian distribution. Fitting the data to extract accurate average lifetimes using the various models proved easier and less time consuming for the FD data than with Time Correlated Single Photon Counting (TCSPC) methods however the analysis of confidence intervals to the computed average lifetimes proved cumbersome for both methods. The uncertainty in the average lifetime was generally larger for the discrete lifetime multi-exponential model when compared to the distribution-based models. For the lifetime distributions, the data from the light crude oils with long lifetimes generally fit to a single decay term. Heavier oils with shorter lifetimes required multiple decay terms. The actual value for the average lifetime is more dependant on the specific fitting model employed than the data acquisition method used. Correlations between average fluorescence lifetimes and physical and chemical parameters of the crude oils were made with a view to developing a quantitative model for predicting the gross chemical composition of crude oils. It was found that there was no significant benefit gained by using FD over TCSPC other than more rapid data analysis in the FD case. For the FD data the Gaussian distribution model for fluorescence lifetime gave the best correlations with chemical composition allowing a qualitative correlation to some bulk oil parameters.

An alternative approach for recording of multidimensional NMR data based on frequency dependent folding mechanism

A new scheme for obtaining HSQC spectra with improved resolution or in a shorter time called SHARC (Shaped Arrayed data aCquisition protocol) is proposed, which uses region selective RF pulses and allows the sweep width to be adjusted individually for each region. It thus bypasses the problems with the Nyquist theorem associated with other method suggested for this purpose. Assignment of the cross-peaks to their respective region is achieved by manipulating the phases of the RF pulses and/or their frequencies. SHARC NMR can be applied without any previous knowledge of the chemical shift distribution, but can be further optimized on the basis of a quick overview spectrum.