Infinite dimensional slow modulations in a well known delayed model for cutting tool vibrations

We apply the method of multiple scales (MMS) to a well-known model of regenerative cutting vibrations in the large delay regime. By ``large'' we mean the delay is much larger than the timescale of typical cutting tool oscillations. The MMS up to second order, recently developed for such systems, is applied here to study tool dynamics in the large delay regime. The second order analysis is found to be much more accurate than the first order analysis. Numerical integration of the MMS slow flow is much faster than for the original equation, yet shows excellent accuracy in that plotted solutions of moderate amplitudes are visually near-indistinguishable. The advantages of the present analysis are that infinite dimensional dynamics is retained in the slow flow, while the more usual center manifold reduction gives a planar phase space; lower-dimensional dynamical features, such as Hopf bifurcations and families of periodic solutions, are also captured by the MMS; the strong sensitivity of the slow modulation dynamics to small changes in parameter values, peculiar to such systems with large delays, is seen clearly; and though certain parameters are treated as small (or, reciprocally, large), the analysis is not restricted to infinitesimal distances from the Hopf bifurcation.

Analysis of flow near a dug well in an unconfined aquifer

A numerical analysis of flow to a dug well in an unconfined aquifer is made, taking into account well storage, elastic storage release, gravity drainage, anisotropy, partial penetration, vertical flow and seepage surface at the well face, and treating the water table in the aquifer and water level in the well as unknown boundaries. The pumped discharge is maintained constant. The solution is obtained by a two-level iterative scheme. The effects of governing parameters on the drawdown, development of seepage surface and contribution from aquifer flow to the total discharge are discussed. The degree of anisotropy and partial penetration are found to be the parameters which affect the flow characteristics most significantly. The effect of anisotropy on the development of seepage surface is very pronounced.

An investigation of well-characterized small gold clusters by photoelectron spectroscopy, tunneling spectroscopy, and cognate techniques

After microscopic characterization of the size distributions of gold clusters, deposited on carbon substrates by vacuum evaporation or by soft landing, Au(4f') binding energy of the clusters has been measured as a function of the mean cluster size. Similar measurements have been carried out on Au clusters prepared from sols by chemical means and high-nuclearity cluster compounds. In general, small clusters with a mean diameter of $2 nm show significantly larger binding energies than the bulk metal value, due to the onset of nonmetallicity. Nonmetallicity manifests itself in terms of a tunneling conductance gap only in clusters of diameter ;5 1 nm containing 40 atoms or fewer.

High sensitive Static fiber Bragg grating strain sensing using lasers locked to relative frequency reference

A novel high sensitive fiber Bragg grating (FBG) strain sensing technique using lasers locked to relative frequency reference is proposed and analyzed theoretically. Static strain on FBG independent of temperature can be measured by locking frequency of diode laser to the mid reflection frequency of matched reference FBG, which responds to temperature similar to that of the sensor FBG, but is immune to strain applied to the same. Difference between light intensities reflected from the sensor and reference FBGs (proportional to the difference between respective pass band gains at the diode laser frequency) is not only proportional to the relative strain between the sensor and reference FBGs but also independent of servo residual frequency errors. Usage of relative frequency reference avoids all complexities involved in the usage of absolute frequency reference, hence, making the system simple and economical. Theoretical limit for dynamic and static strain sensitivities considering all major noise contributions are of the order of 25 (p epsilon) / root Hz and 1.2 n epsilon / root Hz respectively.

Effect of magnetic field on the binding energy of a hydrogenic donor in a vertical bar z vertical bar(2/3) quantum well

We have calculated the binding energy of a hydrogenic donor in a quantum well with potential shape proportional to \z\(2/3) as a function of the width of the quantum well and the barrier height under an applied uniform magnetic field along the a axis. As the well width decreases, the binding energy increases initially up to a critical well width (which is nearly the same for all magnetic fields) at which there is a turnover. The results are qualitatively similar to those of a hydrogenic donor in a rectangular well. We have also calculated [rho(2)](1/2) and [z(2)](1/2) for the donor electron. [rho(2)](1/2) is found to be strongly dependent on the magnetic field for a given well width and weakly dependent on the well width and the barrier height, for a given value of magnetic field [z(2)](1/2) is weakly dependent on the applied magnetic field. The probability of finding the donor electron inside the well shows a rapid decrease as the well width is reduced at nearly the well width at which the binding energy shows a maximum.

A scaling analysis of momentum and heat transport in laser surface melting

In this paper, we outline a systematic procedure for scaling analysis of momentum and heat transfer in laser melted pools. With suitable choices of non-dimensionalising parameters, the governing equations coupled with appropriate boundary conditions are first scaled, and the relative significance of various terms appearing in them are accordingly analysed. The analysis is then utilised to predict the orders of magnitude of some important quantities, such as the velocity scale at the top surface, velocity boundary layer thickness, maximum temperature rise in the pool, fully developed pool-depth, and time required for initiation of melting. Using the scaling predictions, the influence of various processing parameters on the system variables can be well recognised, which enables us to develop a deeper insight into the physical problem of interest. Moreover, some of the quantities predicted from the scaling analysis can be utilised for optimised selection of appropriate grid-size and time-steps for full numerical simulation of the process. The scaling predictions are finally assessed by comparison with experimental and numerical results quoted in the literature, and an excellent qualitative agreement is observed.

