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.

Novel schmitt trigger based on lahbda diode

A new circuit to realise a Schmitt trigger has been conceived. This circuit, which is based on the well known lambda diode, is suitable for integration using CMOS technology. It requires only three devices and is probably simpler than any other conventional Schmitt trigger circuit.

Non-linear resonance in strings under narrow band random excitation, part I: Planar response and stability

Non-linear planar response of a string to planar narrow band random excitation is investigated in this paper. A response equation for the mean square deflection σ2 is obtained under a single mode approximation by using the equivalent linearization technique. It is shown that the response is triple valued, as in the case of harmonic excitation, if the centre frequency of excitation Ω lies in a certain specified range. The triple valued response occurs only if the excitation bandwidth β is smaller than a critical value βcrit which is a monotonically increasing function of the intensity of excitation. An approximate method of investigating the almost sure asymptotic stability of the solution is presented and regions of instability in the Ω-σ2 plane have been charted. It is shown that planar response can become unstable either due to an unbounded growth of the in-plane component of motion or due to a spontaneous appearance of an out-of-plane component.

A 13C-NMR study of non-planar distortions in amides

The technique of 13C-NMR spectroscopy of oriented systems to problems of biological importance has been suggested and used to investigate non-planar distortions in substituted amides—models for peptides. The studies in conjunction with the proton magnetic resonance data on 5N-[13C]methyl[13C]formamide oriented in a nematic solvent provide all the direct dipolar couplings between the interacting nuclei in the system. When the 13C- and the 1H-NMR experiments are performed under non-identical conditions, 22 different direct dipolar couplings are obtained. It is demostrated that they can be used to determine unambiguously non-planar distortions around the nitrogen atom together with other geometrical data and the molecular order.

Approximation algorithm for maximum independent set in planar traingle-free graphs

The maximum independent set problem is NP-complete even when restricted to planar graphs, cubic planar graphs or triangle free graphs. The problem of finding an absolute approximation still remains NP-complete. Various polynomial time approximation algorithms, that guarantee a fixed worst case ratio between the independent set size obtained to the maximum independent set size, in planar graphs have been proposed. We present in this paper a simple and efficient, O(|V|) algorithm that guarantees a ratio 1/2, for planar triangle free graphs. The algorithm differs completely from other approaches, in that, it collects groups of independent vertices at a time. Certain bounds we obtain in this paper relate to some interesting questions in the theory of extremal graphs.

The non-planar peptide unit II. Comparison of theory with crystal structure datastar, open

The theoretical results derived in Part I (Ramachandran, G.N., Lakshminarayan, A.V. and Kolaskar, A.S. (1973) Biochim. Biophys. Acta 303, 8–13) that the three bonds of the peptide unit meeting at N can have a pyramidal structure is confirmed by an analysis of 14 published crystal structures of small peptides. It is shown that the dihedral angles θN and Δω are correlated, while θC, is small and is uncorrelated with Δω, showing that the non-planar distortion at C′ is generally small.

Theory of the non-planar peptide unitstar, open

By means of CNDO/2 calculations on N-methyl acetamide, it is shown that the state of minimum energy of the trans-peptide unit is a non-planar conformation, with the NH and NC2α bonds being significantly out of the plane formed by the atoms C1α, C′, O and N.

Uniformity of film thickness on rotating planetary planar substrates

For the purposes of obtaining a number of components with nearly identical thickness distributions over the substrate area and of minimizing the inhomogeneities of the film, it is logical to presume that a substrate rotating on its own axis and revolving around another axis will give more uniformity in film thickness than a substrate only revolving around one axis. In relation to the practical applications, an investigation has been undertaken to study the refinement that can be achieved by using a planar planetary substrate holder. It is shown theoretically that the use of the planetary substrate holder under ideal conditions of source and geometry does not offer any further improvement in uniformity of thickness over the conventional rotary work-holder. It is also shown that the geometrical parameters alone have little influence over the uniformity achieved on a planetary substrate, because of the complex cyclidal motion of any point on it. However, for any given geometry, a non-integral speed ratio of the planetary substrate and the work-holder shows considerably less variation in thickness over the substrate area.

