Dust ion acoustic waves in non-thermal Cairns bi-Maxwellian plasma

Using kinetic theory approach, the dispersion relation ω_r and Landau damping rate γ for dust ion acoustic waves are investigated numerically and analytically in an unmagnetized collisionless dusty plasma considering Cairns distribution for electrons and ions in stationary dust particles background. The phase velocity and Landau damping rate are calculated in the limits v_td∥ < v_ti∥ << ω/k << v_te∥ . The electrons and ions non-thermality effects are incorporated via the non-thermality parameter (0 ≤ α < 1) . The real frequency ω_r and Landau damping rate γ of the mode in Cairns bi-Maxwellian distributed plasma are graphically shown to depend on plasma parameters namely non-thermality index α , ion to electron temperature ratio T_i∥/T_e∥ and the dust concentration parameter δ (=1 − ηZ_d) .     

An analytical technique for solving a class of strongly nonlinear conservative systems

Recently, an analytical technique has been developed to determine approximate solutions of strongly nonlinear differential equations containing higher order harmonic terms. Usually, a set of nonlinear algebraic equations is solved in this method. However, analytical solutions of these algebraic equations are not always possible, especially in the case of a large oscillation. Previously such algebraic equations for the Duffing equation were solved in powers of a small parameter; but the solutions measure desired results when the amplitude is an order of 1. In this article different parameters of the same nonlinear problems are found, for which the power series produces desired results even for the large oscillation. Moreover, two or three terms of this power series solution measure a good result when the amplitude is an order of 1. Besides these, a suitable truncation formula is found in which the solution measures better results than existing solutions. The method is mainly illustrated by the Duffing oscillator but it is also useful for many other nonlinear problems.     

Long term dynamics in a mathematical model of HIV-1 infection with delay in different variants of the basic drug therapy model

Infection with HIV-1, degrading the human immune system and recent advances of drug therapy to arrest HIV-1 infection, has generated considerable research interest in the area. Bonhoeffer et al. (1997) [1], introduced a population model representing long term dynamics of HIV infection in response to available drug therapies. We consider a similar type of approximate model incorporating time delay in the process of infection on the healthy T cells which, in turn, implies inclusion of a similar delay in the process of viral replication. The model is studied both analytically and numerically. We also include a similar delay in the killing rate of infected CD4⁺ T cells by Cytotoxic T-Lymphocyte (CTL) and in the stimulation of CTL and analyse two resulting models numerically.The models with no time delay present have two equilibria: one where there is no infection and a non-trivial equilibrium where the infection can persist. If there is no time delay then the non-trivial equilibrium is locally asymptotically stable. Both our analytical results (for the first model) and our numerical results (for all three models) indicate that introduction of a time delay can destabilize the non-trivial equilibrium. The numerical results indicate that such destabilization occurs at realistic time delays and that there is a threshold time delay beneath which the equilibrium with infection present is locally asymptotically stable and above which this equilibrium is unstable and exhibits oscillatory solutions of increasing amplitude.     

Pyridines from azabicyclo[3.2.0]hept-2-en-4-ones through a proposed azacyclopentadienone

Pyridines have been formed by heating azabicyclo[3.2.0]hept-2-en-4-ones in toluene. The generation of a 3-azacyclopentadienone intermediate via a [2 + 2]-cycloreversion is proposed as the key step. A Diels-Alder reaction of a styrene, extrusion of carbon monoxide, and loss of hydrogen then gives the pyridine. The process parallels the well-known synthesis of benzenes from cyclopentadienones. The azabicyclo[3.2.0]hept-2-en-4-ones were synthesized from the reaction between readily available cyclopropenones and 1-azetines, in which the cyclopropenones behave as all-carbon 1,3-dipolar equivalents.     

Synthesis and NLO properties of new trans 2-(thiophen-2-yl)vinyl heteroaromatic iodides

The synthesis and characterisation of new trans 2-(thiophen-2-yl)vinyl pyridinium, imidazolium and quinoilinium iodides is reported together with their solvatochromic shifts and EFISH characterization. 2-{(E)-2-[5'-(dibutylamino)-2,2'-bithien-5-yl]vinyl}-1-methyl pyridinium and quinolinium iodides display high μ.β(vec) values up to 1200 × 10(-48) esu. The promising non-linear optical (NLO) properties of this new family of chromophores, which can be further improved by the design of highly efficient systems exploiting the donor and acceptor properties of both heteroaromatic rings and substituents, make them suitable candidates for second harmonic generation imaging with interesting biological applications.     

Hall effects on hydromagnetic flow of an Oldroyd 6-constant fluid between concentric cylinders

The hydromagnetic flow of an electrically conducting, incompressible Oldroyd 6-constant fluid between two concentric cylinders is investigated. The flow is generated by moving inner cylinder and/or application of the constant pressure gradient. Two non-linear boundary value problems are solved numerically. The effects of material parameters, pressure gradient, magnetic field and Hall parameter on the velocity are studied. The graphical representation of velocity reveals that characteristics for shear thinning/shear thickening behaviour of a fluid is dependent upon the rheological properties.     

A glassy carbon electrode modified with SnO2 nanofibers,polyaniline and hemoglobin for improved amperometric sensing of hydrogen peroxide

Microchimica Acta - The authors describe a glassy carbon electrode (GCE) modified with a multiporous nanofibers prepared from SnO2, polyaniline and hemoglobin, and its application to the...     

Two-dimensional atom localization via Raman-driven coherence

A scheme for two-dimensional (2D) atom localization via Raman-driven coherence in a four-level diamond-configuration system is suggested. The atom interacts with two orthogonal standing-wave fields where each standing-wave field is constructed from the superposition of the two-standing wave fields along the corresponding directions. Due to the position-dependent atom–field interaction, the frequency of the spontaneously emitted photon carries the position information about the atom. We investigate the effect of the detunings and phase shifts associated with standing-wave fields. Unique position information of the single atom is obtained by properly adjusting the system parameters. This is an extension of our previous proposal for one-dimensional atom localization via Raman-driven coherence [1].     

Unified Krylov-Bogoliubov-Mitropolskii method for solving nth order non-linear systems with slowly varying coefficients

The unified Krylov-Bogoliubov-Mitropolskii (KBM) method is extended for obtaining the transient response of an n-th order (n?2) non-linear system with slowly varying coefficients. The method is a generalization of KBM method and covers all the three cases when the eigenvalues of the unperturbed equation are real, complex conjugate, or purely imaginary. It is shown that by suitable substitution for the eigenvalues in the general result that the solution corresponding to each of the three cases can be obtained. The method is illustrated by examples.