Time-Resolved Resonance Raman Spectroscopy: Exploring Reactive Intermediates

The study of reaction mechanisms involves systematic investigations of the correlation between structure, reactivity, and time. The challenge is to be able to observe the chemical changes undergone by reactants as they change into products via one or several intermediates such as electronic excited states (singlet and triplet), radicals, radical ions, carbocations, carbanions, carbenes, nitrenes, nitrinium ions, etc. The vast array of intermediates and timescales means there is no single ``do-it-all'' technique. The simultaneous advances in contemporary time-resolved Raman spectroscopic techniques and computational methods have done much towards visualizing molecular fingerprint snapshots of the reactive intermediates in the microsecond to femtosecond time domain. Raman spectroscopy and its sensitive counterpart resonance Raman spectroscopy have been well proven as means for determining molecular structure, chemical bonding, reactivity, and dynamics of short-lived intermediates in solution phase and are advantageous in comparison to commonly used time-resolved absorption and emission spectroscopy. Today time-resolved Raman spectroscopy is a mature technique; its development owes much to the advent of pulsed tunable lasers, highly efficient spectrometers, and high speed, highly sensitive multichannel detectors able to collect a complete spectrum. This review article will provide a brief chronological development of the experimental setup and demonstrate how experimentalists have conquered numerous challenges to obtain background-free (removing fluorescence), intense, and highly spectrally resolved Raman spectra in the nanosecond to microsecond (ns-mu s) and picosecond (ps) time domains and, perhaps surprisingly, laid the foundations for new techniques such as spatially offset Raman spectroscopy.

A simple numerical method for three-dimensional analysis of simple expansion chamber mufflers of rectangular as well as circular cross-section with a stationary medium

Three-dimensional effects are a primary source of discrepancy between the measured values of automotive muffler performance and those predicted by the plane wave theory at higher frequencies. The basically exact method of (truncated) eigenfunction expansions for simple expansion chambers involves very complicated algebra, and the numerical finite element method requires large computation time and core storage. A simple numerical method is presented in this paper. It makes use of compatibility conditions for acoustic pressure and particle velocity at a number of equally spaced points in the planes of the junctions (or area discontinuities) to generate the required number of algebraic equations for evaluation of the relative amplitudes of the various modes (eigenfunctions), the total number of which is proportional to the area ratio. The method is demonstrated for evaluation of the four-pole parameters of rigid-walled, simple expansion chambers of rectangular as well as circular cross-section for the case of a stationary medium. Computed values of transmission loss are compared with those computed by means of the plane wave theory, in order to highlight the onset (cutting-on) of various higher order modes and the effect thereof on transmission loss of the muffler. These are also compared with predictions of the finite element methods (FEM) and the exact methods involving eigenfunction expansions, in order to demonstrate the accuracy of the simple method presented here.

On the cut‐on frequencies of a large round duct with azimuthal as well as radial partitions

This letter deals with a three‐dimensional analysis of circular sectors and annular segments resulting from the partitioning of a round (cylindrical) duct for use in an active noise control system. The relevant frequency equations are derived for stationary medium and solved numerically to arrive at the cut‐on frequencies of the first few modes. The resultant table indicates among other things that azimuthal partitioning does not raise the cutoff frequency (the smallest cut‐on frequency) beyond a particular value, and that radial partitioning is counterproductive in that respect.

Theoretical gain optimization studies in 10.6 μm CO2–N2 gasdynamic lasers. IV. Further results of parametric study

Based on a method proposed by Reddy and Shanmugasundaram, similar solutions have been obtained for the steady inviscid quasi‐one‐dimensional nonreacting flow in the supersonic nozzle of CO2–N2–H2O and CO2–N2–He gasdynamic laser systems. Instead of using the correlations of a nonsimilar function NS for pure N2 gas, as is done in previous publications, the NS correlations are computed here for the actual gas mixtures used in the gasdynamic lasers. Optimum small‐signal optical gain and the corresponding optimum values of the operating parameters like reservoir pressure and temperature and nozzle area ratio are computed using these correlations. The present results are compared with the previous results and the main differences are discussed.

Spontaneous formation of branched nanochains from room temperature molten amides: visible and near-IR active, SERS substrates for non-fluorescent and fluorescent analytes

Highly stable, branched gold nanoworms are formed spontaneously in an acetamide-based room temperature molten solvent without any additional external stabilizing or aggregating agent. The nanoworms can be anchored onto solid substrates such as indium tin oxide (ITO) without any change in morphology. The anchored nanoworms are explored as substrates for surface enhanced Raman scattering (SERS) studies using non-fluorescent 4-mercaptobenzoic acid (4-MBA) and fluorescent rhodamine 6G (R6G) as probe molecules. The anchored nanostructured particles respond to near IR (1064 nm) as well as visible (785, 632.8 and 514 nm) excitation lasers and yield good surface enhancement in Raman signals. Enhancement factors of the order 10(6)-10(7) are determined for the analytes using a 1064 nm excitation source. Minimum detection limits based on adsorption from ethanolic solutions of 1028 M 4-MBA and aqueous solutions of 1027 M R6G are achieved. Experimental Raman frequencies and frequencies estimated by DFT calculations are in fairly good agreement. SERS imaging of the nanostructures suggests that the substrates comprising of three dimensional, highly interlinked particles are more suited than particles fused in one dimension. The high SERS activity of the branched nanoworms may be attributed to both electromagnetic and charge transfer effects.