A Sub-Nyquist Sampling Method For Computing The Level-crossing-times Of An Analog Signal: Theory And Applications

We address the problem of computing the level-crossings of an analog signal from samples measured on a uniform grid. Such a problem is important, for example, in multilevel analog-to-digital (A/D) converters. The first operation in such sampling modalities is a comparator, which gives rise to a bilevel waveform. Since bilevel signals are not bandlimited, measuring the level-crossing times exactly becomes impractical within the conventional framework of Shannon sampling. In this paper, we propose a novel sub-Nyquist sampling technique for making measurements on a uniform grid and thereby for exactly computing the level-crossing times from those samples. The computational complexity of the technique is low and comprises simple arithmetic operations. We also present a finite-rate-of-innovation sampling perspective of the proposed approach and also show how exponential splines fit in naturally into the proposed sampling framework. We also discuss some concrete practical applications of the sampling technique.

Electrochemical phase formation involving multicomponents: hemispherical overlap models for varied nucleation and growth conditions

The phenomenological theory of hemispherical growth in the context of phase formation with more than one component is presented. The model discusses in a unified manner both instantaneous and progressive nucleation (at the substrate) as well as arbitrary growth rates (e.g. constant and diffusion controlled growth rates). A generalized version of Avrami ansatz (a mean field description) is used to tackle the ''overlap'' aspects arising from the growing multicentres of the many components involved, observing that the nucleation is confined to the substrate plane only. The time evolution of the total extent of macrogrowth as well as those of the individual components are discussed explicitly for the case of two phases. The asymptotic expressions for macrogrowth are derived. Such analysis depicts a saturation limit (i.e. the maximum extent of growth possible) for the slower growing component and its dependence on the kinetic parameters which, in the electrochemical context, can be controlled through potential. The significance of this model in the context of multicomponent alloy deposition and possible future directions for further development are pointed out.

Measurement of complex optical flow with use of an augmented generalized gradient scheme

We present a method for measuring the local velocities and first-order variations in velocities in a timevarying image. The scheme is an extension of the generalized gradient model that encompasses the local variation of velocity within a local patch of the image. Motion within a patch is analyzed in parallel by 42 different spatiotemporal filters derived from 6 linearly independent spatiotemporal kernels. No constraints are imposed on the image structure, and there is no need for smoothness constraints on the velocity field. The aperture problem does not arise so long as there is some two-dimensional structure in the patch being analyzed. Among the advantages of the scheme is that there is no requirement to calculate second or higher derivatives of the image function. This makes the scheme robust in the presence of noise. The spatiotemporal kernels are of simple form, involving Gaussian functions, and are biologically plausible receptive fields. The validity of the scheme is demonstrated by application to both synthetic and real video images sequences and by direct comparison with another recently published scheme Biol. Cybern. 63, 185 (1990)] for the measurement of complex optical flow.

Microscopic theory of vortex dynamics

An approach to vortex dynamics is outlined, a new form being obtained for the pair potential forces on a vortex. A microscopic calculation of the vortex inertial mass is presented. Quantum effects on vortex lattice melting are briefly discussed.

Measurement of complex optical flow with use of an augmented generalized gradient scheme

We present a method for measuring the local velocities and first-order variations in velocities in a time-varying image. The scheme is an extension of the generalized gradient model that encompasses the local variation of velocity within a local patch of the image. Motion within a patch is analyzed in parallel by 42 different spatiotemporal filters derived from 6 linearly independent spatiotemporal kernels. No constraints are imposed on the image structure, and there is no need for smoothness constraints on the velocity field. The aperture problem does not arise so long as there is some two-dimensional structure in the patch being analyzed. Among the advantages of the scheme is that there is no requirement to calculate second or higher derivatives of the image function. This makes the scheme robust in the presence of noise. The spatiotemporal kernels are of simple form, involving Gaussian functions, and are biologically plausible receptive fields. The validity of the scheme is demonstrated by application to both synthetic and real video images sequences and by direct comparison with another recently published scheme [Biol. Cybern. 63, 185 (1990)] for the measurement of complex optical flow.

Microscopic theory of vortex dynamics

An approach to vortex dynamics is outlined, a new form being obtained for the pair potential forces on a vortex. A microscopic calculation of the vortex inertial mass is presented. Quantum effects on vortex lattice melting are briefly discussed.

Rudiments of complexity theory for scientists and engineers

Complexity theory is an important and growing area in computer science that has caught the imagination of many researchers in mathematics, physics and biology. In order to reach out to a large section of scientists and engineers, the paper introduces elementary concepts in complexity theory in a informal manner, motivating the reader with many examples.

