Monte-Carlo estimation of time-dependent statistical characteristics of random dynamical systems

The problem of estimating the time-dependent statistical characteristics of a random dynamical system is studied under two different settings. In the first, the system dynamics is governed by a differential equation parameterized by a random parameter, while in the second, this is governed by a differential equation with an underlying parameter sequence characterized by a continuous time Markov chain. We propose, for the first time in the literature, stochastic approximation algorithms for estimating various time-dependent process characteristics of the system. In particular, we provide efficient estimators for quantities such as the mean, variance and distribution of the process at any given time as well as the joint distribution and the autocorrelation coefficient at different times. A novel aspect of our approach is that we assume that information on the parameter model (i.e., its distribution in the first case and transition probabilities of the Markov chain in the second) is not available in either case. This is unlike most other work in the literature that assumes availability of such information. Also, most of the prior work in the literature is geared towards analyzing the steady-state system behavior of the random dynamical system while our focus is on analyzing the time-dependent statistical characteristics which are in general difficult to obtain. We prove the almost sure convergence of our stochastic approximation scheme in each case to the true value of the quantity being estimated. We provide a general class of strongly consistent estimators for the aforementioned statistical quantities with regular sample average estimators being a specific instance of these. We also present an application of the proposed scheme on a widely used model in population biology. Numerical experiments in this framework show that the time-dependent process characteristics as obtained using our algorithm in each case exhibit excellent agreement with exact results. (C) 2010 Elsevier Inc. All rights reserved.

A novel (main chain) (side chain) polymeric peroxide: Synthesis and initiating characteristics of poly(alpha-(tert-butylperoxymethyl)styrene peroxide)

A novel (main chain)-(side chain) vinyl polyperoxide, poly(alpha-(tert-butylperoxymethyl)styrene peroxide) (MCSCPP), an alternating copolymer of alpha-(tert-butylperoxymethyl)styrene (TPMS) and oxygen, has been synthesized by the oxidative polymerization of TPMS. The MCSCPP was characterized by H-1 NMR, C-13 NMR, IR, DSC, EI-MS, and GC-MS studies. The overall activation energy (E(a)) for the degradation of MCSCPP was found to be 27 kcal/mol. Formaldehyde and alpha-(tert-butylperoxy)acetophenone (TPAP) were identified as the primary degradation products of MCSCPP; TPAP was found to undergo further degradation. The side chain peroxy groups were found to be thermally more stable than those in the main chain. Polymerization of styrene in the presence of MCSCPP as initiator, at 80 degrees C, follows classical kinetics. The presence of peroxy segments in the polystyrene chain was confirmed by both H-1 NMR and thermal decomposition studies. Interestingly, unlike other vinyl polyperoxides, the MCSCPP initiator shows an increase in molecular weight with conversion.

A study of partial discharge characteristics in oil impregnated pressboard insulation

An attempt has been made to study the effect of time and test procedure on the behaviour of partial discharge (PD) pulses causing failure of oil-pressboard system under power frequency voltages using circular disc shaped samples and uniform field electrodes. Weibull statistics have been used to handle the large amount of PD data. The PD phenomena has been found to be stress and time dependent. On the basis of stress level, three different regions are identified and in one of the regions, the rate of deterioration of the sample is at a maximum. The work presents some interesting features of Weibull parameters as related to the condition of insulation studied in addition to its usual PD characteristics

Investigation of the characteristics of an SF6 rotating arc by a mathematical model

A mathematical model has been developed for predicting the performance of rotating arcs in SF6 gas by considering the energy balance and force balance equations. The finite difference technique has been adopted for the computer simulation of the arc characteristics. This method helps in considering the spatial variation of the transport and radiative properties of the arc. All the three heat loss mechanisms-conduction, convection, and radiation-have been considered. Results obtained over a 10 ms (half cycle of 50 Hz wave) current flow period for 1.4 kA (peak) and 4.2 kA (peak), show that the proposed arc model gives the expected behavior of the arc over the range of currents studied.

