Quadratic Lyapunov functions for linear systems Journal

The paper deals with the existence of a quadratic Lyapunov function V = x′P(t)x for an exponentially stable linear system with varying coefficients described by the vector differential equation S0305004100044777_inline1 The derivative dV/dt is allowed to be strictly semi-(F) and the locus dV/dt = 0 does not contain any arc of the system trajectory. It is then shown that the coefficient matrix A(t) of the exponentially stable sy

Tailoring of Structural Morphology of Silver Nanowires in Electrochemical Growth

Noble metal such as Ag normally exists in an fcc crystal structure. However as the size of the material is decreased to nanometer lengthscales, a structural transformation from that of its bulk state can be expected with new atomic arrangements due to competition between internal packing and minimization of surface energy. In many previous studies, it has been shown that silver nanowires (AGNWs) grown inside anodic alumina (AAO) templates by ac or dc electrochemical deposition from silver salts or complexes, adopt fcc structure and below some critical diameter ∼ 20 nm they may acquire hcp structure at low temperature. This is, however, critically dependant on the nature of confinement, as AgNWs grown inside nanotube confinement with subnanometer diameter have been reported to have fcc structure. Hence the question of the crystal structure of metal nanowires under combined influence of confinement, temperature and deposition condition remains open. In this abstract we show that the alternative crystal structures of AGNWs at room temperature can be achieved with electrochemical growth processes under specific conditions determined by the deposition parameters and nature of confinement. We fabricated AgNWs of 4H hexagonal structure with diameters 30 – 80 nm inside polycarbonate (PC) templates with a modified dc electrodeposition technique, where the nanowires were grown at deposition potentials as low as 10 mV in 2 M silver nitrate solution[1]. We call this low-potential electrodeposition (LPED) since the electrodeposition process occurs at potential much less than the standard Nernst potential (770 mV) of silver. Two types of electrodes were used – stainless steel and sputtered thin Pt film, neither of which had any influence on the crystal structure of the nanowires. EDS elemental analysis showed the nanowires to consist only of silver. Although the precise atomic dynamics during the LPED process is unclear at present, we investigated this with HRTEM (high-resolution transmission electron microscopy) characterization of nanowires grown over various deposition times, as well as electrical conductivity measurements. These experiments indicate that nanowire growth does not occur through a three-dimensional diffusion controlled process, as proposed for conventional over-potential deposition, but follow a novel instantaneous linear growth mechanism. Further experiments showed that, (a) conventional electrochemical growth at a small over-potential in a 2 mM AgNO3 solution yields nanowires with expected fcc structure inside the same PC templates, and (2) no nanowire was observed under the LPED conditions inside hard AAO templates, indicating that LPED-growth process, and hcp structure of the corresponding nanowires depend on deposition parameters, as well as nature of confinement.

Axially homogeneous, zero mean flow buoyancy-driven turbulence in a vertical pipe

We report an experimental study of a new type of turbulent flow that is driven purely by buoyancy. The flow is due to an unstable density difference, created using brine and water, across the ends of a long (length/diameter=9) vertical pipe. The Schmidt number Sc is 670, and the Rayleigh number (Ra) based on the density gradient and diameter is about 108. Under these conditions the convection is turbulent, and the time-averaged velocity at any point is ‘zero’. The Reynolds number based on the Taylor microscale, Reλ, is about 65. The pipe is long enough for there to be an axially homogeneous region, with a linear density gradient, about 6–7 diameters long in the midlength of the pipe. In the absence of a mean flow and, therefore, mean shear, turbulence is sustained just by buoyancy. The flow can be thus considered to be an axially homogeneous turbulent natural convection driven by a constant (unstable) density gradient. We characterize the flow using flow visualization and particle image velocimetry (PIV). Measurements show that the mean velocities and the Reynolds shear stresses are zero across the cross-section; the root mean squared (r.m.s.) of the vertical velocity is larger than those of the lateral velocities (by about one and half times at the pipe axis). We identify some features of the turbulent flow using velocity correlation maps and the probability density functions of velocities and velocity differences. The flow away from the wall, affected mainly by buoyancy, consists of vertically moving fluid masses continually colliding and interacting, while the flow near the wall appears similar to that in wall-bound shear-free turbulence. The turbulence is anisotropic, with the anisotropy increasing to large values as the wall is approached. A mixing length model with the diameter of the pipe as the length scale predicts well the scalings for velocity fluctuations and the flux. This model implies that the Nusselt number would scale as Ra1/2Sc1/2, and the Reynolds number would scale as Ra1/2Sc−1/2. The velocity and the flux measurements appear to be consistent with the Ra1/2 scaling, although it must be pointed out that the Rayleigh number range was less than 10. The Schmidt number was not varied to check the Sc scaling. The fluxes and the Reynolds numbers obtained in the present configuration are much higher compared to what would be obtained in Rayleigh–Bénard (R–B) convection for similar density differences.

