A new analytical modelling for nonlocal generalized Riesz fractional sine-Gordon equation

AbstractIn this paper, a novel approach comprising the modified decomposition method with Fourier transform has been implemented for the approximate solution of fractional sine-Gordon equation utt-RDxαu+sinu=0 where RDxα is the Riesz space fractional derivative, 1≤α≤2. For α=2, it becomes classical sine-Gordon equation utt−uxx+sin u=0 and corresponding to α=1, it becomes nonlocal sine-Gordon equation utt−Hu+sin u=0 which arises in Josephson junction theory, where H is the Hilbert transform. The fractional sine-Gordon equation is considered as an interpolation between the classical sine-Gordon equation (corresponding to α=2) and nonlocal sine-Gordon equation (corresponding to α=1). Here the analytic solution of fractional sine-Gordon equation is derived by using the modified decomposition method with Fourier transform. Then, we analyze the results by numerical simulations, which demonstrate the simplicity and effectiveness of the present method

Studies on modulation of hemocyte surface antigen through agglutination reaction under arsenic toxicity in edible mudcrab (Scylla serrata)

Scylla serrata (Crustacea: Decapoda), which is widely spread on the intertidal mudflat of West Bengal, India's Sundarbans Biosphere Reserves, is a potential aqua crop and an economically significant edible species. One of the larger crab groups in the mangrove swamp of the Sundarbans is thought to be this one. The S. serrata's multifaceted immune response is directly tied to its diverse habitat and survival technique. It lives in dangerous surroundings and is constantly in danger of physiological stress brought on by various xenobiotics, such as arsenic. By producing a number of polyclonal antisera in rabbits (New Zealand White, albino), the study attempted to evaluate the surface antigen against crab hemocytes and murine lymphocytes. Control hemocytes and hemocytes treated to 1 ppm expressed very identical reactivity to antihemocyte sera for the agglutination reaction. The control results, however, shifted when exposed to 2 and 3 ppm of sodium arsenite, indicating arsenic-induced hemocyte surface modification. The agglutination reaction from the control sets of hemocytes that reacted with murine anti-lymphocyte sera gradually, shifted as the quantity of sodium arsenite in the medium of the treatment sets increased. The maximum equivalence zone of murine lymphocyte and hemocyte agglutination 98.6% and 99% respectively suggested a potential epitope sharing between two phylogenetically separate species. The situation may lead to a possible alteration of immune status and make opportunity for pathogenic foreign invaders within the mud crab body. Chronic arsenic exposure indicated a steady decline of edible and demandable S. serrata in the natural habitat of Sundarbans

Two Reliable Efficient Methods for Solving Time- Fractional Coupled Klein-Gordon-Schrdinger Equations

In this paper, homotopy perturbation method and homotopy perturbation transform method have been implemented for solving time fractional coupled Klein-Gordon-Schrdinger equations. We first applied homotopy perturbation method for solving time fractional coupled Klein-Gordon-Schrdinger equations, which does not require a small parameter in the equations. Then we presented an algorithm of the homotopy perturbation transform method to solve coupled Klein-Gordon-Schrdinger equations. This paper establishs the effectiveness of the homotopy perturbation transformation method in solving fractional coupled Klein-Gordon-Schrdinger equations over homotopy Perturbation method. Here we obtain the solutions of fractional coupled Klein-Gordon-Schrodinger equations, which are obtained by replacing the time derivatives with a fractional derivatives of order a 2 (1,2], b 2 (0,1] respectively. The results obtained by homotopy perturbation transform method are numerically and graphically compared with homotopy Perturbation method in order to exhibit the efficiency of the homotopy perturbation transformation method. The fractional derivatives here are described in Caputo sense

Understanding Nuclei in the upper sd - shell

Nuclei in the upper-$sd$ shell usually exhibit characteristics of spherical single particle excitations. In the recent years, employment of sophisticated techniques of gamma spectroscopy has led to observation of high spin states of several nuclei near A$\simeq$ 40. In a few of them multiparticle, multihole rotational states coexist with states of single particle nature. We have studied a few nuclei in this mass region experimentally, using various campaigns of the Indian National Gamma Array setup. We have compared and combined our empirical observations with the large-scale shell model results to interpret the structure of these nuclei. Indication of population of states of large deformation has been found in our data. This gives us an opportunity to investigate the interplay of single particle and collective degrees of freedom in this mass region.Comment: 8 pages, 13 figures, submitted for publication in the Proceedings of "Frontiers in Gamma-Ray Spectroscopy 2012 (FIG12), held at New Delhi, March 5th - 7th, 2012, Organized by Inter University Accelerator Center, New Delhi, Indi

A numerical technique for solving multi-dimensional fractional optimal control problems using fractional wavelet method

This paper presents an efficient numerical method for solving fractional optimal control problems using an operational matrix for a fractional wavelet. Using well-known formulae such as Caputo and Riemann-Liouville operators to determine fractional derivatives and integral fractional wavelets, operational matrices were devised and utilised to solve fractional optimal control problems. The proposed method reduced the fractional optimal control problems into a system of algebraic equations. To validate the effectiveness of the presented numerical approach, some illustrative problems were solved using fractional Taylor and Taylor wavelets, and the approximate cost function value derived by approximating state and control functions was compared. In addition, convergence rate and error bound of the proposed method have been derived