Centrifugal pump transient characteristics and analysis using the method of characteristics

A theoretical and experimental study has been carried out on the transient characteristics of a centrifugal pump during starting and stopping periods. Experiments have been conducted on a volute pump with different valve openings to study the dynamic behaviour of the pump during normal start up and stopping, when a small length of discharge pipe line is connected to discharge flange of the pump. Similar experiments have also been conducted when the test pump was part of a hydraulic system to study the system effect on the transient characteristics. Instantaneous rotational speed, flowrate, and delivery and suction pressures of the pump are recorded and it is observed in ail the tested cases that the change of pump behaviour during the transient period is quasi-steady. The dynamic characteristics of the pump have been analysed by a numerical model using the method of characteristics. The model is presented and the results are compared with the experimental data. As the model contains speed acceleration and unsteady discharge terms, the model can be applied for analyses of purely unsteady cases where the pump dynamic characteristics show considerable departure from their steady-state characteristics.

On the dual head-discharge characteristics of a modified chimney weir

This paper is concerned with the dual head-discharge characteristics of a modified chimney weir. It is shown by an optimization procedure that the modified chimney weir having an inward trapezoidal weir over an inverted V-notch can produce discharges proportional to both the logarithm of the head as well as the linear power of the head reckoned independently over two different reference planes, within a prefixed maximum allowable percentage error from the theoretical discharge. A new technique is adopted to optimize the weir parameters, in order to obtain the maximum ranges of measurement under logarithmic, linear as well as combined characteristics. In the case of linear weir it is shown that it is possible to enhance the linearity range of the chimney weir by more than 540% and for a weir with constant indication accuracy by more than 350%. In addition, about 86% of the overall depth of the designed linear weir and over 90% of the logarithmic weir is converted as the corresponding measurable ranges. Experiments with four typical weirs give consistent constant average coefficient of discharge for each weir confirming the theory. The practical application of the weir in minor irrigation, hydraulic and other engineering fields is highlighted.

Effect of Alkyl Chain Arrangement on Conformation and Dynamics in a Surfactant Intercalated Layered Double Hydroxide: Spectroscopic Measurements and MD Simulations

The anionic surfactant dodecyl sulfate (DDS) has been intercalated in an Mg-Al layered double hydroxide (LDH). Monolayer and bilayer arrangements of the alkyl chains of the intercalated surfactant can be engineered by tuning the Al/Mg ratio of the LDH. In both arrangements the anionic headgroup of the surfactant is tethered to the LDH sheets, and consequently translational mobility of the chains is absent. The degrees of freedom of the confined alkyl chains are restricted to changes in conformation. The effects of the arrangement of the intercalated surfactant chains on conformational order and dynamics have been,investigated by spectroscopic measurements and molecular dynamics simulations. Infrared, Raman, and C-13 NMR spectroscopies were used to investigate conformation of the alkyl chains in the monolayer and bilayer arrangements and variable contact time cross-polarization magic angle spinning (VCT CPMAS) NMR measurements to probe molecular motion. The alkyl chains in the monolayer arrangement of the intercalated DDS chains showed considerably greater conformational disorder and faster dynamics as compared to chains in the bilayer arrangement, in spite of the fact that the volume available per chain in the monolayer is smaller than that in the bilayer. Atomistic MD simulations of the two arrangements of the intercalated surfactant were carried out using an isothermal-isobaric ensemble. The simulations are able to reproduce the essential results of the experiment-greater conformational disorder and faster dynamics for the alkyl chains in the monolayer arrangement of the intercalated surfactant. The MD simulations show that these results are a consequence of the fact that the nature of conformational disorder in the two arrangements is different. In the monolayer arrangement the alkyl chains can sustain isolated gauche defects, whereas in the bilayer arrangement gauche conformers occur only as part of a kink a gauche(+) trans gauche(-) sequence.