Effect of screening of intermicellar interactions on the linear and nonlinear rheology of a viscoelastic gel

We report our studies of the linear and nonlinear rheology of aqueous solutions of the surfactant cetyl trimethylammonium tosylate (CTAT) with varying amounts of sodium chloride (NaCl). The CTAT concentration is fixed at 42 mM, and the salt concentration is varied between 0 and 120 mM. On increasing the salt (NaCl) concentration, we see three distinct regimes in the zero-shear viscosity and the high-frequency plateau modulus data. In regime 1, the zero-shear viscosity shows a weak increase with salt concentration due to enhanced micellar growth. The decrease in the zero-shear viscosities with salt concentration in regimes II and III can be explained in terms of intermicellar branching. The most intriguing feature of our data, however, is the anomalous behavior of the high-frequency plateau modulus in regime II (0.12 less than or equal to [NaCl]/[CTAT] less than or equal to 1.42). In this regime, the plateau modulus increases with an increase in NaCl concentration. This is highly interesting, since the correlation length of concentration fluctuations and hence the plateau modulus G(0) are not expected to change appreciably in the semidilute regime. We propose to explain the changes in regime II in terms of a possible unbinding of the organic counterions (tosylate) from the CTA(+) surfaces on the addition of NaCl. In the nonlinear flow curves of the samples with high salt content, significant deviations from the predictions of the Giesekus model for entangled micelles are observed.

High energy Li ion irradiation effects in ferroelectric PZT and SBT thin films

The ferroelectric Pb(Zr0.53Ti0.47)O-3 (PZT) and SrBi2Ta2O9 (SBT) thin films were prepared by laser ablation technique. The dielectric analysis, capacitance-voltage, ferroelectric hysteresis and DC leakage current measurements were performed before and after 50 MeV Li3+ ion irradiation. In both thin films, the irradiation produced some amount of amorphisation, considerable degradation in the ferroelectric properties and change in DC conductivity. On irradiation of these thin films, the phase transition temperature [T-c] of PZT decreased considerably from 628 to 508 K, while SBT exhibited a broad and diffuse transition with its T-c decreased from 573 to 548 K. The capacitance-voltage curve at 100 kHz showed a double butterfly loop with a large decrease in the capacitance and switching voltage. There was decrease in the ferroelectric hysteresis loop, remanant polarisation and coercive field. After annealing at a temperature of 673 K for 10 min while PZT partially regained the ferroelectric properties, while SBT did not. The DC conductivity measurements showed a shift in the onset of non-linear conduction region in irradiated SBT. The degradation of ferroelectric properties of the irradiated thin films is attributed to the irradiation-induced partial amorphization and the pinning of the ferroelectric domains by trapped charges. The regaining of properties after annealing is attributed to the thermal annealing of the defects generated during the irradiation. (C) 2003 Elsevier Science B.V. All rights reserved.

Magnetic properties and specific heat of LaMn1-xTixO3+delta (0 < x <= 0.2)

We present a magnetic study of the insulating perovskite LaMn1-xTixO3+delta (0measurements of magnetization, susceptibility, and magnetic relaxation. The Curie temperature was found to decrease with increasing content of Ti. Two distinct magnetic transitions, irreversibility, non-exponential relaxation and aging effects confirm a reentrant spin-glass state for x = 0.2. The time decay of the magnetization has an algebraic functional form for times up to 2 h. The specific heat also displays characteristic features of a spin-glass system by a linear low-temperature dependence and a broadened peak near the temperature of the reentrant transition. (C) 2002 Elsevier Science B.V. All rights reserved.

