Adaptive projective synchronization between different chaotic systems with parametric uncertainties and external disturbances

The article deals with adaptive projective synchronization between two different chaotic systems with parametric uncertainties and external disturbances. Based on Lyapunov stability theory, the projective synchronization between a pair of different chaotic systems with fully unknown parameters are derived. An adaptive control law and a parameter update rule for uncertain parameters are designed such that the chaotic response system controls the chaotic drive system. Numerical simulation results are performed to explain the effectiveness and feasibility of the techniques.     

Arc plasma devices: Evolving mechanical design from numerical simulation

Wide ranges of technological applications involve arc plasma devices as the primary plasma source for processing work. Recent findings exhibit the existence of appreciable thermal non-equilibrium in these so-called thermal plasma devices. Commercially available magnetohydrodynamic codes are not capable of handling such systems due to unavailability of non-equilibrium thermodynamic and transport property data and self-consistent models. A recipe for obtaining mechanical design of arc plasma devices from numerical simulation incorporating two-temperature thermal non-equilibrium model is presented in this article with reference to the plasma of the mixture of molecular gases like nitrogen and oxygen. Such systems are technologically important as they correspond to the plasma devices operating with air, oxygen plasma torches in cutting industries and plasma devices using nitrogen as shielding gas. Temperature field, associated fluid dynamics and electrical characteristics of a plasma torch are computed in a systematic manner to evaluate the performance of a conceived design using a two-fluid CFD model coupled with a two-temperature thermodynamic and transport property code. Important effects of different nozzle designs and plasma gases obtained from the formalism are discussed. Non-equilibrium thermodynamic properties are computed using modified two-temperature Saha equations and transport properties are computed using standard Chapman–Enskog approach.     

Spectral narrowing of coherent population trapping resonance in laser-cooled and room-temperature atomic gas

We have investigated coherent population trapping (CPT) in laser-cooled as well as room-temperature (with and without buffer gas) rubidium atoms. The characteristic broad signal profile emerging from the two-photon Raman resonance for room-temperature atomic vapour is consistent with the theoretical calculation incorporating associated thermal averaging. The spectral width of the dark resonance obtained with cold atoms is found to be broadened, compared to room-temperature vapour cell, due to the feeble role played by thermal averaging, although the cold atomic sample significantly overcomes the limitation of the transit time broadening. An alternative way to improve transit time is to use a buffer gas, with which we demonstrate that the coherent population trapping signal width is reduced to < 540 Hz.     

Zagreb indices of graphs

The first Zagreb index M₁(G) is equal to the sum of squares of the degrees of the vertices, and the second Zagreb index M₂(G) is equal to the sum of the products of the degrees of pairs of adjacent vertices of the underlying molecular graph G. In this paper, we obtain lower and upper bounds on the first Zagreb index M₁(G) of G in terms of the number of vertices (n), number of edges (m), maximum vertex degree (Δ), and minimum vertex degree (δ). Using this result, we find lower and upper bounds on M₂(G). Also, we present lower and upper bounds on M₂(G) +M₂(G) in terms of n, m, Δ, and δ, where G denotes the complement of G. Moreover, we determine the bounds on first Zagreb coindex M₁(G) and second Zagreb coindex M₂(G). Finally, we give a relation between the first Zagreb index and the second Zagreb index of graph G.     

A study of fractional Schrödinger equation composed of Jumarie fractional derivative

In this paper we have derived the fractional-order Schrödinger equation composed of Jumarie fractional derivative. The solution of this fractional-order Schrödinger equation is obtained in terms of Mittag–Leffler function with complex arguments, and fractional trigonometric functions. A few important properties of the fractional Schrödinger equation are then described for the case of particles in one-dimensional infinite potential well. One of the motivations for using fractional calculus in physical systems is that the space and time variables, which we often deal with, exhibit coarse-grained phenomena. This means infinitesimal quantities cannot be arbitrarily taken to zero – rather they are non-zero with a minimum spread. This type of non-zero spread arises in the microscopic to mesoscopic levels of system dynamics, which means that, if we denote x as the point in space and t as the point in time, then limit of the differentials dx (and dt) cannot be taken as zero. To take the concept of coarse graining into account, use the infinitesimal quantities as (Δx) ^α (and (Δt) ^α ) with 0 < α < 1; called as ‘fractional differentials’. For arbitrarily small Δx and Δt (tending towards zero), these ‘fractional’ differentials are greater than Δx (and Δt), i.e. (Δx) ^α > Δx and (Δt) ^α > Δt. This way of defining the fractional differentials helps us to use fractional derivatives in the study of dynamic systems.     

Rayleigh light scattering from hydrogen‐bonded dimers of small astrophysical molecules

High level ab initio calculations of the Rayleigh scattering activities of the hydrogen‐bonded dimers of formic acid (HCOOH), nitrosyl hydride (HNO), and hydrogen cyanide (HCN) molecules have been performed. All these molecules have already been detected in interstellar space and are of great importance from the astrochemical point of view. The geometries of the homo‐ and hetero‐dimers have been optimized using Hartree–Fock and second‐order Møller‐Plesset perturbation theory. Dipole moment, mean dipole polarizability, and polarizability anisotropy have been calculated utilizing Pople‐type 6‐311++G(d,p) and Dunning's aug‐cc‐pVDZ basis sets for all the complexes. The polarizabilities are then used to calculate and analyze the Rayleigh scattering parameters. The results for the dimers, HCN···HCN, HCOOH···HCOOH, HNO···HNO, HCN···HCOOH, HCN···HNO, and HNO···HCOOH are compared with those of the isolated molecules, HCN, HCOOH, and HNO to see the effect of hydrogen bond formation on the molecular interaction with radiation. © 2011 Wiley Periodicals, Inc.     

Magnetic field modulation spectroscopy of rubidium atoms

The magnetically modulated saturation absorption profile is studied for a wide range of external DC magnetic field. The salient features of Doppler-free signal generated by laser frequency modulation and atomic energy level modulation are compared. The DC offset of the signal profile is found to be unstable as the external DC magnetic field is changed. The technical difficulty of tuning laser frequency under locked condition over a large frequency span is discussed along with possible solutions.