Detection of a periodic structure embedded in surface roughness, for various correlation functions

This paper deals with surface profilometry, where we try to detect a periodic structure, hidden in randomness using the matched filter method of analysing the intensity of light, scattered from the surface. From the direct problem of light scattering from a composite rough surface of the above type, we find that the detectability of the periodic structure can be hindered by the randomness, being dependent on the correlation function of the random part. In our earlier works, we had concentrated mainly on the Cauchy-type correlation function for the rough part. In the present work, we show that this technique can determine the periodic structure of different kinds of correlation functions of the roughness, including Cauchy, Gaussian etc. We study the detection by the matched filter method as the nature of the correlation function is varied.

The variation of N-gamma with footing roughness using the method of characteristics

By using the method of characteristics, the effect of footing-soil interface friction angle (delta) on the bearing capacity factor N-gamma was computed for a strip footing. The analysis was performed by employing a curved trapped wedge under the footing base; this wedge joins the footing base at a distance B-t from the footing edge. For a given footing width (B), the value of B-t increases continuously with a decrease in delta. For delta = 0, no trapped wedge exists below the footing base, that is, B-t/B = 0.5. On the contrary, with delta = phi, the point of emergence of the trapped wedge approaches toward the footing edge with an increase in phi. The magnitude of N-gamma increases substantially with an increase in delta/phi. The maximum depth of the plastic zone becomes higher for greater values of delta/phi. The results from the present analysis were found to compare well with those reported in the literature.

Scattering of electromagnetic waves from chirally coated cylinders

The problem of electromagnetic scattering from an isotropic homogeneous chirally coated conducting cylinder is analysed. The cylinder is assumed to be illuminated by either a transverse magnetic or a transverse electric wave. Mie's analysis is used to evaluate the scattering characteristics. The computed results include the evaluation of the normalized scattering width and the absorption efficiency. The results show that there is a significant reduction in the normalized scattering width as compared to a RAM coated cylinder. This reduction has been attributed to increased absorption.

Small-angle neutron scattering study of micellar structures of dimeric surfactants

Dimeric or gemini surfactants consist of two hydrophobic chains and two hydrophilic head groups co; valently connected by a hydrocarbon spacer. Small-angle neutron scattering measurements from bis-cationic C16H33N+(CH3)(2)-(CH2)(m)-N+(CH3)(2)C(16)H(33)2Br(-) dimeric surfactants, referred to-as 16-m-16, for different length of hydrocarbon spacers m-3-6, 8, 10, and 12, are reported. The measurements have been carried out at various concentrations: C=2.5 and 10 mM for all m and C=30 and 50 mM for m greater than or equal to 5. It is found that micellar structure depends on the length of the spacer. Micelles are disks for m=3, cylindrical for m=4, and prolate ellipsoidals for other values of m. These structural results are in agreement with the theoretical predictions based on the packing parameter. It has also been observed that conformation of the spacer and the hydrophobic chains in the interior of the micelle change as the length of the spacer is increased. The concentration dependence for m greater than or equal to 5 shows that the effect of surfactant concentration on the size of the micelle is more pronounced for m=5 and 12 than for the intermediate spacers. The fractional charge on the micelle increases with the increase in spacer length and decreases when the concentration is increased.

Evidence of clustering in an aqueous electrolyte solution: a small-angle X-ray scattering study

The work reported hen was motivated by a desire to verify the existence of structure - specifically MP-rich clusters induced by sodium bromide (NaBr) in the ternary liquid mixture 3-methylpyridine (Mf) + water(W) + NaBr. We present small-angle X-ray scattering (SAXS) measurements in this mixture. These measurements were obtained at room temperature (similar to 298 K) in the one-phase region (below the relevant lower consolute points, T(L)s) at different values of X (i.e., X = 0.02 - 0.17), where X is the weight fraction of NaBr in the mixture. Cluster-size distribution, estimated on the assumption that the clusters are spherical, shows systematic behaviour in that the peak of the distribution shifts rewards larger values of cluster radius as X increases. The largest spatial extent of the clusters (similar to 4.5 nm) is seen at X = 0.17. Data analysis assuming arbitrary shapes and sizes of clusters gives a limiting value of cluster size (- 4.5 nm) that is not very sensitive to X. It is suggested that the cluster size determined may not be the same as the usual critical-point fluctuations far removed from the critical point (T-L). The influence of the additional length scale due to clustering is discussed from the standpoint of crossover from Ising to mean-field critical behaviour, when moving away from the T-L.

Measurement of Partition Coefficients of Substituted Benzoic Acids between Two Immiscible Solvents by Hyper-Rayleigh Scattering

We demonstrate that the hyper-Rayleigh scattering technique can be employed to measure the partition coefficient (k(p)) of a solute in a mixture of two immiscible solvents. Specifically, partition coefficients of six substituted benzoic acids in water/toluene (1:1 v/v) and water/chloroform (1:1 v/v) systems have been measured. Our values compare well with the k(p) values measured earlier by other techniques, The advantages offered by this technique are also discussed.