Determination of solid fraction evolution during solidification of aluminum alloy in presence of linear electromagnetic stirring

In many industrial casting processes, knowledge of the solid fraction evolution during the solidification process is a key factor in determining the process parameters such as cooling rate, stirring intensity and in estimating the total solidification time. In the present work, a new method of estimating solid fraction is presented, which is based on calorimetric principles. In this method, the cooling curve data at each point in the melt, along with the thermal boundary conditions, are used to perform energy balance in the mould, from which solid fraction generation during any time interval can be estimated. This method is applied to the case of a rheocasting process, in which Al-Si alloy (A356 alloy) is solidified by stirring in a cylindrical mould placed in the annulus of a linear electromagnetic stirrer. The metal in the mould is simultaneously cooled and stirred to produce a cylindrical billet with non-dendritic globular microstructure. Temperature is measured at key locations in the mould to assess the various heat exchange processes prevalent in the mould and to monitor the solidification rate. The results obtained by energy balance method are compared with those by the conventional procedure of calculating solid fraction using the Schiel equation.

Qualitative theorem proving in linear constraints

We know, from the classical work of Tarski on real closed fields, that elimination is, in principle, a fundamental engine for mechanized deduction. But, in practice, the high complexity of elimination algorithms has limited their use in the realization of mechanical theorem proving. We advocate qualitative theorem proving, where elimination is attractive since most processes of reasoning take place through the elimination of middle terms, and because the computational complexity of the proof is not an issue. Indeed what we need is the existence of the proof and not its mechanization. In this paper, we treat the linear case and illustrate the power of this paradigm by giving extremely simple proofs of two central theorems in the complexity and geometry of linear programming.

Synthesis, biological studies of linear and branched arabinofuranoside-containing glycolipids and their interaction with surfactant protein A

Oligoarabinofuranoside-containing glycolipids relevant to mycobacterial cell wall components were synthesized in order to understand the functional roles of such glycolipids. A series of linear tetra-, hexa-, octa-and a branched heptasaccharide oligoarabinofuranosides, with 1 -> 2 and 1 -> 5 a-linkages between the furanoside residues, were synthesized by chemical methods from readily available monomer building blocks. Upon the synthesis of glycolipids, constituted with a double alkyl chain-substituted sn-glycerol core and oligosaccharide fragments, biological studies were performed to identify the effect of synthetic glycolipids on the biofilm formation and sliding motilities of Mycobacterium smegmatis. Synthetic glycolipids and arabinofuranosides displayed an inhibitory effect on the growth profile, but mostly on the biofilm formation and maturation. Similarly, synthetic compounds also influenced the sliding motility of the bacteria. Further, biophysical studies were undertaken, so as to identify the interactions of the glycolipids with a pulmonary surfactant protein, namely surfactant protein A (SP-A), with the aid of the surface plasmon resonance technique. Specificities of each glycolipid interacting with SP-A were thus evaluated. From this study, glycolipids were found to exhibit higher apparent association constants than the corresponding oligosaccharide portion alone, without the double alkyl group-substituted glycerol core.

Fluorescence quenching of biologically active carboxamide by aniline and carbon tetrachloride in different solvents using Stern-Volmer plots

Fluorescence quenching of biologically active carboxamide namely (E)-2-(4-chlorobenzylideneamino)-N-(2-chlorophenyl)-4,5,6,7-tetrahydrobe nzo[b]thiophene-3-carboxamide [ECNCTTC] by aniline and carbon tetrachloride (CCl(4)) quenchers in different solvents using steady state method and time resolved method using only one solvent has been carried out at room temperature to understand the role of quenching mechanisms. The Stern-Volmer plot has been found to be linear for all the solvents studied. The probability of quenching per encounter p (p') was determined in all the solvents and was found to be less than unity. Further, from the studies of rate parameters and life time measurements in n-heptane and cyclohexane with aniline and carbon tetrachloride as quenchers have been shown that, the phenomenon of quenching is generally governed by the well-known Stern-Volmer (S-V) plot. The activation energy E(a) (or E(a)') of quenching was determined using the literature values of activation energy of diffusion E(d) and the experimentally determined values of p (or p'). It has been found that, the activation energy E(a) (E(a)') is greater than the activation energy for diffusion E(d) in all solvents. Hence, from the magnitudes of E(a) (or E(a)') as well as p (or p') infer that, the quenching mechanism is not solely due to the material diffusion, but there is also contribution from the activation energy. (C) 2011 Elsevier B.V. All rights reserved.

