Analytical solutions for protective filters based on soil-retention and permeability criteria with respect to the phenomenon of soil boiling

For the successful performance of a granular filter medium, existing design guidelines, which are based on the particle size distribution (PSD) characteristics of the base soil and filter medium, require two contradictory conditions to be satisfied, viz., soil retention and permeability. In spite of the wider applicability of these guidelines, it is well recognized that (i) they are applicable to a particular range of soils tested in the laboratory, (ii) the design procedures do not include performance-based selection criteria, and (iii) there are no means to establish the sensitivity of the important variables influencing performance. In the present work, analytical solutions are developed to obtain a factor of safety with respect to soil-retention and permeability criteria for a base soil - filter medium system subjected to a soil boiling condition. The proposed analytical solutions take into consideration relevant geotechnical properties such as void ratio, permeability, dry unit weight, effective friction angle, shape and size of soil particles, seepage discharge, and existing hydraulic gradient. The solution is validated through example applications and experimental results, and it is established that it can be used successfully in the selection as well as design of granular filters and can be applied to all types of base soils.

Semi-analytical finite element analysis of a strip footing on an elastic reinforced soil

A plane strain elastic interaction analysis of a strip footing resting on a reinforced soil bed has been made by using a combined analytical and finite element method (FEM). In this approach the stiffness matrix for the footing has been obtained using the FEM, For the reinforced soil bed (halfplane) the stiffness matrix has been obtained using an analytical solution. For the latter, the reinforced zone has been idealised as (i) an equivalent orthotropic infinite strip (composite approach) and (ii) a multilayered system (discrete approach). In the analysis, the interface between the strip footing and reinforced halfplane has been assumed as (i) frictionless and (ii) fully bonded. The contact pressure distribution and the settlement reduction have been given for different depths of footing and scheme of reinforcement in soil. The load-deformation behaviour of the reinforced soil obtained using the above modelling has been compared with some available analytical and model test results. The equivalent orthotropic approach proposed in this paper is easy to program and is shown to predict the reinforcing effects reasonably well.

Analytical And Experimental Aeroacoustic Studies Of Open-Ended 3-Duct Perforated Elements Used In Mufflers

Perforated element mufflers have been known to have good acousticp erformancew, henu sedo n automotive xhausst ystemsIn. thel astd ecadea nda half, plugm ufflersc, oncentrihc oler esonators, and three-ductc losed-endp erforatede lementsh ave been studied.T he presenti nvestigation concernso pen-endedt,h ree-ducpt erforatede lementsw, hich are knownt o combineh igh acoustic transmissiolno ss with low back pressuresT. he governinge quationsh ave been solved in the frequencyd omain,u singt he recouplinga pproacha longw ith appropriatbe oundaryc onditionst,o derivet he transferm atrixa ndt hent o calculaten oiser eductiona ndt ransmissiolno ss.T he predicted noiser eductionv aluesh aveb eens hownt o corroboratew ell with experimentallyo bservedv alues. Finally,p arametrics tudiesh aveb eend onet o draw designc urvesf or suchm ufflers.

Analytical approximation solutions for 3-D optical waveguides: Review

The rectangular dielectric waveguide is the most commonly used structure in integrated optics, especially in semi-conductor diode lasers. Demands for new applications such as high-speed data backplanes in integrated electronics, waveguide filters, optical multiplexers and optical switches are driving technology toward better materials and processing techniques for planar waveguide structures. The infinite slab and circular waveguides that we know are not practical for use on a substrate because the slab waveguide has no lateral confinement and the circular fiber is not compatible with the planar processing technology being used to make planar structures. The rectangular waveguide is the natural structure. In this review, we have discussed several analytical methods for analyzing the mode structure of rectangular structures, beginning with a wave analysis based on the pioneering work of Marcatili. We study three basic techniques with examples to compare their performance levels. These are the analytical approach developed by Marcatili, the perturbation techniques, which improve on the analytical solutions and the effective index method with examples.

