Maximal regularity for second order non-autonomous Cauchy problems

We consider some non-autonomous second order Cauchy problems of the form u + B(t)(u) over dot + A(t)u = f (t is an element of [0, T]), u(0) = (u) over dot(0) = 0. We assume that the first order problem (u) over dot + B(t)u = f (t is an element of [0, T]), u(0) = 0, has L-p-maximal regularity. Then we establish L-p-maximal regularity of the second order problem in situations when the domains of B(t(1)) and A(t(2)) always coincide, or when A(t) = kappa B(t).

Probing the Neutral Edge Modes in Transport across a Point Contact via Thermal Effects in the Read-Rezayi Non-Abelian Quantum Hall States

Non-Abelian quantum Hall states are characterized by the simultaneous appearance of charge and neutral gapless edge modes, with the structure of the latter being intricately related to the existence of bulk quasiparticle excitations obeying non-Abelian statistics. Here we propose a scenario for detecting the neutral modes by having two point contacts in series separated by a distance set by the thermal equilibration length of the charge mode. We show that by using the first point contact as a heating device, the excess charge noise measured at the second point contact carries a nontrivial signature of the presence of the neutral mode. We also obtain explicit expressions for the thermal conductance and corresponding Lorentz number for transport across a quantum point contact between two edges held at different temperatures and chemical potentials.

Influence of non-stoichiometric defects on nonlinear absorption and refraction in Nd:Zn co-doped lithium niobate

Nonlinear absorption and refraction phenomena in stoichiometric lithium niobate (SLN) pure and co-doped with Zn and Nd, and congruent lithium niobate (CLN) were investigated using Z-scan technique. Femtosecond laser pulses from Ti:Sapphire laser (800 nm, 110 fs pulse width and 1 kHz repetition rate) were utilized for the experiment. The process responsible for nonlinear behavior of the samples was identified to be three photon absorption (3PA). This is in agreement with the band gap energies of the samples obtained from the linear absorption cut off and the slope of the plot of Ln(1 − TOA) vs. Ln(I0) using Sutherland’s theory (s = 2.1, for 3PA). The nonlinear refractive index (n2) of Zn doped samples was found to be lower than that of pure samples. Our experiments show that there exists a correlation between the nonlinear properties and the stoichiometry of the samples. The values of n2 fall into the same range as those obtained for the materials of similar band gap.

Long Wavelength Peristaltic Transport of Non-Newton Fluids

Solutions are obtained for the stream function and the pressure field for the flow of non-Newtonian fluids in a tube by long peristaltic waves of arbitrary shape. The axial velocity profiles and stress distributions on the wall are discussed for particular waves of some practical interest. The effect of non- Newtonian character of the fluid is examined.

The nature of non-equilibrium solidification of undercooled Agsingle bondCu alloys in contact with primary copper dendrites

Liquids of silver-copper alloys with near eutectic compositions embedded in a copper matrix were undercooled. The structural and microstructural investigations of these alloys solidified from undercooled temperature indicated the absence of both the eutectic reaction and diffusionless transformation below the equal free energy curve (T0). Instead the liquid maintained local equilibrium with the copper dendrites continuously until it intersected the extended solidus of the silver rich solid solution.

Non-linear flapping vibrations of rotating blades

The non-linear equations of motion of a rotating blade undergoing extensional and flapwise bending vibration are derived, including non-linearities up to O (ε3). The strain-displacement relationship derived is compared with expressions derived by earlier investigators and the errors and the approximations made in some of those are brought out. The equations of motion are solved under the inextensionality condition to obtain the influence of the amplitude on the fundamental flapwise natural frequency of the rotating blade. It is found that large finite amplitudes have a softening effect on the flapwise frequency and that this influence becomes stronger at higher speeds of rotation.

Non-stationary signal analysis by least mean fourth (LMF) adaptive algorithm

A modified least mean fourth (LMF) adaptive algorithm applicable to non-stationary signals is presented. The performance of the proposed algorithm is studied by simulation for non-stationarities in bandwidth, centre frequency and gain of a stochastic signal. These non-stationarities are in the form of linear, sinusoidal and jump variations of the parameters. The proposed LMF adaptation is found to have better parameter tracking capability than the LMS adaptation for the same speed of convergence.

A non-linear analogue-to-digital converter for linearization of transducer input-output relationships

Analogue and digital techniques for linearization of non-linear input-output relationship of transducers are briefly reviewed. The condition required for linearizing a non-linear function y = f(x) using a non-linear analogue-to-digital converter, is explained. A simple technique to construct a non-linear digital-to-analogue converter, based on ' segments of equal digital interval ' is described. The technique was used to build an N-DAC which can be employed in a successive approximation or counter-ramp type ADC to linearize the non-linear transfer function of a thermistor-resistor combination. The possibility of achieving an order of magnitude higher accuracy in the measurement of temperature is shown.

Natural convection from a vertical cone in a porous medium due to the combined effects of heat and mass diffusion with non-uniform wall temperature/concentration or heat/mass flux and suction/injection

An analysis has been carried out to study the non-Darcy natural convention flow of Newtonian fluids on a vertical cone embedded in a saturated porous medium with power-law variation of the wall temperature/concentration or heat/mass flux and suction/injection with the streamwise distance x. Both non-similar and self-similar solutions have been obtained. The effects of non-Darcy parameter, ratio of the buoyancy forces due to mass and heat diffusion, variation of wall temperature/concentration or heat/mass flux and suction/injection on the Nusselt and Sherwood numbers have been studied.

