• Volume 77, Issue 2

August 2011,   pages  233-404

• Integrability of two coupled Kadomtsev–Petviashvili equations

The integrability of two coupled KP equations is studied. The simpliﬁed Hereman form of Hirota’s bilinear method is used to examine the integrability of each coupled equation. Multiplesoliton solutions and multiple singular soliton solutions are formally derived for each coupled KdV equation.

• Anharmonic solution of Schrödinger time-independent equation

We present here a mathematical explanation of how the Schrödinger equation for a class of harmonic oscillators possesses exact solutions. Some of the extended potentials used here are not present in the literature.

• Exact travelling solutions for some nonlinear physical models by ($G'/G$)-expansion method

In this paper, we establish exact solutions for some special nonlinear partial differential equations. The ($G'/G$)-expansion method is used to construct travelling wave solutions of the twodimensional sine-Gordon equation, Dodd–Bullough–Mikhailov and Schrödinger–KdV equations, which appear in many ﬁelds such as, solid-state physics, nonlinear optics, ﬂuid dynamics, ﬂuid ﬂow, quantum ﬁeld theory, electromagnetic waves and so on. In this method we take the advantage of general solutions of second-order linear ordinary differential equation (LODE) to solve many nonlinear evolution equations effectively. The ($G'/G$)-expansion method is direct, concise and elementary and can be used with a wider applicability for handling many nonlinear wave equations.

• Experimental study of the $\pi h_{11/2}$ band in 113Sb

In the present work, the excited states of 113Sb were populated in the 100Mo(20Ne, $p6n$) reaction at a beam energy of 136 MeV. States only up to $59/2^−$ were observed in the $\Delta J = 2$ band. Mean lifetimes for the ﬁve states (from 4460 to 7998 keV) were measured for the ﬁrst time using Doppler shift attenuation method. An upper limit of the lifetime (0.14 ps) was estimated for the 9061 keV, $47/2^−$ state. The $B(E2)$ values, derived from the present lifetime results, correspond to a large quadrupole deformation of $\beta_2 = 0.32$. The observed reduction in the experimental $B(E2)$ values for the 918.4 keV (spin $39/2^− \to 35/2^−$) and 985 keV (spin $43/2^− \to 39/2^−$) transitions may be interpreted as due to the proton alignement in the $g_{7/2}$ orbital. The dynamic moment of inertia was observed to be about half of the rigid body value at the highest observed frequency.

• Geometry of vanishing ﬂow: A new probe to determine the in-medium nucleon–nucleon cross-section

We studied the transverse ﬂow throughout the mass range from 20Ne+20Ne to 131Xe+131Xe as a function of the impact parameter. We found that at smaller impact parameters the ﬂow is negative while going through the impact parameter, transverse ﬂow vanishes at a particular colliding geometry named GVF. We found that the mass dependence of GVF is insensitive to the equation of state and momentum-dependent interactions whereas it is quite sensitive to the cross-section. So it can act as a useful tool to pin down the nucleon–nucleon cross-section.

• Rapidity dependence of multiplicity ﬂuctuations and correlations in high-energy nucleus–nucleus interactions

The multiplicity ﬂuctuations of the produced pions were studied using scaled variance method in 16O–AgBr interactions at 2.1 AGeV, 24Mg–AgBr interactions at 4.5 AGeV, 12C–AgBr interactions at 4.5 AGeV, 16O–AgBr interactions at 60 AGeV and 32S–AgBr interactions at 200 AGeV at two different binning conditions. In the ﬁrst binning condition, the rapidity interval was varied in steps of one centring about the central rapidity until it reached 14. In the second case, the rapidity interval was increased in steps of 1.6 up to 14.4. Multiplicity distributions and their scaled variances were presented as a function of the dependence on the rapidity width for both the binning conditions. Multiplicity ﬂuctuations were found to increase with the increase of rapidity interval and later found to saturate at larger rapidity window for all the interactions and in both the binning conditions. Multiplicity ﬂuctuations were found to increase with the energy of the projectile beam. The values of the scaled variances were found to be greater than one in all the cases in both the binning conditions indicating the presence of correlation during the multiparticle production process in high-energy nucleus–nucleus interactions. Experimental results were compared with the results obtained from the Monte Carlo simulated events for all the interactions. The Monte Carlo simulated data showed very small values of scaled variance suggesting very small ﬂuctuations for the simulated events. Experimental results obtained from 16O–AgBr interactions at 60 AGeV and 32S–AgBr interactions at 200 AGeV were compared with the events generated by Lund Monte Carlo code (FRITIOF model). FRITIOF model failed to explain the multiplicity ﬂuctuations of pions emitted from 16O–AgBr interactions at 60 AGeV for both the binning conditions. However, the experimental data agreed well with the FRITIOF model for 32S–AgBr interactions at 200 AGeV.

• Improved analysis on multiple recycling of fuel in prototype fast breeder reactor in a closed fuel cycle

An FBR closed fuel cycle involves recycling of the discharge fuel, after reprocessing and refabrication, to utilize the unburnt fuel remains and the freshly bred ﬁssile material. Our previous study in this regard for the PFBR indicated a comfortable feasibility of multiple recycling with selfsufﬁciency. In the present work, more reﬁned estimations are done using the most recent nuclear data, viz. ENDF/B-VII.0, and with the most recent speciﬁcation of the fuel composition. Among others, this paper brings out the importance of taking into account the energy self-shielding effects in the cross-section averages used in the study. While self-shielded averages lead to realistic predictions, unshielded averages signiﬁcantly overpredict breeding in the blankets and underpredict loss in the cores.

