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

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

Comparison of two efficient numerical techniques based on Chelyshkov polynomial for solving stochastic It\^o-Volterra integral equation

In this study, two reliable approaches to solving the nonlinear stochastic It\^o-Volterra integral equation are provided. These equations have been evaluated using the orthonormal Chelyshkov spectral collocation technique and the orthonormal Chelyshkov spectral Galerkin method. The techniques presented here transform this problem into a collection of nonlinear algebraic equations that have been numerically solved using the Newton method. Also, the convergence analysis has been studied for both approaches. Two illustrative examples have been provided to show the efficacy, plausibility, proficiency, and applicability of the current approaches

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 new numerical technique based on Chelyshkov polynomials for solving two-dimensional stochastic It\^o-Volterra Fredholm integral equation

In this paper, a two-dimensional operational matrix method based on Chelyshkov polynomials is implemented to numerically solve the two-dimensional stochastic It\^o-Volterra Fredholm integral equations. These equations arise in several problems such as an exponential population growth model with several independent white noise sources. In this paper a new stochastic operational matrix has been derived first time ever by using Chelyshkov polynomials. After that, the operational matrices are used to transform the It\^o-Volterra Fredholm integral equation into a system of linear algebraic equations by using Newton cotes nodes as collocation point that can be easily solved. Furthermore, the convergence and error bound of the suggested method are well established. In order to illustrate the effectiveness, plausibility, reliability, and applicability of the existing technique, two typical examples have been presented

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