A waveguide problem involving a thick iris in the theory of electromagnetism

The problem of electromagnetic wave propagation in a rectangular waveguide containing a thick iris is considered for its complete solution by reducing it to two suitable integral equations, one of which is of the first kind and the other is of the second kind. These integral equations are solved approximately, by using truncated Fourier series for the unknown functions. The reflection coefficient is computed numerically from the two integral equation approaches, and almost the same numerical results are obtained. This is also depicted graphically against the wave number and compared with thin iris results, which are computed by using complementary formulations coupled with Galerkin approximations. While the reflection coefficient for a thin iris steadily increases with the wave number, for a thick iris it fluctuates and zero reflection occurs. The number of zeros of the reflection coefficient for a thick iris increases with the thickness. Thus a thick iris becomes completely transparent for some discrete wave numbers. This phenomenon may be significant in the modelling of rectangular waveguides.

Theory of Gas Hydrates: Effect of the Approximation of Rigid Water Lattice

One of the assumptions of the van der Waals and Platteeuw theory for gas hydrates is that the host water lattice is rigid and not distorted by the presence of guest molecules. In this work, we study the effect of this approximation on the triple-point lines of the gas hydrates. We calculate the triple-point lines of methane and ethane hydrates via Monte Carlo molecular simulations and compare the simulation results with the predictions of van der Waals and Platteeuw theory. Our study shows that even if the exact intermolecular potential between the guest molecules and water is known, the dissociation temperatures predicted by the theory are significantly higher. This has serious implications to the modeling of gas hydrate thermodynamics, and in spite of the several impressive efforts made toward obtaining an accurate description of intermolecular interactions in gas hydrates, the theory will suffer from the problem of robustness if the issue of movement of water molecules is not adequately addressed.

Novel Algorithm for estimation of Swell Pressure of Fine Grained Soils Based on Diffuse Double Layer (DDL) Theory

Use of engineered landfills for the disposal of industrial wastes is currently a common practice. Bentonite is attracting a greater attention not only as capping and lining materials in landfills but also as buffer and backfill materials for repositories of high-level nuclear waste around the world. In the design of buffer and backfill materials, it is important to know the swelling pressures of compacted bentonite with different electrolyte solutions. The theoretical studies on swell pressure behaviour are all based on Diffuse Double Layer (DDL) theory. To establish a relation between the swell pressure and void ratio of the soil, it is necessary to calculate the mid-plane potential in the diffuse part of the interacting ionic double layers. The difficulty in these calculations is the elliptic integral involved in the relation between half space distance and mid plane potential. Several investigators circumvented this problem using indirect methods or by using cumbersome numerical techniques. In this work, a novel approach is proposed for theoretical estimations of swell pressures of fine-grained soil from the DDL theory. The proposed approach circumvents the complex computations in establishing the relationship between mid-plane potential and diffused plates’ distances in other words, between swell pressure and void ratio.

Classical screw theory: A fresh look using dual eigenvalue approach

This paper presents a novel algebraic formulation of the central problem of screw theory, namely the determination of the principal screws of a given system. Using the algebra of dual numbers, it shows that the principal screws can be determined via the solution of a generalised eigenproblem of two real, symmetric matrices. This approach allows the study of the principal screws of the general screw systems associated with a manipulator of arbitrary geometry in terms of closed-form expressions of its architecture and configuration parameters. The formulation is illustrated with examples of practical manipulators.

A relook at Reissner's theory of plates in bending

Shear deformation and higher order theories of plates in bending are (generally) based on plate element equilibrium equations derived either through variational principles or other methods. They involve coupling of flexure with torsion (torsion-type) problem and if applied vertical load is along one face of the plate, coupling even with extension problem. These coupled problems with reference to vertical deflection of plate in flexure result in artificial deflection due to torsion and increased deflection of faces of the plate due to extension. Coupling in the former case is eliminated earlier using an iterative method for analysis of thick plates in bending. The method is extended here for the analysis of associated stretching problem in flexure.

A Kinematic Theory for Planar Hoberman and Other Novel Foldable Mechanisms

In this paper, we present a kinematic theory for Hoberman and other similar foldable linkages. By recognizing that the building blocks of such linkages can be modeled as planar linkages, different classes of possible solutions are systematically obtained including some novel arrangements. Criteria for foldability are arrived by analyzing the algebraic locus of the coupler curve of a PRRP linkage. They help explain generalized Hoberman and other mechanisms reported in the literature. New properties of such mechanisms including the extent of foldability, shape-preservation of the inner and outer profiles, multi-segmented assemblies and heterogeneous circumferential arrangements are derived. The design equations derived here make the conception of even complex planar radially foldable mechanisms systematic and easy. Representative examples are presented to illustrate the usage of the design equations and the kinematic theory.

Multi-UAV Task Allocation using Team Theory

A multiple UAV search and attack mission in a battlefield involves allocating UAVs to different target tasks efficiently. This task allocation becomes difficult when there is no communication among the UAVs and the UAVs sensors have limited range to detect the targets and neighbouring UAVs, and assess target status. In this paper, we propose a team theoretic approach to efficiently allocate UAVs to the targets with the constraint that UAVs do not communicate among themselves and have limited sensor range. We study the performance of team theoretic approach for task allocation on a battle field scenario. The performance obtained through team theory is compared with two other methods, namely, limited sensor range but with communication among all the UAVs, and greedy strategy with limited sensor range and no communication. It is found that the team theoretic strategy performs the best even though it assumes limited sensor range and no communication.