G. Purohit

Image Encryption through a Novel Permutation-Substitution Scheme Based on Chaotic Standard Map

A novel permutation-substitution scheme, which is based on chaotic standard map, for the image encryption is proposed. It is loss-less symmetric block cipher and specifically designed for the colour images. The initial condition & system parameter of the chaotic standard map, number of iterations and number of rounds constitute the secret key of the algorithm. Firstly we mix all three colour layers (3 D matrix) of the plain image and convert them into a 2D matrix. Each encryption round comprises of three stages: permutation rounds, substitution rounds and again permutation rounds. To increase the speed of encryption, the permutation and substitution are done row-by-row and column-by-column instead of pixel-by-pixel. The permutation process is controlled through the pseudo random number sequences (PRNS) generated from the discretization of chaotic standard map, however in the substitution, the properties of rows and column pixels of various layers are mixed with the PRNS generated from the standard map. The security of the proposed image encryption has been analyzed thoroughly using various statistical analysis, key sensitivity analysis, differential analysis, key space analysis, etc. Results suggest that the proposed image encryption technique can be used for the real time secure image and video communication applications.

(e, 2e) triple differential cross sections of alkali and alkali earth atoms: Na, K and Mg, Ca

Recently low-energy measurements have been reported for alkali targets Na and K and alkali earth targets Mg and Ca in coplanar symmetric geometry. We report the results of our calculation of triple differential cross section (TDCS) for electron impact single ionization (i.e. (e, 2e) processes) of alkali atoms Na, K and alkali earth atoms Mg, Ca in coplanar symmetric geometry. We have performed the present calculations using the distorted-wave Born approximation (DWBA) formalism at intermediate incident electron energies used in the recently performed experiments. Ionization takes place from the valence shell for all the targets investigated and the outgoing electrons share the excess energy equally. We have also considered the effect of target polarization in our DWBA calculations which may be an important quantity at incident electron energies used in the present investigation. We find that the DWBA formalism is able to reproduce most of the trend of experimental data and may provide a future direction for further investigation of ionization process on alkali and alkali earth metals. It is also observed that the second-order effects are more important to understand the collision dynamics of (e, 2e) processes on alkali earth targets

(e, 2e) triple differential cross sections of Ca atoms at low energies

Recently, several theoretical studies (Hitawala et al 2008 J. Phys. B: At. Mol. Opt. Phys. 41 035205; Khajuria and Deshmukh 2008 Phys. Rev. A 78 024702; Chauhan et al 2005 Phys. Rev. A 71 032708) have been reported to analyze the measurements of triple differential cross section (TDCS) for (e, 2e) processes on Ca (4s2) atom in coplanar geometry (Murray 2005 Phys. Rev. A 72 062711). In this paper, the (e, 2e) TDCS of the Ca atom has been revisited with the inclusion of correlation-polarization potential and post-collision interaction in the distorted wave Born approximation formalism. We note that the present attempt significantly improves the understanding of (e, 2e) processes at low energies on Ca atom. Still there are several discrepancies between the experimental and theoretical results that require more theoretical attempts to explain them properly.

Bifurcation and Chaos in Periodically Forced and Nonlinearly Damped Pendulum

Abstract In this communication, we mainly focus our attention on the global dynamical behavior of forced and nonlinearly damped pendulum. We consider the nonlinear damping term proportional to the power of velocity (v|v|p−1). Analytically we obtain the threshold condition for the occurrence of homoclinic bifurcation using Melnikov technique. We carry out the bifurcation analysis to identify the route to chaos for various cases of damping (p = 1, 2 and 3) and analyze the topological shape and fractalness of phase space attractor by computing Kaplan-Yorke dimension and Correlation dimension. We identify the regions of 2D parameter space (consists of external forcing amplitude and damping coefficient) corresponding to various types of asymptotic dynamics through extensive Lyapunov exponent calculation and analyze the fragileness and globalness of chaos in the parameter space with the introduction of nonlinear damping. We also analyze the complexity of basin of attraction for all three cases (p = 1, 2 and 3) and compute the correlation dimension to quantify the fractalness of basin boundaries.

A Numerical Exploration of the Dynamical Behaviour of q-Deformed Nonlinear Maps

In this paper we explore the dynamical behaviour of the qdeformed versions of widely studied 1D nonlinear map-the Gaussian map and another famous 2D nonlinear map-the Henon map. The Gaussian map is perhaps the only 1D nonlinear map which exhibits the co-existing attractors. In this study we particularly, compare the dynamical behaviour of the Gaussian map and q-deformed Gaussian map with a special attention on the regions of the parameter space, where these maps exhibit co-existing attarctors. We also generalize the q-deformation scheme of 1D nonlinear map to the 2D case and apply it to the widely studied 2D quadratic map-the Henon map which is the simplest nonlinear model exhibiting strange attractor.

(e, 2e) processes on Ne, Ar and Xe targets

Recently, there have been several attempts to explain the features of triple differential cross section (TDCS) for the (e, 2e) processes on inert targets Ne, Ar and Xe but there are still certain discrepancies in theoretical results and measurements, which require more theoretical efforts to understand the collision dynamics of these targets. We present in this paper the results of our modified distorted wave Born approximation (DWBA) calculation of TDCS for the ionization of Ne (2p), Ar (3p) and Xe (5p) targets. We modify the standard DWBA formalism by including the correlation-polarization potential (which is function of electron density) and compare our computed results with the available experimental and theoretical data. We observe that the polarization potential is able to improve the agreement with experimental results.

An analogue circuit to study the forced and quadratically damped Duffing oscillator

In this communication we study the forced and quadratically damped Duffing oscillator system experimentally through an analogue circuit. For this purpose we design a circuit and observe its dynamical behaviour under various sets of control parameters and also compare the experimental results with the numerical simulation results.

An Approach to Improve the Classification Accuracy of Leaf Images with Dorsal and Ventral Sides by Adding Directionality Features with Statistical Feature Sets

The basic purpose of this work is to study statistical feature set obtained from digital leaf image with dorsal and ventral sides and to find the degree of classification accuracy for each dorsal and ventral leaf image dataset. Moreover, the effect of adding directional features to statistical feature set on the overall classification accuracy, is also investigated. The work also studies whether the ventral side of the digital leaf image can be a suitable alternative for classification of leaf image data set or not.

Calculation of fully differential cross sections for the near threshold double ionization of helium atoms

Fully differential cross sectional (FDCS) results are reported for the electron-impact double ionization of helium atoms at 5 and 27 eV excess energy. The present attempt to calculate the FDCS in the second Born approximation and treating the postcollision interaction is helpful to analyze the measurements of Ren et al (2008 Phys. Rev. Lett. 101 093201) and Durr et al (2007 Phys. Rev. Lett. 98 193201). The second-order processes and postcollision interaction have been found to be significant in describing the trends of the FDCS. More theoretical effort is required to describe the collision dynamics of electron-impact double ionization of helium atoms at near threshold.

Calculation of FDCS for the low and intermediate energy electron impact ionization of water molecules

Fully differential cross sections (FDCS) results for the electron impact ionization of water molecules taking place from 1b1, 1b2 and 2a1 orbitals are presented. The FDCS calculations have been performed in second Born approximation.