Genesis of workpiece roughness generated in surface grinding and polishing of metals

Assuming the grinding wheel surface to be fractal in nature, the maximum envelope profile of the wheel and contact deflections are estimated over a range of length scales. This gives an estimate of the 'no wear' roughness of a surface ground metal. Four test materials, aluminum, copper, titanium, and steel are surface ground and their surface power spectra were estimated. The departure of this power spectra from the 'no wear' estimates is studied in terms of the traction-induced wear damage of the surfaces. The surface power spectra in grinding are influenced by hardness and the power is enhanced by wear damage. No such correlation with hardness was found for the polished surface, the roughness of which is insensitive to mechanical properties and appears to be influenced by microstructure and physical properties of the material.

pi-conjugation and conformation in a semiconducting polymer: small angle x-ray scattering study

Small angle x-ray scattering (SAXS) in a poly[2-methoxy-5-(2'-ethyl-hexyloxy)-1,4-phenylene vinylene] (MEH-PPV) solution has shown the important role of pi-electron conjugation in controlling the chain conformation and assembly. By increasing the extent of conjugation from 30 to 100%, the persistence length (l(p)) increases from 20 to 66 angstrom. Moreover, a pronounced second peak in the pair distribution function has been observed in a fully conjugated chain, at larger length scales. This feature indicates that the chain segments tend to self-assemble as the conjugation along the chain increases. Xylene enhances the rigidity of the PPV backbone to yield extended structures, while tetrahydrofuran solvates the side groups to form compact coils in which the lp is much shorter.

Raman scattering investigation of the phase transitions in (NH4)2ZnBr4

Results of Raman spectroscopic studies of (NH4)2ZnBr4 crystal in the spectral range from 20-250 cm-1 and over a range of temperature from 90K to 440K covering the low temperature ferroelectric and high temperature incommensurate phases are presented. The plots of the integrated areas and peak heights of the strong Raman lines versus temperature show anomalous behaviour near the two phase transitions.

Light scattering studies on solutions of chlorinated rubber

Measurements have been made of the depolarisation factors \sigma u ,\sigma v ,\sigma h, and the intensity of scattering in the horizontal transverse direction, in the case of solutions of four different samples of chlorinated rubber in carbon tetrachloride. The size, shape and molecular weight of the micelles have been deduced by the application of the light scattering theories of Gans, Vrklajan and Katalinic and Debye. The extent to which the degradation of the rubber molecule occurs on chlorination has also been assessed.

Optimum choice of wavelengths in the anomalous scattering technique with synchrotron radiation

A formula has been derived for the mean-square error in the phases of crystal reflections determined through the multiwavelength anomalous scattering method.The error is written in terms of a simple function of the positions in the complex plane of the 'centres' corresponding to the different wavelengths. For the case of three centres, the mean-square error is inversely proportional to the area of the triangle formed by them.

Resonances, scattering theory, and rigged Hilbert spaces

The problem of decaying states and resonances is examined within the framework of scattering theory in a rigged Hilbert space formalism. The stationary free,''in,'' and ''out'' eigenvectors of formal scattering theory, which have a rigorous setting in rigged Hilbert space, are considered to be analytic functions of the energy eigenvalue. The value of these analytic functions at any point of regularity, real or complex, is an eigenvector with eigenvalue equal to the position of the point. The poles of the eigenvector families give origin to other eigenvectors of the Hamiltonian: the singularities of the ''out'' eigenvector family are the same as those of the continued S matrix, so that resonances are seen as eigenvectors of the Hamiltonian with eigenvalue equal to their location in the complex energy plane. Cauchy theorem then provides for expansions in terms of ''complete'' sets of eigenvectors with complex eigenvalues of the Hamiltonian. Applying such expansions to the survival amplitude of a decaying state, one finds that resonances give discrete contributions with purely exponential time behavior; the background is of course present, but explicitly separated. The resolvent of the Hamiltonian, restricted to the nuclear space appearing in the rigged Hilbert space, can be continued across the absolutely continuous spectrum; the singularities of the continuation are the same as those of the ''out'' eigenvectors. The free, ''in'' and ''out'' eigenvectors with complex eigenvalues and those corresponding to resonances can be approximated by physical vectors in the Hilbert space, as plane waves can. The need for having some further physical information in addition to the specification of the total Hamiltonian is apparent in the proposed framework. The formalism is applied to the Lee–Friedrichs model and to the scattering of a spinless particle by a local central potential. Journal of Mathematical Physics is copyrighted by The American Institute of Physics.

Electron-electron scattering and ultrasonic attenuation in potassium

The electron-electron scattering contribution to the ultrasonic attenuation in potassium at low temperatures is evaluated using the Landau Fermi liquid theory. The scattering function is evaluated using the approximation suggested by MacDonald and Geldart. The results are compared with theoretically evaluated electron-phonon scattering contributions. The results show that the electron-electron scattering contribution is of the same order as the electron-phonon scattering contribution in the 2–5 K range. Below 2 K the electron-electron scattering predominates.