Contrained linear spectral unmixing technique for regional land cover mapping using MODIS data

Over the last few decades, there has been a significant land cover (LC) change across the globe due to the increasing demand of the burgeoning population and urban sprawl. In order to take account of the change, there is a need for accurate and up- to-date LC maps. Mapping and monitoring of LC in India is being carried out at national level using multi-temporal IRS AWiFS data. Multispectral data such as IKONOS, Landsat- TM/ETM+, IRS-1C/D LISS-III/IV, AWiFS and SPOT-5, etc. have adequate spatial resolution (~ 1m to 56m) for LC mapping to generate 1:50,000 maps. However, for developing countries and those with large geographical extent, seasonal LC mapping is prohibitive with data from commercial sensors of limited spatial coverage. Superspectral data from the MODIS sensor are freely available, have better temporal (8 day composites) and spectral information. MODIS pixels typically contain a mixture of various LC types (due to coarse spatial resolution of 250, 500 and 1000 m), especially in more fragmented landscapes. In this context, linear spectral unmixing would be useful for mapping patchy land covers, such as those that characterise much of the Indian subcontinent. This work evaluates the existing unmixing technique for LC mapping using MODIS data, using end- members that are extracted through Pixel Purity Index (PPI), Scatter plot and N-dimensional visualisation. The abundance maps were generated for agriculture, built up, forest, plantations, waste land/others and water bodies. The assessment of the results using ground truth and a LISS-III classified map shows 86% overall accuracy, suggesting the potential for broad-scale applicability of the technique with superspectral data for natural resource planning and inventory applications.

Linear Filtering in MDCT domain

In this paper, expressions for convolution multiplication properties of MDCT are derived starting from the equivalent DFT representations. Using these expressions, methods for implementing linear filtering through block convolution in the MDCT domain are presented. The implementation is exact for symmetric filters and approximate for non-symmetric filters in the case of rectangular window based MDCT. For a general MDCT window function, the filtering is done on the windowed segments and hence the convolution is approximate for symmetric as well as non-symmetric filters. This approximation error is shown to be perceptually insignificant for symmetric impulse response filters. Moreover, the inherent $50 \%$ overlap between adjacent frames used in MDCT computation does reduce this approximation error similar to smoothing of other block processing errors. The presented techniques are useful for compressed domain processing of audio signals.

Altitude variation of aerosol properties over the Himalayan range inferred from spatial measurements

Altitude variations of the mass concentration of black carbon, number concentration of composite aerosols are examined along with the columnar spectral aerosol optical depths using state of the art instruments and the Angstrom parameters are inferred from the ground based measurements at several altitude levels, en route from Manora Peak, Nainital (similar to 1950 m above mean sea level) to a low altitude station Haldwani (similar to 330 m above mean sea level) at its foothill within an aerial distance of <10,000 m. The measurements were done during the winter months (November-February) of 2005, 2006 and 2007 under fair weather conditions. The results show a rapid decrease in all the measured parameters with increase in altitude, with >60% contribution to the AOD coming from the regions below 1000 m. The Angstrom wavelength exponent remained high in the well mixed region, and decreased above. The normalized AOD gradient was used to estimate aerosol mixing height, which was found to be in the altitude range 1000-1500 m, above which the particle concentrations are slowly varying as a function of altitude. The heating rate at the surface is found to be maximum but decreases sharply with increase in altitude. Analysis of the wavelength dependence of absorption aerosol optical depth (AAOD) showed that the aerosol absorption over the site is generally due to mixed aerosols. (C) 2011 Elsevier Ltd. All rights reserved.