Double focus systems for holography

Some very simple, compact optical systems for holography of diffusely reflecting objects, using off-axis, double-focus elements as beam splitters, are described. These are free from disadvantages inherent in earlier systems of this type.

On the L2 stability of linear multidimensional time varying systems

This paper analyzes the L2 stability of solutions of systems with time-varying coefficients of the form [A + C(t)]x′ = [B + D(t)]x + u, where A, B, C, D are matrices. Following proof of a lemma, the main result is derived, according to which the system is L2 stable if the eigenvalues of the coefficient matrices are related in a simple way. A corollary of the theorem dealing with small periodic perturbations of constant coefficient systems is then proved. The paper concludes with two illustrative examples, both of which deal with the attitude dynamics of a rigid, axisymmetric, spinning satellite in an eccentric orbit, subject to gravity gradient torques.

Specification-driven approach for protocol design of distributed computing systems

An important issue in the design of a distributed computing system (DCS) is the development of a suitable protocol. This paper presents an effort to systematize the protocol design procedure for a DCS. Protocol design and development can be divided into six phases: specification of the DCS, specification of protocol requirements, protocol design, specification and validation of the designed protocol, performance evaluation, and hardware/software implementation. This paper describes techniques for the second and third phases, while the first phase has been considered by the authors in their earlier work. Matrix and set theoretic based approaches are used for specification of a DCS and for specification of the protocol requirements. These two formal specification techniques form the basis of the development of a simple and straightforward procedure for the design of the protocol. The applicability of the above design procedure has been illustrated by considering an example of a computing system encountered on board a spacecraft. A Petri-net based approach has been adopted to model the protocol. The methodology developed in this paper can be used in other DCS applications.

A Simple Five-Level Inverter Topology for Induction Motor Drive Using Conventional Two-Level Inverters and Flying Capacitor Technique

This paper proposes a new five-level inverter topology for open-end winding induction motor (IM) drive. The popular existing circuit configurations for five-level inverter include the NPC inverter and flying capacitor topologies. Compared to the NPC inverter, the proposed topology eliminates eighteen clamping diodes having different voltage ratings in the present circuit. Moreover it requires only one capacitor bank per phase, whereas flying capacitor schemes for five level topologies require six capacitor banks per phase. The proposed topology is realized by feeding the phase winding of an open-end induction motor with two-level inverters in series with flying capacitors. The flying capacitor voltages are balanced using the switching state redundancy for full modulation range. The proposed inverter scheme is capable of producing two-level to five-level pulse width modulated voltage across the phase winding depending on the modulation range. Additionally, in case of any switch failure in the flying capacitor connection, the proposed inverter topology can be operated as a three-level inverter for full modulation range. The proposed scheme is experimentally verified on a four pole, 5hp induction motor drive.

Extended colored Petri net: An efficient tool for analyzing concurrent systems

This paper proposes a novel and simple definition of general colored Petri nets. This definition is coherent with that of (uncolored) Petri nets, preserves the reflexivity of the original net and is extended to represent inhibitors. Also suggested are systematic and formal merging rules to obtain a well-formed structure of the extended colored Petri net by folding a given uncolored net. Finally, we present a technique to compute colored invariants by selecting colored RP-subnets. On the average, the proposed technique performs better than the existing ones. The analysis procedure is explained through an illustrative example of a three-level interrupt-priority-handler scheme.

Stiffness Coefficients of Layered Soil Systems

One of the most important dynamic properties required in the design of machine foundations is the stiffness or spring constant of the supporting soil. For a layered soil system, the stiffness obtained from an idealization of soils underneath as springs in series gives the same value of stiffness regardless of the location and extent of individual soil layers with respect to the base of the foundation. This paper aims to develop the importance of the relative positioning of soil layers and their thickness beneath the foundation. A simple and approximate procedure called the weighted average method has been proposed to obtain the equivalent stiffness of a layered soil system knowing the individual values of the layers, their relative position with respect to foundation base, and their thicknesses. The theoretically estimated values from the weighted average method are compared with those obtained by conducting field vibration tests using a square footing over different two- and three-layered systems and are found to be very good. The tests were conducted over a range of static and dynamic loads using three different materials. The results are also compared with the existing methods available in the literature.

