Spherical aberration and its correction using Lie algebraic methods

We discuss three methods to correct spherical aberration for a point to point imaging system. First, results obtained using Fermat's principle and the ray tracing method are described briefly. Next, we obtain solutions using Lie algebraic techniques. Even though one cannot always obtain analytical results using this method, it is often more powerful than the first method. The result obtained with this approach is compared and found to agree with the exact result of the first method.

Application of novel method for surface-ray tracing over hyperboloidal scatterers

A novel geodesic constant method has been developed for the hitherto unsolved problem of surface-ray tracing over a class of surface, namely the general hyperboloid of revolution (GHOR). All the ray-geometric parameters are obtained analytically in a one-parameter form. The ray parameters derived here for the first time can be readily used in the UTD formulation for computing the mutual coupling between the antennas located on the GHOR.

A geodesic constant method for computing high-frequency mutual coupling between antennas on general quadric cylinders

A Geodesic Constant Method (GCM) is outlined which provides a common approach to ray tracing on quadric cylinders in general, and yields all the surface ray-geometric parameters required in the UTD mutual coupling analysis of conformal antenna arrays in the closed form. The approach permits the incorporation of a shaping parameter which permits the modeling of quadric cylindrical surfaces of desired sharpness/flatness with a common set of equations. The mutual admittance between the slots on a general parabolic cylinder is obtained as an illustration of the applicability of the GCM.

Surface-ray tracing on hybrid surfaces of revolution for UTD mutual coupling analysis

An angle invariance property based on Hertz's principle of particle dynamics is employed to facilitate the surface-ray tracing on nondevelopable hybrid quadric surfaces of revolution (h-QUASOR's). This property, when used in conjunction with a Geodesic Constant Method, yields analytical expressions for all the ray-parameters required in the UTD formulation. Differential geometrical considerations require that some of the ray-parameters (defined heuristically in the UTD for the canonical convex surfaces) be modified before the UTD can be applied to such hybrid surfaces. Mutual coupling results for finite-dimensional slots have been presented as an example on a satellite launch vehicle modeled by general paraboloid of revolution and right circular cylinder.

Surface-ray tracing solution of ellipsoid of revolution for UTD mutual coupling applications

An analytical surface-ray tracing has been carried out for the prolate ellipsoid of revolution using a novel geodesic constant method. This method yields closed form expressions for all the ray-geometric parameters required for the UTD mutual coupling calculations for the antennas located arbitrarily in three dimensions, on the ellipsoid of revolution.

Tracing the source of bottled water using stable isotope techniques

The Indian Summer Monsoon (ISM) precipitation recharges ground water aquifers in a large portion of the Indian subcontinent. Monsoonal precipitation over the Indian region brings moisture from the Arabian Sea and the Bay of Bengal (BoB). A large difference in the salinity of these two reservoirs, owing to the large amount of freshwater discharge from the continental rivers in the case of the BoB and dominating evaporation processes over the Arabian Sea region, allows us to distinguish the isotopic signatures in water originating in these two water bodies. Most bottled water manufacturers exploit the natural resources of groundwater, replenished by the monsoonal precipitation, for bottling purposes. The work presented here relates the isotopic ratios of bottled water to latitude, moisture source and seasonality in precipitation isotope ratios. We investigated the impact of the above factors on the isotopic composition of bottled water. The result shows a strong relationship between isotope ratios in precipitation (obtained from the GNIP data base)/bottled water with latitude. The approach can be used to predict the latitude at which the bottled water was manufactured. The paper provides two alternative approaches to address the site prediction. The limitations of this approach in identifying source locations and the uncertainty in latitude estimations are discussed. Furthermore, the method provided here can also be used as an important forensic tool for exploring the source location of bottled water from other regions. Copyright (C) 2011 John Wiley & Sons, Ltd.

Ray tracing based path-length calculations for polarized light tomographic imaging

A ray tracing based path length calculation is investigated for polarized light transport in a pixel space. Tomographic imaging using polarized light transport is promising for applications in optical projection tomography of small animal imaging and turbid media with low scattering. Polarized light transport through a medium can have complex effects due to interactions such as optical rotation of linearly polarized light, birefringence, diattenuation and interior refraction. Here we investigate the effects of refraction of polarized light in a non-scattering medium. This step is used to obtain the initial absorption estimate. This estimate can be used as prior in Monte Carlo (MC) program that simulates the transport of polarized light through a scattering medium to assist in faster convergence of the final estimate. The reflectance for p-polarized (parallel) and s-polarized (perpendicular) are different and hence there is a difference in the intensities that reach the detector end. The algorithm computes the length of the ray in each pixel along the refracted path and this is used to build the weight matrix. This weight matrix with corrected ray path length and the resultant intensity reaching the detector for each ray is used in the algebraic reconstruction (ART) method. The proposed method is tested with numerical phantoms for various noise levels. The refraction errors due to regions of different refractive index are discussed, the difference in intensities with polarization is considered. The improvements in reconstruction using the correction so applied is presented. This is achieved by tracking the path of the ray as well as the intensity of the ray as it traverses through the medium.

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.

A new two point method of obtaining Cv from a consolidation test: Discussion

Careful study of various aspects presented in the note reveals basic fallacies in the concept and final conclusions.The Authors claim to have presented a new method of determining C-v. However, the note does not contain a new method. In fact, the method proposed is an attempt to generate settlement vs. time data using only two values of (t,8). The Authors have used a rectangular hyperbola method to determine C-v from the predicated 8- t data. In this context, the title of the paper itself is misleading and questionable. The Authors have compared C-v values predicated with measured values, both of them being the results of the rectangular hyperbola method.