Laboratory notebooks: a cautionary tale

A mathematician tends to have an intense relationship with treatises – one which is more akin to that of a historian than that of her colleagues in the ‘hard’ sciences. A book may be a century or two old and still be relevant as a source of information or inspiration, well-thumbed textbooks from youth might be still consulted decades later, and fierce arguments rage about relative merits of different treatments of the same subject. And much like any book-lover, a mathematician is forever arguing with herself whether she can afford to buy this volume or the other. When the price label is in dollars or euros and the salary paid in rupees, this last dilemma is particularly acute.

Analytical solution of unsteady three-dimensional MHD boundary layer flow and heat transfer due to impulsively stretched plane surface

The unsteady magnetohydrodynamic viscous flow and heat transfer of Newtonian fluids induced by an impulsively stretched plane surface in two lateral directions are studied by using an analytic technique, namely, the homotopy method. The analytic series solution presented here is highly accurate and uniformly valid for all time in the entire region. The effects of the stretching ratio and the magnetic field on the surface shear stresses and heat transfer are studied. The surface shear stresses in x- and y-directions and the surface heat transfer are enchanced by increasing stretching ratio for a fixed value of the magnetic parameter. For a fixed stretching ratio, the surface shear stresses increase with the magnetic parameter, but the heat transfer decreases. The Nusselt number takes longer time to reach the steady state than the skin friction coefficients. There is a smooth transition from the initial unsteady state to the steady state.

A do-it-yourself (DIY) switched mode power conversion laboratory

In the education of physical sciences, the role of the laboratory cannot be overemphasised. It is the laboratory exercises which enable the student to assimilate the theoretical basis, verify the same through bench-top experiments, and internalize the subject discipline to acquire mastery of the same. However the resources essential to put together such an environment is substantial. As a result, the students go through a curriculum which is wanting in this respect. This paper presents a low cost alternative to impart such an experience to the student aimed at the subject of switched mode power conversion. The resources are based on an open source circuit simulator (Sequel) developed at IIT Mumbai, and inexpensive construction kits developed at IISc Bangalore. The Sequel programme developed by IIT Mumbai, is a circuit simulation program under linux operating system distributed free of charge. The construction kits developed at IISc Bangalore, is fully documented for anyone to assemble these circuit which minimal equipment such as soldering iron, multimeter, power supply etc. This paper puts together a simple forward dc to dc converter as a vehicle to introduce the programming under sequel to evaluate the transient performance and small signal dynamic model of the same. Bench tests on the assembled construction kit may be done by the student for study of operation, transient performance and closed loop stability margins etc.

Effect of curve crossing on absorption and resonance Raman spectra: analytical treatment for delta-function coupling in parabolic potentials

We propose an exactly solvable model for the two-state curve-crossing problem. Our model assumes the coupling to be a delta function. It is used to calculate the effect of curve crossing on the electronic absorption spectrum and the resonance Raman excitation profile.

Analytical studies of gain optimization in CO2-N2 gasdynamic lasers employing two-dimensional wedge nozzles

An analytical method has been proposed to optimise the small-signaloptical gain of CO2-N2 gasdynamic lasers (gdl) employing two-dimensional (2D) wedge nozzles. Following our earlier work the equations governing the steady, inviscid, quasi-one-dimensional flow in the wedge nozzle of thegdl are reduced to a universal form so that their solutions depend on a single unifying parameter. These equations are solved numerically to obtain similar solutions for the various flow quantities, which variables are subsequently used to optimize the small-signal-gain. The corresponding optimum values like reservoir pressure and temperature and 2D nozzle area ratio also have been predicted and graphed for a wide range of laser gas compositions, with either H2O or He as the catalyst. A large number of graphs are presented which may be used to obtain the optimum values of small signal gain for a wide range of laser compositions without further computations.

Experimental and Analytical Investigations of the actions taking place in a Synchronous machine during the starting period when the starting Is effected by means of alternating current

The literature on the subject of the present investigation is somewhat meagre. A rotary converter or synchronous motor no! provided with any special starting devices forms, when started from the alternating current side, a type of induction motor whoso Htator is provided with a polyphase winding, and whoso rotor has a single-phase (or single magnetic axis) winding.