Planar pursuit-evasion with variable speeds, part 1, extremal trajectory maps

Pursuit evasion in a plane is formulated with both players allowed to vary their speeds between fixed limits. A suitable choice of real-space coordinates confers open-loop optimality on the game. The solution in the small is described in terms of the individual players'' extremal trajectory maps (ETM). Each map is independent of role, adversary, and capture radius. An ETM depicts the actual real-space trajectories. A template method of generating constant control arcs is described. Examples of ETM for an aircraft flying at a constant altitude with fixed and varying speeds are presented.

Planar pursuit-evasion with variable speeds, part 2, barrier sections

An iterative method of constructing sections of the game surfaces from the players'' extremal trajectory maps is discussed. Barrier sections are presented for aircraft pursuit-evasion at constant altitude, with one aircraft flying at sustained speed and the other varying its speed.

A geometric approach for determining inner and exterior boundaries of workspaces of planar manipulators

In this paper a method to determine the internal and external boundaries of planar workspaces, represented with an ordered set of points, is presented. The sequence of points are grouped and can be interpreted to form a sequence of curves. Three successive curves are used for determining the instantaneous center of rotation for the second one of them. The two extremal points on the curve with respect to the instantaneous center are recognized as singular points. The chronological ordering of these singular points is used to generate the two envelope curves, which are potentially intersecting. Methods have been presented in the paper for the determination of the workspace boundary from the envelope curves. Strategies to deal with the manipulators with joint limits and various degenerate situations have also been discussed. The computational steps being completely geometric, the method does not require the knowledge about the manipulator's kinematics. Hence, it can be used for the workspace of arbitrary planar manipulators. A number of illustrative examples demonstrate the efficacy of the proposed method.

A kinematic theory for radially foldable planar linkages

By using the algebraic locus of the coupler curve of a PRRP planar linkage, in this paper, a kinematic theory is developed for planar, radially foldable closed-loop linkages. This theory helps derive the previously invented building blocks, which consist of only two inter-connected angulated elements, for planar foldable structures. Furthermore, a special case of a circumferentially actuatable foldable linkage (which is different from the previously known cases) is derived from the theory, A quantitative description of some known and some new properties of planar foldable linkages, including the extent of foldability, shape-preservation of the interior polygons, multi-segmented assemblies and heterogeneous circumferential arrangemants, is also presented. The design equations derived here make the conception of even complex planar radially foldable linkages systematic and straightforward. Representative examples are presented to illustrate the usage of the design equations and the construction of prototypes. The current limitations and some possible extensions of the theory are also noted. (c) 2007, Elsevier Ltd. All ri-hts reserved.

Electromechanical interactions in a carbon nanotube based thin film field emitting diode

Carbon nanotubes (CNTs) have emerged as promising candidates for biomedical x-ray devices and other applications of field emission. CNTs grown/deposited in a thin film are used as cathodes for field emission. In spite of the good performance of such cathodes, the procedure to estimate the device current is not straightforward and the required insight towards design optimization is not well developed. In this paper, we report an analysis aided by a computational model and experiments by which the process of evolution and self-assembly (reorientation) of CNTs is characterized and the device current is estimated. The modeling approach involves two steps: (i) a phenomenological description of the degradation and fragmentation of CNTs and (ii) a mechanics based modeling of electromechanical interaction among CNTs during field emission. A computational scheme is developed by which the states of CNTs are updated in a time incremental manner. Finally, the device current is obtained by using the Fowler–Nordheim equation for field emission and by integrating the current density over computational cells. A detailed analysis of the results reveals the deflected shapes of the CNTs in an ensemble and the extent to which the initial state of geometry and orientation angles affect the device current. Experimental results confirm these effects.