Integrability of a linearly damped two-coupled non-linear oscillators equation$$\begin{gathered} \mathop x\limits^{..} = - d\mathop {\mathop x\limits^. - \alpha x - \delta _1 (x^2 + y^2 ) - 2\delta _2 xy}\limits^. \hfill \\ \mathop y\limits^{..} = d\mathop y\limits^. - \beta y - \delta _2 (x^2 + y^2 ) - 2\delta _1 xy \hfill \\ \end{gathered} $$ is investigated by employing the Painlevé analysis. The following two integrable cases are identified: (i)d = 0, α =β, δ_1 and δ_2 are arbitrary, (ii) d^2= 25α/6, α =β, δ_1 and δ_2 are arbitrary. Exact analytical solution is constructed for the integrable choices.

By introducing an invariant operator, we obtain exact wave functions for a general time-dependent quadratic harmonic oscillator. The coherent states, both inx- andp-spaces, are calculated. We confirm that the uncertainty product in coherent state is always larger thankh/2 and is equal to the minimum of the uncertainty product of the number states. The displaced wave packet for Caldirola-Kanai oscillator in coherent state oscillates back and forth with time about the center as for a classical oscillator. The amplitude of oscillation with no driving force decreases due to the dissipation in the system. However, the oscillation with resonant frequency oscillates with a large amplitude, even after a sufficient time elapse.

The ionization of real hydrogen atom is studied under the action of a two-color pulsed laser field of duration 2.12 fs consisting of a fundamental frequencyω and one of its harmonics. We study the effect of phase difference (φ betweenω and its harmonic on the ionization probability. It is found that ionization can be switched on and off by varying the relative phaseφ betweenω and its harmonic.

Novel effects resulting from joint action of chirality and non-linearity are discussed using a basic equation describing the temporal evolution of fields in a chiral medium with Kerr non-linearity. The spatial chirality effect is characterized through the Born-Fedorov formalism. Our simulations are based on the split-step Fourier method and the solution of the Stokes parameters. The numerical results show the chiral effect on solitons with circular polarization and mixed polarization spatial solitons.

This paper addresses optimization of a high-speed digital feedback controller for a plasma position in Damavand tokamak. Damavand tokamak discharges have plasma currents up to 40 kA with discharge duration greater than 15 ms and toroidal magnetic fields up to 1.2 T. The plasma position is measured using saddle-loops and Rogowski coil and is controlled by electromagnetic forces generated by passing currents through control coils placed around the plasma. A desired control objective is maintaining the plasma in the center of vacuum vessel and to stabilize the plasma in the presence of disturbances in a time domain of the order of few milliseconds. In order to achieve maximum performance it is essential to optimize the control system. In this paper plasma position measurement and the details of implementing high-speed PID controllers based on a TMS320c25 digital signal processor along with the system optimization are presented.

The thermorheological effect on magnetoconvection in fluids with weak electrical conductivity is studied numerically under lg and μg conditions. The results with a non-linear thermorheological equation considered in the problem when compared with those of the classical approach with constant viscosity delineate the fact that the latter approach results in an over-prediction of the critical eigenvalue. The results have possible astrophysical applications involving sunspots as also in space applications under /ig.

It is shown that in magnetically quantized plasmas, static Debye screening is changed. Furthermore, it is shown that under special circumstances, two electrons in such media may attract each other.

Single crystal EPR studies of Mn(II)-doped zinc ammonium phosphate hexahydrate (ZnNH₄PC₄·6H₂O) have been reinvestigated at room temperature. Single crystal rotations along the three orthogonal axes indicate that the spin Hamiltonian parameters for the interstitial site are:g_xx = 1.966,g_yy = 1.972,g_zz = 1.976;D_xx = -12.28 mT,D_yy = -2.09 mT andD_zz = 14.37 mT;A_xx = 9.06 mT,A_yy = 9.06 mT andA_zz = 11.09 mT;a = -0.11 mT. These parameters differ considerably from the previous report of Chand and Agarwal and indicate the orthorhombic nature of the paramagnetic impurity. The impurity is found to enter the lattice interstitially, in contrast to earlier prediction of substitutional position. The percentage covalency of the Mn-0 bond has been estimated.

Certain organic crystals are found to possess high non-linear optical coefficients, often one to two orders of magnitude higher than those of the well-known inorganic non-linear optical materials. Benzoyl glycine is one such crystal whose optical second-harmonic generation efficiency is much higher than that of potassium dihydrogen phosphate. Single crystals of benzoyl glycine are grown by solvent evaporation technique usingN, N-dimethyl formamide as the solvent. All the nine second-order elastic stiffness constants of this orthorhombic crystal are determined from ultrasonic wave velocity measurements employing the pulse echo overlap technique. The anisotropy of elastic wave propagation in this crystal is demonstrated by plotting the phase velocity, slowness, Young’s modulus and linear compressibility surfaces along symmetry planes. The volume compressibility, bulk modulus and relevant Poisson’s ratios are also determined. Variation of the diagonal elastic stiffness constants with temperature over a limited range are measured and reported.

The melting temperatures of H₂, D₂; N₂ and CH₄ are analysed. The computed results are in very good agreement with the experimental data in each solid. Further, the analysis indicates the presence of the melting maximum in these solids.

It is shown that gauge theories are most naturally studied via a polar decomposition of the field variable. Gauge transformations may be viewed as those that leave the density invariant but change the phase variable by additive amounts. The path integral approach is used to compute the partition function. When gauge fields are included, the constraint brought about by gauge invariance simply means an appropriate linear combination of the gradients of the phase variable and the gauge field is invariant. No gauge fixing is needed in this approach that is closest to the spirit of the gauge principle. We derive an exact formula for the condensate fraction and in case it is zero, an exact formula for the anomalous exponent. We also derive a formula for the vortex strength which involves computing radiation corrections.

It is shown how Luttinger liquids may be studied using sea-bosons. The main advantage of the sea-boson method is its ability to provide information about short-wavelength physics in addition to the asymptotics and is naturally generalizable to more than one dimension. In this article, we solve the Luttinger model and the Calogero-Sutherland model, the latter in the weak-coupling limit. The anomalous exponent we obtain in the former case is identical to the one obtained by Mattis and Lieb. We also apply this method to solve the two-dimensional analog of the Luttinger model and show that the system is a Landau-Fermi liquid. Then we solve the model of spinless fermions in one dimension with long-range (gauge) interactions and map the Wigner crystal phase of the system.

In the present paper, a study of the deep-sea water wave caused by an oscillatory wind stress due to the atmospheric depression, resulting in spiral cyclonic wind pressure on the surface of the sea is made. It has been observed that the motion of the water wave in the case of wind stress exhibits a greater elevation on the sea surface asg the acceleration due to gravity decreases and maintains the oscillatory nature with the increase of time. For the case of spiral cyclonic motion for which the sea surface experiences the elliptical pressure on the surface, the motion diminishes asg diminishes and oscillates with the variation of time. The motion also diminishes asymptotically as the radius vector of the elliptical pressure approaches unity.

Indoor radon has been recognized as one of the health hazards for mankind. Building materials constitute the second most important source of radon in dwellings. The common building materials used in the construction of dwellings are studied for radon exhalation rate. The ‘Can’ technique using LR-115 type-II solid-state nuclear track detector has been used for these measurements. The radon exhalation rate in these samples varies from 4.75 m Bq m⁻² h⁻¹ (0.14 m Bq kg⁻¹ h⁻¹) for limestone to 506.76 m Bq m⁻² h⁻¹ (15.24 m Bq kg⁻¹ h⁻¹) for soil.