Exact evaluation of Gaussian path integrals involving non-local potentials

An exact expression for the calculation of gaussian path integrals involving non-local potentials is given. Its utility is demonstrated by using it to evaluate a path integral arising in the study of an electron gas in a random potential.

Analysis of an internally mountable accelerometer balance system for use with non-isotropic models in shock tunnels

Knowledge of drag force is an important design parameter in aerodynamics. Measurement of aerodynamic forces at hypersonic speed is a challenge and usually ground test facilities like shock tunnels are used to carry out such tests. Accelerometer based force balances are commonly employed for measuring aerodynamic drag around bodies in hypersonic shock tunnels. In this study, we present an analysis of the effect of model material on the performance of an accelerometer balance used for measurement of drag in impulse facilities. From the experimental studies performed on models constructed out of Bakelite HYLEM and Aluminum, it is clear that the rigid body assumption does not hold good during the short testing duration available in shock tunnels. This is notwithstanding the fact that the rubber bush used for supporting the model allows unconstrained motion of the model during the short testing time available in the shock tunnel. The vibrations induced in the model on impact loading in the shock tunnel are damped out in metallic model, resulting in a smooth acceleration signal, while the signal become noisy and non-linear when we use non-isotropic materials like Bakelite HYLEM. This also implies that careful analysis and proper data reduction methodologies are necessary for measuring aerodynamic drag for non-metallic models in shock tunnels. The results from the drag measurements carried out using a 60 degrees half angle blunt cone is given in the present analysis.

Constitutive modeling of shape memory alloy wire with non-local rate kinetics

A constitutive modeling approach for shape memory alloy (SMA) wire by taking into account the microstructural phase inhomogeneity and the associated solid-solid phase transformation kinetics is reported in this paper. The approach is applicable to general thermomechanical loading. Characterization of various scales in the non-local rate sensitive kinetics is the main focus of this paper. Design of SMA materials and actuators not only involve an optimal exploitation of the hysteresis loops during loading-unloading, but also accounts for fatigue and training cycle identifications. For a successful design of SMA integrated actuator systems, it is essential to include the microstructural inhomogeneity effects and the loading rate dependence of the martensitic evolution, since these factors play predominant role in fatigue. In the proposed formulation, the evolution of new phase is assumed according to Weibull distribution. Fourier transformation and finite difference methods are applied to arrive at the analytical form of two important scaling parameters. The ratio of these scaling parameters is of the order of 10(6) for stress-free temperature-induced transformation and 10(4) for stress-induced transformation. These scaling parameters are used in order to study the effect of microstructural variation on the thermo-mechanical force and interface driving force. It is observed that the interface driving force is significant during the evolution. Increase in the slopes of the transformation start and end regions in the stress-strain hysteresis loop is observed for mechanical loading with higher rates.

Enzyme-catalysed non-oxidative decarboxylation of aromatic acids: I.Purification and spectroscopic properties of 2,3 dihydroxybenzoic acid decarboxylase from Image Image

In order to understand the molecular mechanism of non-oxidative decarboxylation of aromatic acids observed in microbial systems, 2,3 dihydroxybenzoic acid (DHBA) decarboxylase from Image Image was purified to homogeneity by affinity chromatography. The enzyme (Mr 120 kDa) had four identical subunits (28 kDa each) and was specific for DHBA. It had a pH optimum of 5.2 and Km was 0.34mM. The decarboxylation did not require any cofactors, nor did the enzyme had any pyruvoyl group at the active site. The carboxyl group and hydroxyl group in the Image -position were required for activity. The preliminary spectroscopic properties of the enzyme are also reported.

Non-linear resonance in strings under narrow band random excitation, part I: Planar response and stability

Non-linear planar response of a string to planar narrow band random excitation is investigated in this paper. A response equation for the mean square deflection σ2 is obtained under a single mode approximation by using the equivalent linearization technique. It is shown that the response is triple valued, as in the case of harmonic excitation, if the centre frequency of excitation Ω lies in a certain specified range. The triple valued response occurs only if the excitation bandwidth β is smaller than a critical value βcrit which is a monotonically increasing function of the intensity of excitation. An approximate method of investigating the almost sure asymptotic stability of the solution is presented and regions of instability in the Ω-σ2 plane have been charted. It is shown that planar response can become unstable either due to an unbounded growth of the in-plane component of motion or due to a spontaneous appearance of an out-of-plane component.

Non-bonded interactions in 2,2,4,4-tetramethyl-1,3-cyclobutanedithione and 2,2,4,4-tetramethyl-3-thio-1,3-cyclobutanedione

Electronic absorption and emission spectra as well as He(I) photoelectron spectra of 2,2,4,4-tetramethyl-,3-cyclobutanedithione and 2,2,4,4-tetramethyl-1-3-thio-1,3-cyclobutanedione have been interpreted on the basis of molecular orbital calculations. The results show that the non-bonded orbital of the dithione is split owing to through-bond interaction, the magnitude of splitting being 0.4 eV. The π* orbital of the dithione appears to be split by about 0.2 eV. Electronic absorption spectra show evidence for the existence of four n—π* transitions, arising out of the splitting of the orbitals referred to above, just as in the case of 2,2,4,4-tetramethyl-1,3-cyclobutanedione. Electronic and photoelectron spectra of the thio-dione show evidence for weak interaction between the C=S and C&.zdbnd;O groups, probably via π* orbitals. Infrared spectra of both the dithione and the thio-dione are consistent with the planar cyclobutane ring; the ring-puckering frequency responsible for non-bonded interactions is around 67 cm−1 in both the dithione and the thio-dione, the value not being very different from that in the dione. The 1,3-transannular distance is also similar in the three molecules.