• Experimental measurement of effective atomic number of composite materials for Compton effect in the 𝛾-ray region 280–1115 keV by a new method

In this paper, we report a new method to determine the effective atomic number, $Z_{\text{eff}}$, of composite materials for Compton effect in the γ -ray region 280–1115 keV based on the theoretically obtained Klein–Nishina scattering cross-sections in the angular range $50^{\circ}–100^{\circ}$ as well as a method to experimentally measure differential incoherent (Compton) scattering cross-sections in this angular range. The method was employed to evaluate $Z_{\text{eff}}$ for different inorganic compounds containing elements in the range $Z = 1–56$, at three scattering angles 60°, 80° and 100° at three incident gamma energies 279.1 keV, 661.6 keV and 1115.5 keV and we have veriﬁed this method to be an appropriate method. Interestingly, the $Z_{\text{eff}}$ values so obtained for the inorganic compounds were found to be equal to the total number of electrons present in the sample as given by the atomic number of the elements constituting the sample in accordance with the chemical formula of the sample. This was the case at all the three energies.

• Experimental investigation of ultrasonic velocity anisotropy in magnetic ﬂuids: Inﬂuence of grain–grain interaction

Magnetic ﬁeld-induced dispersion of ultrasonic velocity in a Mn0.7Zn0.3Fe2O4 ﬂuid (applied magnetic ﬁeld is perpendicular to the ultrasonic propagation vector) is determined by employing continuous wave method. The magnitude of dispersion initially decreases with increasing ﬁeld, then increases and reaches a plateau at higher ﬁelds. Results indicate that the velocity anisotropy is dominated by grain–grain interactions rather than grain–ﬁeld interaction. At the critical temperature, the grain–grain interaction becomes weak as the transverse component of the particle/cluster moment is larger than the longitudinal one and the system reaches saturation even at low ﬁeld. These observed variations in the ﬁeld-induced anisotropy are analysed by incorporating the moment distribution of particles in Tarapov’s theory (J. Magn. Magn. Mater. 39, 51 (1983)).

• Nonlinear dust-ion-acoustic waves in a multi-ion plasma with trapped electrons

A dusty multi-ion plasma system consisting of non-isothermal (trapped) electrons, Maxwellian (isothermal) light positive ions, warm heavy negative ions and extremely massive charge ﬂuctuating stationary dust have been considered. The dust-ion-acoustic solitary and shock waves associated with negative ion dynamics, Maxwellian (isothermal) positive ions, trapped electrons and charge ﬂuctuating stationary dust have been investigated by employing the reductive perturbation method. The basic features of such dust-ion-acoustic solitary and shock waves have been identiﬁed. The implications of our ﬁndings in space and laboratory dusty multi-ion plasmas are discussed.

• Propagation and oblique collision of electron-acoustic solitons in two-electron-populated quantum plasmas

Oblique interaction of small- but ﬁnite-amplitude KdV-type electron-acoustic solitary excitations is examined in an unmagnetized two-electron-populated degenerate quantum electron–ion plasma in the framework of quantum hydrodynamics model using the extended Poincaré–Lighthill–Kuo (PLK) perturbation method. Critical plasma parameter is found to distinguish the types of solitons and their interaction phase-shifts. It is shown that, depending on the critical quantum diffraction parameter $H_{cr}$, both compressive and rarefactive solitary excitations may exist in this plasma and their collision phase-shifts can be either positive or negative for the whole range of collision angles $0 &lt; θ &lt; π$.

• Electronic structure and band alignments of ZnTe/CrTe(0 0 1), CdSe/CrTe(0 0 1) and CdTe/CrTe(0 0 1) interfaces

All-electron full potential calculations based on spin density functional theory were performed to study cubic zincblende (ZB) and hexagonal NiAs structures of bulk CrTe and ZnTe/CrTe(0 0 1), CdTe/CrTe(0 0 1) and CdSe/CrTe(0 0 1) interfaces. The lattice mismatch effect in ZB CrTe and magnetic properties of CrTe in the ideal ZB CrTe structure were investigated. The band alignment properties of the ZnTe/CrTe(0 0 1), CdTe/CrTe(0 0 1) and CdSe/CrTe(0 0 1) interfaces were computed and a rather large minority valence band offset of about 1.09 eV was observed in ZnTe/CrTe(0 0 1) heterojunction. Also in the CdTe/CrTe(0 0 1) and CdSe/CrTe(0 0 1) interfaces, the conduction band minimum of minority spin in CrTe was above the conduction band minimum of CdTe and CdSe and so the majority spin electrons could be directly injected to both semiconductors, indicating the possibility of highly efﬁcient spin injection into the CdSe and CdTe semiconductors.

• Dielectric behaviour of some amides and formamides dissolved in nonpolar solvents under static electric ﬁeld

Structural and associational aspects of polar amides (𝑗) like formamide, acetamide, Nmethyl acetamide (NMA), N,N-dimethyl formamide (DMF), N,N-dimethyl acetamide (DMA) and acetanilide dissolved in the nonpolar solvent (𝑖) benzene or 1,4-dioxan have been estimated from the measured static relative permittivity $\varepsilon_{0ij}$ and high-frequency permittivity $\varepsilon_{\infty ij}$ at different weight fractions $w_j$s of polar solute at 35°C under static electric ﬁeld using Debye model of polar liquid molecule. The static dipole moments $\mu_s$s are compared with $\mu_j$s reported from conductivity method and theoretical $\mu_{\text{theo}$s to get exact $\mu_{\text{cal}} \cdot \mu_{\text{theo}$s of the molecules are predicted from the available bond angles and bond moments where difference in electron afﬁnity exists between two adjacent atoms of a polar group due to inductive, mesomeric and electromeric effects in them. Solute–solute molecular association for NMA in benzene and solute–solvent association for other amides are ascertained to arrive at their conformational structures.

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