A simple computational model for predicting .pi.-facial selectivity in reductions of sterically unbiased ketones. Relative importance of electrostatic and orbital interactions

Various factore controlling the preferred facial selectivity in the reductions of a number of sterically unbiased ketones have been evaluated using a semiempirical MO procedure. MNDO optimized geometries do not reveal any significant ground-state distortions which can be correlated with the observed face selectivities. Electrostatic effecta due to an approaching reagent were modeled by placing a test negative charge at a fixed distance from the carbonyl carbon on each of the two faces. A second series of calculations was carried out using the hydride ion as a test nucleophile. The latter calculations effectively include orbital interactions involving the u and u* orbitals of the newly formed bond in the reaction. The computed energy differences with the charge model are generally much larger compared to those with the hydride ion. However, both models lead to predictions which are qualitatively consistent with the experimentally determined facial preferences for most of the systems. Thus, electrostatic interactions between the nucleophile and the substrate seem to effectively determine the face selectivities in these molecules. However, there are a few exceptions in which orbital interactions are found to contribute significantly and occasionally reverse the preference dictated by electrostatic effecta. The remarkable succew of the hydride model calculations, in spite of retaining the unperturbed geometries of the substrates, points to the unimportance of torsional effeds and orbital distortions associated with the pyramidalized carbonyl unit in the transition state in most of the substrates considered. Additional experimental results are reported which provide useful calibration for the present computational approach.

An optimal dynamic inversion approach for controlling a class of one-dimensional nonlinear distributed parameter systems

Combining the principles of dynamic inversion and optimization theory, a new approach is presented for stable control of a class of one-dimensional nonlinear distributed parameter systems, assuming the availability a continuous actuator in the spatial domain. Unlike the existing approximate-then-design and design-then-approximate techniques, here there is no need of any approximation either of the system dynamics or of the resulting controller. Rather, the control synthesis approach is fairly straight-forward and simple. The controller formulation has more elegance because we can prove the convergence of the controller to its steady state value. To demonstrate the potential of the proposed technique, a real-life temperature control problem for a heat transfer application is solved. It has been demonstrated that a desired temperature profile can be achieved starting from any arbitrary initial temperature profile.

Monte Carlo simulation of network formation based on structural fragments in epoxy-anhydride systems

A method combining the Monte Carlo technique and the simple fragment approach has been developed for simulating network formation in amine-catalysed epoxy-anhydride systems. The method affords a detailed insight into the nature and composition of the network, showing the distribution of various fragments. It has been used to characterize the network formation in the reaction of the diglycidyl ester of isophthalic acid with hexahydrophthalic anhydride, catalysed by benzyldimethylamine. Pre-gel properties like number and weight distributions and average molecular weights have been calculated as a function of epoxy conversion, leading to a prediction of the gel-point conversion. Analysis of the simulated network further yields other characteristic properties such as concentration of crosslink points, distribution and concentration of elastically active chains, average molecular weight between crosslinks, sol content and mass fraction of pendent chains. A comparison has been made of the properties obtained through simulation with those predicted by the fragment approach alone, which, however, gives only average properties. The Monte Carlo simulation results clearly show that loops and other cyclic structures occur in the gel. This may account for the differences observed between the results of the simulation and the fragment model in the post-gel phase. Copyright (C) 1996 Elsevier Science Ltd.

Orientational relaxation in dipolar systems: How much do we understand the role of correlations

Dipolar systems, both liquids and solids, constitute a class of naturally abundant systems that are important in all branches of natural science. The study of orientational relaxation provides a powerful method to understand the microscopic properties of these systems and, fortunately, there are many experimental tools to study orientational relaxation in the condensed phases. However, even after many years of intense research, our understanding of orientational relaxation in dipolar systems has remained largely imperfect. A major hurdle towards achieving a comprehensive understanding is the long range and complex nature of dipolar interactions which also made reliable theoretical study extremely difficult. These difficulties have led to the development of continuum model based theories, which although they provide simple, elegant expressions for quantities of interest, are mostly unsatisfactory as they totally neglect the molecularity of inter-molecular interactions. The situation has improved in recent years because of renewed studies, led by computer simulations. In this review, we shall address some of the recent advances, with emphasis on the work done in our laboratory at Bangalore. The reasons for the failure of the continuum model, as revealed by the recent Brownian dynamics simulations of the dipolar lattice, are discussed. The main reason is that the continuum model predicts too fast a decay of the torque-torque correlation function. On the other hand, a perturbative calculation, based on Zwanzig's projection operator technique, provides a fairly satisfactory description of the single particle orientational dynamics for not too strongly polar dipolar systems. A recently developed molecular hydrodynamic theory that properly includes the effects of intermolecular orientational pair correlations provides an even better description of the single-particle orientational dynamics. We also discuss the rank dependence of the dielectric friction. The other topics reviewed here includes dielectric relaxation and solvation dynamics, as they are intimately connected with orientational relaxation. Recent molecular dynamics simulations of the dipolar lattice are also discussed. The main theme of the present review is to understand the effects of intermolecular interactions on orientational relaxation. The presence of strong orientational pair correlation leads to a strong coupling between the single particle and the collective dynamics. This coupling can lead to rich dynamical properties, some of which are detailed here, while a major part remains yet unexplored.

