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.

Ultrafast underdamped solvation: Agreement between computer simulation and various theories of solvation dynamics

A theoretical analysis of the three currently popular microscopic theories of solvation dynamics, namely, the dynamic mean spherical approximation (DMSA), the molecular hydrodynamic theory (MHT), and the memory function theory (MFT) is carried out. It is shown that in the underdamped limit of momentum relaxation, all three theories lead to nearly identical results when the translational motions of both the solute ion and the solvent molecules are neglected. In this limit, the theoretical prediction is in almost perfect agreement with the computer simulation results of solvation dynamics in the model Stockmayer liquid. However, the situation changes significantly in the presence of the translational motion of the solvent molecules. In this case, DMSA breaks down but the other two theories correctly predict the acceleration of solvation in agreement with the simulation results. We find that the translational motion of a light solute ion can play an important role in its own solvation. None of the existing theories describe this aspect. A generalization of the extended hydrodynamic theory is presented which, for the first time, includes the contribution of solute motion towards its own solvation dynamics. The extended theory gives excellent agreement with the simulations where solute motion is allowed. It is further shown that in the absence of translation, the memory function theory of Fried and Mukamel can be recovered from the hydrodynamic equations if the wave vector dependent dissipative kernel in the hydrodynamic description is replaced by its long wavelength value. We suggest a convenient memory kernel which is superior to the limiting forms used in earlier descriptions. We also present an alternate, quite general, statistical mechanical expression for the time dependent solvation energy of an ion. This expression has remarkable similarity with that for the translational dielectric friction on a moving ion.

Microscopic Mechanism of 1/f Noise in Graphene: Role of Energy Band Dispersion

A distinctive feature of single-layer graphene is the linearly dispersive energy bands, which in the case of multilayer graphene become parabolic. A simple electrical transport-based probe to differentiate between these two band structures will be immensely valuable, particularly when quantum Hall measurements are difficult, such as in chemically synthesized graphene nanoribbons. Here we show that the flicker noise, or the 1/f noise, in electrical resistance is a sensitive and robust probe to the band structure of graphene. At low temperatures, the dependence of noise magnitude on the carrier density was found to be opposite for the linear and parabolic bands. We explain our data with a comprehensive theoretical model that clarifies several puzzling issues concerning the microscopic origin of flicker noise in graphene field-effect transistors (GraFET).

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

Molecular interpretation of the linear relationship between the entropy and the enthalpy of activation of charge transfer reactions in polar liquids

The well-known linear relationship (T?S# =??H# +?, where 1 >? > 0,? > 0) between the entropy (?S#) and the enthalpy (?H#) of activation for reactions in polar liquids is investigated by using a molecular theory. An explicit derivation of this linear relation from first principles is presented for an outersphere charge transfer reaction. The derivation offers microscopic interpretation for the quantities? and?. It has also been possible to make connection with and justify the arguments of Bell put forward many years ago.

Collective Effects on Single Particle Orientational Relaxation in Slow Dipolar Liquids

Theoretical and computer simulation studies of orientational relaxation in dense molecular liquids are presented. The emphasis of the study is to understand the effects of collective orientational relaxation on the single-particle orientational dynamics. The theoretical analysis is based on a recently developed molecular hydrodynamic theory which allows a self-consistent description of both the collective and the single-particle orientational relaxation. The molecular hydrodynamic theory can be used to derive a relation between the memory function for the collective orientational correlation function and the frequency-dependent dielectric function. A novel feature of the present work is the demonstration that this collective memory function is significantly different from the single-particle rotational friction. However, a microscopic expression for the single-particle rotational friction can be derived from the molecular hydrodynamic theory where the collective memory function can be used to obtain the single-particle orientational friction. This procedure allows, us to calculate the single-particle orientational correlation function near the alpha-beta transition in the supercooled liquid. The calculated correlation function shows an interesting bimodal decay below the bifurcation temperature as the glass transition is approached from above. Brownian dynamics simulations have been carried out to check the validity of the above procedure of translating the memory function from the dielectric relaxation data. We have also investigated the following two issues important in understanding the orientational relaxation in slow liquids. First, we present an analysis of the ''orientational caging'' of translational motion. The value of the translational friction is found to be altered significantly by the orientational caging. Second, we address the question of the rank dependence of the dielectric friction using both simulation and the molecular hydrodynamic theory.

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.

The principle of microscopic reversibility in organic chemistry - a critique

The principle of microscopic reversibility is one of the few generalising principles used in organic chemistry which have their roots in the fundamental laws of thermodynamics. It has, therefore, been highly popular. However, although the principle has some important uses, its general application is not without pitfalls. The principle is easy to misunderstand and to misapply: indeed, some of its formulations are semantically dubious. The principle is most dangerous when used as a charm, for it is more subtle than some of its formulations suggest. But above all, the principle may not be used for deducing or disproving the mechanism of a reaction, except when the mechanism in the reverse direction is known independently. For, such use is, perhaps, the deadliest misapplication.

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.

Limiting ionic conductance of symmetrical, rigid ions in aqueous solutions: Temperature dependence and solvent isotope effects

Limiting ionic conductance (Lambda(0)) of rigid symmetrical unipositive ions in aqueous solution shows a strong temperature dependence. For example, Lambda(0) more than doubles when the temperature is increased from 283 to 318 K. A marked variation also occurs when the solvent is changed from ordinary water (H2O) to heavy water (D2O). In addition, Lambda(0) shows a nonmonotonic size dependence with a skewed maximum near Cs+. Although these important results have been known for a long time, no satisfactory theoretical explanation exists for these results. In this article we present a simple molecular theory which provides a nearly quantitative explanation in terms of microscopic structure and dynamics of the solvent. A notable feature of this theory is that it does not invoke any nonquantifiable models involving solvent-berg or clatherates. We find the strong temperature dependence of Lambda(0) to arise from a rather large number of microscopic factors, each providing a small but nontrivial contribution, but all acting surprisingly in the same direction. This work, we believe, provides, for the first time, a satisfactory explanation of both the anomalous size and temperature dependencies of Lambda(0) of unipositive ions in molecular terms. The marked change in Lambda(0) as the solvent is changed from H2O to D2O is found to arise partly from a change in the dielectric relaxation and partly from a change in the effective interaction of the ion with the solvent.