A New Method For The Generation Of 5,6-Quinolinedione 5-Methide .5. Synthesis Of Polycyclic Heteroaromatics

Reaction of 6-acetoxy-5-bromomethylquinoline (1c) and 2-bromomethyl-4-(2'-pyridyl)phenyl acetate (2b) with tetrachlorocatechol in acetone in the presence of anhydrous potassium carbonate resulted in the formation of diastereomeric products 3c, 3d, 4e and 4f.

Finite volume evolution Galerkin method for hyperbolic conservation laws with spatially varying flux functions

We present a generalization of the finite volume evolution Galerkin scheme [M. Lukacova-Medvid'ova,J. Saibertov'a, G. Warnecke, Finite volume evolution Galerkin methods for nonlinear hyperbolic systems, J. Comp. Phys. (2002) 183 533-562; M. Luacova-Medvid'ova, K.W. Morton, G. Warnecke, Finite volume evolution Galerkin (FVEG) methods for hyperbolic problems, SIAM J. Sci. Comput. (2004) 26 1-30] for hyperbolic systems with spatially varying flux functions. Our goal is to develop a genuinely multi-dimensional numerical scheme for wave propagation problems in a heterogeneous media. We illustrate our methodology for acoustic waves in a heterogeneous medium but the results can be generalized to more complex systems. The finite volume evolution Galerkin (FVEG) method is a predictor-corrector method combining the finite volume corrector step with the evolutionary predictor step. In order to evolve fluxes along the cell interfaces we use multi-dimensional approximate evolution operator. The latter is constructed using the theory of bicharacteristics under the assumption of spatially dependent wave speeds. To approximate heterogeneous medium a staggered grid approach is used. Several numerical experiments for wave propagation with continuous as well as discontinuous wave speeds confirm the robustness and reliability of the new FVEG scheme.

Improved root t method to evaluate consolidation test results - Discussion

Taylor (1948) suggested the method for determination of the settlement, d, corresponding to 90% consolidation utilizing the characteristics of the degree of consolidation, U, versus the square root of the time factor, square root of T, plot. Based on the properties of the slope of U versus square root of T curve, a new method is proposed to determine d corresponding to any U above 70% consolidation for evaluation of the coefficient of consolidation, Cn. The effects of the secondary consolidation on the Cn value at different percentages of consolidation can be studied. Cn, closer to the field values, can be determined in less time as compared to Taylor's method. At any U in between 75 and 95% consolidation, Cn(U) due to the new method lies in between Taylor's Cn and Casagrande's Cn.

A rapid and highly selective method for the estimation of pyro-,tri- and orthophosphates

A rapid, highly selective and simple method has been developed for the quantitative determination of pyro-, tri- and orthophosphates. The method is based on the formation of a solid complex of bis(ethylenediamine)cobalt(III) species with pyrophosphate at pH 4.2-4.3, with triphosphate at pH 2.0-2.1 and with orthophosphate at pH 8.2-8.6. The proposed method for pyro- and triphosphates differs from the available method, which is based on the formation of an adduct with tris(ethylenediamine)cobalt(III) species. The complexes have the composition [Co(en)(2)HP2O7]4H(2)O and [Co(en)(2)H2P3O10]2H(2)O, respectively. The precipitation is instantaneous and quantitative under the recommended optimum conditions giving 99.5% gravimetric yield in both cases. There is no interferences from orthophosphate, trimetaphosphate and pyrophosphate species in the triphosphate estimation up to 5% of each component. The efficacy of the method has been established by determining pyrophosphate and triphosphate contents in various matrices. In the case of orthophosphate, the proposed method differs from the available methods such as ammonium phosphomolybdate, vanadophosphomolybdate and quinoline phosphomolybdate, which are based on the formation of a precipitate, followed by either titrimetry or gravimetry. The precipitation is instantaneous and the method is simple. Under the recommended pH and other reaction conditions, gravimetric yields of 99.6-100% are obtainable. The method is applicable to orthophosphoric acid and a variety of phosphate salts.

A Simple and Convenient One Step Method for the Reductive Deoxygenation of Aryl Ketones to Hydrocarbons

A one step, clean and efficient, conversion of arylaldehydes, ketones and ketals into the corresponding hydrocarbon using ionic hydrogenation conditions employing sodium cyanoborohydride in the presence of two to three equivalents of BF3. OEt(2) is described.

On the sensitivity of elastic waves due to structural damages:Time-frequency based indexing method

Time-frequency analysis of various simulated and experimental signals due to elastic wave scattering from damage are performed using wavelet transform (WT) and Hilbert-Huang transform (HHT) and their performances are compared in context of quantifying the damages. Spectral finite element method is employed for numerical simulation of wave scattering. An analytical study is carried out to study the effects of higher-order damage parameters on the reflected wave from a damage. Based on this study, error bounds are computed for the signals in the spectral and also on the time-frequency domains. It is shown how such an error bound can provide all estimate of error in the modelling of wave propagation in structure with damage. Measures of damage based on WT and HHT is derived to quantify the damage information hidden in the signal. The aim of this study is to obtain detailed insights into the problem of (1) identifying localised damages (2) dispersion of multifrequency non-stationary signals after they interact with various types of damage and (3) quantifying the damages. Sensitivity analysis of the signal due to scattered wave based on time-frequency representation helps to correlate the variation of damage index measures with respect to the damage parameters like damage size and material degradation factors.