Theory of electron transfer processes via chemisorbed intermediates: Part II. Current-potential characteristics

Current-potential characteristics are obtained numerically for a lone-adsorbate-mediated anodic charge transfer at the electrode-solution interface. An increase in the overpotential leads to the appearance of maxima in the anodic current-potential plots instead of the extended activationless region (i.e. a saturation current at large positive overpotentials) predicted by the direct heterogeneous outer-sphere anodic charge transfer process. A detailed analysis of the dependence of current-potential profiles and other kinetic parameters on various system parameters is also presented.

Time-resolved resonance Raman spectroscopic investigations of the photochemistry of ubiquinone

Time-resolved resonance Raman spectroscopy has been used to investigate the photochemistry of ubiquinone in cyclohexane, water and ethanol. In water the absorption of a single 248 nm photon produces triplet ubiquinone which then oxidises water, via electron transfer, to form the ubiquinone radical anion. In ethanol, however, the triplet state reacts with the solvent via both electron and hydrogen-atom transfer, the latter process forming the semihydroquinone. Only in the less reactive solvent, cyclohexane, is triplet quinone observed. The Raman bands observed for each of the species are assigned on the basis of similarities of their spectra to other quinones.

Synthetic, spectroscopic and structural studies on uranium and thorium complexes of diphosphazane dioxides

Co-ordination complexes of the diphosphazane dioxides Ph(2)P(O)N(Pr-i)P(O)Ph(2) L(1). Ph(2)P(O)N(Pr-i)P(O)Ph(OC(6)H(4)Me-4) L(2) and Ph(2)P(O)N(Pr-i)P(O)(O2C12H8) L(3) with UO22+ or Th4+ ions have been synthesised and characterised by IR and NMR spectroscopy. The structures of [UO2(NO3)(2)L(1)] and [Th(NO3)(2)L(3)(1)][Th(NO3)(6)] are established by X-ray crystallography. In the former, the uranyl ion is bonded to two bidentate nitrate groups and the two phosphoryl groups of the ligand L(1); the co-ordination polyhedron around the metal is a hexagonal bipyramid. The cationic moiety in the thorium complex contains three bidentate diphosphazane dioxide ligands and two bidentate nitrate groups around the ten-co-ordinated metal.

Water Modeling Study Of The Jet Characteristics In A Continuous-Casting Mold

The jet characteristics and the fluid flow pattern in a continuous slab caster have been studied using a water model. The fluid jet is studied under free fall and submerged discharge conditions. In the latter case, the jet was followed by dye-injection technique and image analyser was used to find out the effect of nozzle parameters on jet-spread angle, jet-discharge angle and the volume entrainment by the jet. All free-fall jets with nozzle port angle zero and upward are found to be spinning. Some of the free-fall jets with downward nozzle-port angle are found to be spinning and rest are smooth. The spinning direction of the jets are found to change with time. The well depth, port diameter and the inner diameter of the nozzle have a clear effect on the free-fall jets with downward port angle. The jet-spread angle is found to be about 17-degrees for smooth jets. The spread angle for spinning jet increases as the nozzle-port angle is increased from downward 25 to upward 15-degrees. The jet-discharge angle is always downward even when the nozzle-discharge ports are angled upward. The extent of volume entrainment by the spinning jet is higher and it increases as the nozzle-port angle is increased from 25 downward to 15-degrees upward.