Molecular-dynamics studies of systems of confined dumbbell molecules

We present the results of molecular-dynamics simulations of systems of dumbbell molecules confined by parallel molecular walls. We have carried out systematic studies of three cases: freezing, steady flows, and stick-slip friction. We find that the molecular orientational degrees of freedom cause the surface layers to deviate from a planar configuration. Nevertheless, steady flows, in a channel as narrow as 15 molecular sizes, display continuum behavior. A range of mechanisms in the dynamics of the freezing of a confined fluid is found, as a function of the wall-fluid interactions and the bond length of the dumbbell molecules. The simple order-disorder transition associated with stick-slip motion in the presence of a layer of monoatomic lubricant molecules is supplanted by more complex behavior due to rotational degrees of freedom of the diatomic molecules.

A current error space vector based hysteresis controller with constant switching frequency and simple online boundary computation for VSI fed IM drive

This paper proposes a simple current error space vector based hysteresis controller for two-level inverter fed Induction Motor (IM) drives. This proposed hysteresis controller retains all advantages of conventional current error space vector based hysteresis controllers like fast dynamic response, simple to implement, adjacent voltage vector switching etc. The additional advantage of this proposed hysteresis controller is that it gives a phase voltage frequency spectrum exactly similar to that of a constant switching frequency space vector pulse width modulated (SVPWM) inverter. In this proposed hysteresis controller the boundary is computed online using estimated stator voltages along alpha and beta axes thus completely eliminating look up tables used for obtaining parabolic hysteresis boundary proposed in. The estimation of stator voltage is carried out using current errors along alpha and beta axes and steady state model of induction motor. The proposed scheme is simple and capable of taking inverter upto six step mode operation, if demanded by drive system. The proposed hysteresis controller based inverter fed drive scheme is simulated extensively using SIMULINK toolbox of MATLAB for steady state and transient performance. The experimental verification for steady state performance of the proposed scheme is carried out on a 3.7kW IM.

The R-x, R2-x Planes; Some New Ideas for the Study of Nonlinear Systems

Use of some new planes such as the R-x, R2-x (where R represents in the n-dimensional phase space, the radius vector from the origin to any point on the trajectory described by the system) is suggested for analysis of nonlinear systems of any kind. The stability conditions in these planes are given. For easy understanding of the method, the transformation from the phase plane to the R-x, R2-x planes is brought out for second-order systems. In general, while these planes serve as useful as the phase plane, they have proved to be simpler in determining quickly the general behavior of certain classes of second-order nonlinear systems. A chart and a simple formula are suggested to evaluate time easily from the R-x and R2-x trajectories, respectively. A means of solving higher-order nonlinear systems is also illustrated. Finally, a comparative study of the trajectories near singular points on the phase plane and on the new planes is made.

The x¿n-x Plane for Analysis of Certain Second-Order Nonlinear Systems

Analysis of certain second-order nonlinear systems, not easily amenable to the phase-plane methods, and described by either of the following differential equations xÿn-2ÿ+ f(x)xÿ2n+g(x)xÿn+h(x)=0 ÿ+f(x)xÿn+h(x)=0 n≫0 can be effected easily by drawing the entire portrait of trajectories on a new plane; that is, on one of the xÿnÿx planes. Simple equations are given to evaluate time from a trajectory on any of these n planes. Poincaré's fundamental phase plane xÿÿx is conceived of as the simplest case of the general xÿnÿx plane.

Techniques for Analysis of Certain Nonlinear Systems

This paper suggests the use of simple transformations like ÿ=kx, kx2 for second-order nonlinear differential equations to effect rapid plotting of the phase-plane trajectories. The method is particularly helpful in determining quickly the trajectory slopes along simple curves in any desired region of the phase plane. New planes such as the tÿ-x, tÿ2-x are considered for the study of some groups of nonlinear time-varying systems. Suggestions for solving certain higher-order nonlinear systems are also made.