Application of scaled particle theory to alkyl-aryl surfactants: a two zone model of micellar core

Scaled Particle Theory (SPT) has been applied to predict the total free energies of micellization of ionic as well as nonionic micellar systems containing an aryl ring. A modification of the previously developed model has been made, proposing a two-zone model of micellar core which corroborates with the structural information available for such systems. The results are in good agreement with experimental data and also confirm the dictating role of cavity forming free energies for such systems

Capturability of realistic generalized true proportional navigation

The capturability of a realistic generalized true proportional navigation (RGTPN) guidance law, against a nonmaneuvering target, is analyzed. The RGTPN law is obtained by relaxing the somewhat unrealistic assumption of constant closing velocity, made in all earlier studies on generalized true proportional navigation (GTPN), and incorporating the actual time-varying value in the guidance law. Closed-form solutions for the complete capture region of RGTPN is obtained in terms of both zero and acceptable non-zero miss distances. It is shown that the capture region of RGTPN in the initial relative velocity space is significantly smaller than that of GTPN, for reasonable values of navigation constant (N) and angular direction (eta) of the missile commanded latax. However, for certain values of N and eta, capturability of RGTPN is found to be better. It is also shown that if in one of the versions of GTPN, which uses constant values of both the closing velocity and the line-of-sight (LOS) angular velocity in the guidance law, the corresponding realistic time-varying quantities are used, the capture region actually expands to cover the whole of the initial relative velocity space. A number of examples are given to compare the capture performance of RGTPN with other versions of the GTPN guidance laws.

Potential-distance relationships of clay-water systems considering the Stern theory

This paper deals with the use of Stem theory as applied to a clay-water electrolyte system, which is more realistic to understand the force system at micro level man the Gouy-Chapman theory. The influence of the Stern layer on potential-distance relationship has been presented quantitatively for certain specified clay-water systems and the results are compared with the Gouy-Chapman model. A detailed parametric study concerning the number of adsorption spots on the clay platelet, the thickness of the Stern layer, specific adsorption potential and the value of dielectric constant of the pore fluid in the Stern layer, was carried out. This study investigates that the potential obtained at any distance using the Stern theory is higher than that obtained by the Gouy-Chapman theory. The hydrated size of the ion is found to have a significant influence on the potential-distance relationship for a given clay, pore fluid characteristics and valence of the exchangeable ion.

The structural theory and physical organic chemistry

Woolley's revolutionary proposal that quantum mechanics does not sanction the concept of ''molecular structure'' - which is but only a ''metaphor'' - has fundamental implications for physical organic chemistry. On the one hand, the Uncertainty Principle limits the precision with which transition state structures may be defined; on the other, extension of the structure concept to the transition state may be unviable. Attempts to define transition states have indeed caused controversy. Consequences for molecular recognition, and a mechanistic classification, are also discussed.

Theory of electron transfer processes via chemisorbed intermediates: Part II. Current-potential characteristics

Current-potential characteristics are obtained numerically for a lone-adsorbate-mediated anodic charge transfer at the electrode-solution interface. An increase in the overpotential leads to the appearance of maxima in the anodic current-potential plots instead of the extended activationless region (i.e. a saturation current at large positive overpotentials) predicted by the direct heterogeneous outer-sphere anodic charge transfer process. A detailed analysis of the dependence of current-potential profiles and other kinetic parameters on various system parameters is also presented.

Network approach for capturing ligand-induced subtle global changes in protein structures

Ligand-induced conformational changes in proteins are of immense functional relevance. It is a major challenge to elucidate the network of amino acids that are responsible for the percolation of ligand-induced conformational changes to distal regions in the protein from a global perspective. Functionally important subtle conformational changes (at the level of side-chain noncovalent interactions) upon ligand binding or as a result of environmental variations are also elusive in conventional studies such as those using root-mean-square deviations (r.m.s.d.s). In this article, the network representation of protein structures and their analyses provides an efficient tool to capture these variations (both drastic and subtle) in atomistic detail in a global milieu. A generalized graph theoretical metric, using network parameters such as cliques and/or communities, is used to determine similarities or differences between structures in a rigorous manner. The ligand-induced global rewiring in the protein structures is also quantified in terms of network parameters. Thus, a judicious use of graph theory in the context of protein structures can provide meaningful insights into global structural reorganizations upon perturbation and can also be helpful for rigorous structural comparison. Data sets for the present study include high-resolution crystal structures of serine proteases from the S1A family and are probed to quantify the ligand-induced subtle structural variations.