Design of time delayed chaotic circuit with threshold controller

A novel time delayed chaotic oscillator exhibiting mono- and double scroll complex chaotic attractors is designed. This circuit consists of only a few operational amplifiers and diodes and employs a threshold controller for flexibility. It efficiently implements a piecewise linear function. The control of piecewise linear function facilitates controlling the shape of the attractors. This is demonstrated by constructing the phase portraits of the attractors through numerical simulations and hardware experiments. Based on these studies, we find that this circuit can produce multi-scroll chaotic attractors by just introducing more number of threshold values.Comment: 21 pages, 12 figures; Submitted to IJB

Quantal Two-Centre Coulomb Problem treated by means of the Phase-Integral Method I. General Theory

The present paper concerns the derivation of phase-integral quantization conditions for the two-centre Coulomb problem under the assumption that the two Coulomb centres are fixed. With this restriction we treat the general two-centre Coulomb problem according to the phase-integral method, in which one uses an {\it a priori} unspecified {\it base function}. We consider base functions containing three unspecified parameters $C, \tilde C$ and $\Lambda$. When the absolute value of the magnetic quantum number $m$ is not too small, it is most appropriate to choose $\Lambda=|m|\ne 0$. When, on the other hand, $|m|$ is sufficiently small, it is most appropriate to choose $\Lambda = 0$. Arbitrary-order phase-integral quantization conditions are obtained for these choices of $\Lambda$. The parameters $C$ and $\tilde C$ are determined from the requirement that the results of the first and the third order of the phase-integral approximation coincide, which makes the first-order approximation as good as possible. In order to make the paper to some extent self-contained, a short review of the phase-integral method is given in the Appendix.Comment: 23 pages, RevTeX, 4 EPS figures, submitted to J. Math. Phy

Quantal Two-Centre Coulomb Problem treated by means of the Phase-Integral Method II. Quantization Conditions in the Symmetric Case Expressed in Terms of Complete Elliptic Integrals. Numerical Illustration

The contour integrals, occurring in the arbitrary-order phase-integral quantization conditions given in a previous paper, are in the first- and third-order approximations expressed in terms of complete elliptic integrals in the case that the charges of the Coulomb centres are equal. The evaluation of the integrals is facilitated by the knowledge of quasiclassical dynamics. The resulting quantization conditions involving complete elliptic integrals are solved numerically to obtain the energy eigenvalues and the separation constants of the $1s\sigma$ and $2p\sigma$ states of the hydrogen molecule ion for various values of the internuclear distance. The accuracy of the formulas obtained is illustrated by comparison with available numerically exact results.Comment: 19 pages, RevTeX 4, 4 EPS figures, submitted to J. Math. Phy

Modulational instability in PT\cal{PT}-symmetric Bragg grating structures with saturable nonlinearity

We investigate the nontrivial characteristics of modulational instability (MI) in a system of Bragg gratings with saturable nonlinearity. We also introduce an equal amount of gain and loss into the existing system which gives rise to an additional degree of freedom, thanks to the concept of $\cal PT$- symmetry. We obtain the nonlinear dispersion relation of the saturable model and discover that such dispersion relations for both the conventional and $\cal PT$- symmetric cases contradict with the conventional Kerr and saturable systems by not displaying the typical signature of loop formation in either the upper branch or lower branch of the curve drawn against the wavenumber and detuning parameter. We then employ a standard linear stability analysis in order to study the MI dynamics of the continuous waves perturbed by an infinitesimal perturbation. The main objective of this paper is twofold. We first investigate the dynamics of the MI gain spectrum at the top and bottom of the photonic bandgap followed by a comprehensive analysis carried out in the anomalous and normal dispersion regimes. As a result, this perturbed system driven by the saturable nonlinearity and gain/loss yields a variety of instability spectra, which include the conventional side bands, monotonically increasing gain, the emergence of a single spectrum in either of the Stokes wavenumber region, and so on. In particular, we observe a remarkably peculiar spectrum, which is caused predominantly by the system parameter though the perturbation wavenumber boosts the former. We also address the impact of all the physical parameters considered in the proposed model which include coupling coefficient, dispersion parameter, and saturable nonlinearity on the phenomenon of MI for different $\cal PT$- symmetric regimes ranging from unbroken to broken one in greater detail.Comment: To appear in Phys. Rev.

A combined approach to data mining of textual and structured data to identify cancer-related targets

BACKGROUND: We present an effective, rapid, systematic data mining approach for identifying genes or proteins related to a particular interest. A selected combination of programs exploring PubMed abstracts, universal gene/protein databases (UniProt, InterPro, NCBI Entrez), and state-of-the-art pathway knowledge bases (LSGraph and Ingenuity Pathway Analysis) was assembled to distinguish enzymes with hydrolytic activities that are expressed in the extracellular space of cancer cells. Proteins were identified with respect to six types of cancer occurring in the prostate, breast, lung, colon, ovary, and pancreas. RESULTS: The data mining method identified previously undetected targets. Our combined strategy applied to each cancer type identified a minimum of 375 proteins expressed within the extracellular space and/or attached to the plasma membrane. The method led to the recognition of human cancer-related hydrolases (on average, ~35 per cancer type), among which were prostatic acid phosphatase, prostate-specific antigen, and sulfatase 1. CONCLUSION: The combined data mining of several databases overcame many of the limitations of querying a single database and enabled the facile identification of gene products. In the case of cancer-related targets, it produced a list of putative extracellular, hydrolytic enzymes that merit additional study as candidates for cancer radioimaging and radiotherapy. The proposed data mining strategy is of a general nature and can be applied to other biological databases for understanding biological functions and diseases

Synthesis and characterization of Nano sulphur: Exploring its potential as slow release fertilizer

Sulphur is rapidly being recognized as the fourth key nutrient for plants after nitrogen, phosphorus, and potassium. It functions in several critical metabolic and physiological processes, such as Chlorophyll synthesis, Protein synthesis, Activation of enzymes, Stress tolerance and Seed production. In this background, an attempt was made to synthesize nano sulphur fertilizers for slow release using the reverse microemulsion (water-in-oil microemulsion) technique. Cyclohexane was used as oil phase. Tween-80 and ethanol were used as surfactant and co-surfactant, respectively. Hydrochloric acid and sodium polysulfide solution acted as an aqueous phase. This technique resulted in the successful synthesis of nano sulphur fertilizer. The sulphur nano fertilizer was characterized using X-ray diffraction (XRD), Fourier-Transform infrared spectroscopy (FT-IR), Scanning electron microscope (SEM) and Thermogravimetric analysis (TGA). The XRD pattern revealed the orthorhombic nature of nano sulphur and the lattice face-centred. The FTIR spectra at 1406 cm-1 confirmed the sulphur vibrations. The microemulsion method yielded stable, uniform, spherical nano sulphur particles with dimensions ranging from 25 to 47 nm. The thermal disintegration between 117°C to 122°C in TGA graph was attributed to the sublimation of sulphur in orthorhombic crystalline form, indicating the successful synthesis of nano sulphur. A laboratory study on nano sulphur fertilizer and conventional sulphur fertilizer was studied with a Percolator reaction system to evaluate the slow release of sulphur from both fertilizers at ambient temperature. Percolation reactor experiment indicated that sulphate release from nano sulphur was longer for 42 days than gypsum amended soil which exhausted within 35 days. Hence, synthesized nano sulphur fertilizer maximizes nutrient retention, eliminates environmental nutrient loses and decreases fertilizer requirements