On an analytical-numerical procedure for the analysis of cylindrical shells with arbitrarily oriented cracks

An analytical-numerical procedure for obtaining stress intensity factor solutions for an arbitrarily oriented crack in a long, thin circular cylindrical shell is presented. The method of analysis involves obtaining a series solution to the governing shell equation in terms of Mathieu and modified Mathieu functions by the method of separation of variables and satisfying the crack surface boundary conditions numerically using collocation. The solution is then transformed from elliptic coordinates to polar coordinates with crack tip as the origin through a Taylor series expansion and membrane and bending stress intensity factors are computed. Numerical results are presented and discussed for the pressure loading case.

Swarm intelligence-based solver for parameter estimation of laboratory through-diffusion transport of contaminants

Theoretical approaches are of fundamental importance to predict the potential impact of waste disposal facilities on ground water contamination. Appropriate design parameters are generally estimated be fitting theoretical models to data gathered from field monitoring or laboratory experiments. Transient through-diffusion tests are generally conducted in the laboratory to estimate the mass transport parameters of the proposed barrier material. Thes parameters are usually estimated either by approximate eye-fitting calibration or by combining the solution of the direct problem with any available gradient-based techniques. In this work, an automated, gradient-free solver is developed to estimate the mass transport parameters of a transient through-diffusion model. The proposed inverse model uses a particle swarm optimization (PSO) algorithm that is based on the social behavior of animals searching for food sources. The finite difference numerical solution of the forward model is integrated with the PSO algorithm to solve the inverse problem of parameter estimation. The working principle of the new solver is demonstrated and mass transport parameters are estimated from laboratory through-diffusion experimental data. An inverse model based on the standard gradient-based technique is formulated to compare with the proposed solver. A detailed comparative study is carried out between conventional methods and the proposed solver. The present automated technique is found to be very efficient and robust. The mass transport parameters are obtained with great precision.

Analytical estimation of stress intensity factors in patched cracked plates

The fatigue and fracture performance of a cracked plate can be substantially improved by providing patches as reinforcements. The effectiveness of the patches is related to the reduction they cause in the stress intensity factor (SIF) of the crack. So, for reliable design, one needs an accurate evaluation of the SIF in terms of the crack, patch and adhesive parameters. In this investigation, a centrally cracked large plate with a pair of symmetric bonded narrow patches, oriented normally to the crack line, is analysed by a continuum approach. The narrow patches are treated as transversely flexible line members. The formulation leads to an integral equation which is solved numerically using point collocation. The convergence is rapid. It is found that substantial reductions in SIF are possible with practicable patch dimensions and locations. The patch is more effective when placed on the crack than ahead of the crack. The present analysis indicates that a little distance inwards of the crack tip, not the crack tip itself, is the ideal location, for the patch.

Laboratory Test Methods For The Evaluation Of Flammability Of Polymers

Combustion is a complex phenomena involving a multiplicity of variables. Some important variables measured in flame tests follow [1]. In order to characterize ignition, such related parameters as ignition time, ease of ignition, flash ignition temperature, and self-ignition temperature are measured. For studying the propagation of the flame, parameters such as distance burned or charred, area of flame spread, time of flame spread, burning rate, charred or melted area, and fire endurance are measured. Smoke characteristics are studied by determining such parameters as specific optical density, maximum specific optical density, time of occurrence of the densities, maximum rate of density increase, visual obscuration time, and smoke obscuration index. In addition to the above variables, there are a number of specific properties of the combustible system which could be measured. These are soot formation, toxicity of combustion gases, heat of combustion, dripping phenomena during the burning of thermoplastics, afterglow, flame intensity, fuel contribution, visual characteristics, limiting oxygen concentration (OI), products of pyrolysis and combustion, and so forth. A multitude of flammability tests measuring one or more of these properties have been developed [2]. Admittedly, no one small scale test is adequate to mimic or assess the performance of a plastic in a real fire situation. The conditions are much too complicated [3, 4]. Some conceptual problems associated with flammability testing of polymers have been reviewed [5, 6].