Ultracold bosons in a synthetic periodic magnetic field: Mott phases and re-entrant superfluid-insulator transitions

We study Mott phases and superfluid-insulator (SI) transitions of ultracold bosonic atoms in a two-dimensional square optical lattice at commensurate filling and in the presence of a synthetic periodic vector potential characterized by a strength $p$ and a period $l=qa$, where $q$ is an integer and $a$ is the lattice spacing. We show that the Schr\"odinger equation for the non-interacting bosons in the presence of such a periodic vector potential can be reduced to an one-dimensional Harper-like equation which yields $q$ energy bands. The lowest of these bands have either single or double minima whose position within the magnetic Brillouin zone can be tuned by varying $p$ for a given $q$. Using these energies and a strong-coupling expansion technique, we compute the phase diagram of these bosons in the presence of a deep optical lattice. We chart out the $p$ and $q$ dependence of the momentum distribution of the bosons in the Mott phases near the SI transitions and demonstrate that the bosons exhibit several re-entrant field-induced SI transitions for any fixed period $q$. We also predict that the superfluid density of the resultant superfluid state near such a SI transition has a periodicity $q$ ($q/2$) in real space for odd (even) $q$ and suggest experiments to test our theory.Comment: 8 pages, 11 figures, v

Temporal dynamics of sucking pest and field response of promising insecticidal molecules in okra

To investigate the response due to application of newer insecticide on sucking pest in okra, a trial was designed at field level for three consecutive years from 2011-12 to 2013-14 in kharif season. Moreover, impacts of applied insecticides on natural enemies were also assessed. Based on experimental finding thiamethoxam 25WG 0.003% (2.83 per 3 leaves, 0.93 per 3 leaves), imidacloprid 70WG 0.004% (3.49 per 3 leaves, 1.30 per 3 leaves) and thiacloprid 21.7 SC 0.006% (4.28 per 3 leaves, 1.75 per 3 leaves) provided superior control of leafhoppers and whiteflies population on okra. Effectiveness of these treatments was reflected in terms of reduction in population of both insects and significantly increases (thiamethoxam: 95.50 q/ha, imidacloprid: 86.96 q/ha and thiacloprid: 80.99 q/ha) the fruit yield in comparison to others. However, the incidence of Yellow Vein Mosaic disease was recorded least in thiamethoxam 0.003% sprayed plots followed by imidacloprid 0.004%. Slow progress in the population ofwhitefly and leaf hopper was recorded in thiamethoxam 0.003% applied plots. There was positive correlation between whitefly and virus incidence in conducted field trial. Under the experiment, neonicotinoids group of insecticides have not adverse effect on natural enemies in okra crop. The information generated under the study can be incorporated in management modules in crop okra without disturbing the ecology of natural enemy and cropping system. In our findings, the quantitative data of temporal increment of whiteflies and mosaic disease will be helpful in understanding or formulating of epidemiological models

Ab-initio study of disorder effects on the electronic and magnetic structures of Sr2_2FeMoO6_6

We have investigated the electronic structure of ordered and disordered Sr$_2$FeMoO$_6$ using {\it ab-initio} band structure methods. The effect of disorder was simulated within super-cell calculations to realize several configurations with mis-site disorders. It is found that such disorder effects destroy the half-metallic ferro-magnetic state of the ordered compound. It also leads to a substantial reduction of the magnetic moments at the Fe sites in the disordered configurations. Most interestingly, it is found for the disordered configurations, that the magnetic coupling within the Fe sub-lattice as well as that within the Mo sub-lattice always remain ferro-magnetic, while the two sub-lattices couple anti-ferromagnetically, in close analogy to the magnetic structure of the ordered compound, but in contrast to recent suggestions.Comment: 7 pages, 3 figure

High-spin structure and Band Termination in 103^{103}Cd

Excited states of the neutron deficient $^{103}$Cd nucleus have been investigated via the $^{72}$Ge($^{35}$Cl, p3n) reaction at beam energy of 135 MeV by use of in-beam spectroscopic methods. Gamma rays depopulating the excited states were detected using the Gammasphere spectrometer with high-fold $\gamma$-ray coincidences. A quadrupole $\gamma$-ray coincidence analysis ($\gamma^{4}$) has been used to extend the known level scheme. The positive parity levels have been established up to $J = 35/2\hbar$ and $E_{x} = 7.071$ MeV. In addition to the observation of highly-fragmented level scheme belonging to the positive-parity sequences at E$_{x}\sim$ 5 MeV, the termination of a negative-parity sequence connected by $E2$ transitions has been established at $J = 47/2 \hbar$ and $E_{x} = 11.877$ MeV. The experimental results corresponding to both the positive- and negative-parity sequences have been theoretically interpreted in the framework of the core particle coupling model. Evidence is presented for a shape change from collective prolate to non-collective oblate above the $J^{\pi} = 39/2^{-}$ (8011 keV) level and for a smooth termination of the negative-parity band.Comment: 19 pages, 8 figures. Submitted to Phys. Rev.