Spectroscopic Observation of Oscillations in the Corona During the Total Solar Eclipse of 22 July 2009

We performed high resolution spectroscopy of the solar corona during the total solar eclipse of 22 July 2009 in two emission lines: the green line at 5303 due to Fe xiv and the red line at 6374 due to Fe x, simultaneously from Anji (latitude 30A degrees 28.1' N; longitude 119A degrees 35.4' E; elevation 890 m), China. A two-mirror coelostat with 100 cm focal length lens produced a 9.2 mm image of the Sun. The spectrograph using 140 cm focal length lens in Littrow mode and a grating with 600 lines per millimeter blazed at 2 mu m provided a dispersion of 30 m and 43 m per pixel in the fourth order around the green line and third order around the red line, respectively. Two Peltier cooled 1k x 1k CCD cameras, with a pixel size of 13 mu m square and 14-bit readout at 10 MHz operated in frame transfer mode, were used to obtain the time sequence spectra in two emission lines simultaneously. The duration of totality was 341 s, but we could get spectra for 270 s after a trial exposure at an interval of 5 s. We report here on the detection of intensity, velocity, and line width oscillations with periodicity in the range of 25 -50 s. These oscillations can be interpreted in terms of the presence of fast magnetoacoustic waves or torsional Alfv,n waves. The intensity ratios of green to red emission lines indicate the temperature of the corona to be 1.65 MK in the equatorial region and 1.40 MK in the polar region, relatively higher than the expected temperature during the low activity period. The width variation of the emission lines in different coronal structures suggests different physical conditions in different structures.

Use of finite wordlength FIR digital filter structures with improved magnitude and phase characteristics for reduction of muscle noise in EEG signals

One of the main disturbances in EEG signals is EMG artefacts generated by muscle movements. In the paper, the use of a linear phase FIR digital low-pass filter with finite wordlength precision coefficients is proposed, designed using the compensation procedure, to minimise EMG artefacts in contaminated EEG signals. To make the filtering more effective, different structures are used, i.e. cascading, twicing and sharpening (apart from simple low-pass filtering) of the designed FIR filter Modifications are proposed to twicing and sharpening structures to regain the linear phase characteristics that are lost in conventional twicing and sharpening operations. The efficacy of all these transformed filters in minimising EMG artefacts is studied, using SNR improvements as a performance measure for simulated signals. Time plots of the signals are also compared. Studies show that the modified sharpening structure is superior in performance to all other proposed methods. These algorithms have also been applied to real or recorded EMG-contaminated EEG signal. Comparison of time plots, and also the output SNR, show that the proposed modified sharpened structure works better in minimising EMG artefacts compared with other methods considered.

Ultrasonic wave characteristics of a monolayer graphene on silicon substrate

The present work deals with an ultrasonic type of wave propagation characteristics of monolayer graphene on silicon (Si) substrate. An atomistic model of a hybrid lattice involving a hexagonal lattice of graphene and surface atoms of diamond lattice of Si is developed to identify the carbon-silicon bond stiffness. Properties of this hybrid lattice model is then mapped into a nonlocal continuum framework. Equivalent force constant due to Si substrate is obtained by minimizing the total potential energy of the system. For this equilibrium configuration, the nonlocal governing equations are derived to analyze the ultrasonic wave dispersion based on spectral analysis. From the present analysis we show that the silicon substrate affects only the flexural wave mode. The frequency band gap of flexural mode is also significantly affected by this substrate. The results also show that, the silicon substrate adds cushioning effect to the graphene and it makes the graphene more stable. The analysis also show that the frequency bang gap relations of in-plane (longitudinal and lateral) and out-of-plane (flexural) wave modes depends not only on the y-direction wavenumber but also on nonlocal scaling parameter. In the nonlocal analysis, at higher values of the y-directional wavenumber, a decrease in the frequency band gap is observed for all the three fundamental wave modes in the graphene-silicon system. The atoms movement in the graphene due to the wave propagation are also captured for all the tree fundamental wave modes. The results presented in this work are qualitatively different from those obtained based on the local analysis and thus, are important for the development of graphene based nanodevices such as strain sensor, mass and pressure sensors, atomic dust detectors and enhancer of surface image resolution that make use of the ultrasonic wave dispersion properties of graphene. (C) 2011 Elsevier Ltd. All rights reserved.