Numerical studies of anomalous diffusion in undamped but periodically-driven and parametrically-driven pendulum systems are presented. When the frequency of the periodic driving force is varied, the exponent 𝜇, which is the rate of divergence of the mean square displacement with time, is found to vary in an oscillatory manner. We show the presence of such a variation in other statistical measures such as variance of position, kurtosis, and exponents in the power-exponential law of probability distribution of position.

In this paper, the inverse synchronization problem of fractional-order dynamical systems is investigated. A general explicit coupling via an open-plus-closed-loop control for inverse synchronization of two arbitrary unidirectionally or bidirectionally coupled fractional-order systems is proposed. The inverse synchronization is proved analytically based on the stability theorem of the fractional differential equations. A key feature of this proposed scheme is that it can be applied not only to nonchaotic but also to chaotic fractional-order systems whenever they exhibit regular or irregular oscillations. Feasibility of the proposed inverse synchronization scheme is illustrated through numerical simulations.

The scalar products of polarization tensor and unit vectors are presented explicitly in spherical coordinate system expanded in terms of spherical harmonic functions. By applying the obtained formulae, different wave components in the Salpeter wave function can be shown explicitly, and the results are consistent with the results obtained by $L -S$ coupling analysis. The cancelation formula is given, by which the terms with pure $L = J + 1$ wave components in the Salpeter wave function for the bound state with $\eta_P = (-1)^J$ can be obtained by separating the $L = J - 1$ wave components from mixing terms. This separation provides the basis for studying higher-order contributions from the coupling of $L = J - 1$ and $J + 1$ wave states, and for solving the Salpeter equation exactly without approximation.

We study a particular approach for analysing worldsheet conformal invariance for bosonic string propagating in a curved background using Hamiltonian formalism. We work in the Schrödinger picture of a single-particle description of the problem where the particle moves in an infinite-dimensional space. Background independence is maintained in this approach by adopting DeWitt’s (Phys. Rev. 85, 653–661, 1952) coordinate-independent formulation of quantum mechanics. This enables us to construct certain background-independent notion of Virasoro generators, called DeWitt–Virasoro (DWV) generators, and invariant matrix elements of an arbitrary operator constructed out of them in spin-zero representation. We show that the DWV algebra is given by the Witt algebra with additional anomalous terms that vanish for Ricci-flat backgrounds. The actual quantum Virasoro generators should be obtained by first introducing the vacuum state and then normal ordering the DWV generators with respect to that. We demonstrate the procedure in flat and pp-wave backgrounds.

Drell–Yan process at LHC, $q\bar{q} \to Z/ \gamma^{\ast} \to \ell^+ \ell^-$, is one of the benchmarks for confirmation of Standard Model at TeV energy scale. Since the theoretical prediction for the rate is precise and the final state is clean as well as relatively easy to measure, the process can be studied at the LHC even at relatively low luminosity. Importantly, the Drell–Yan process is an irreducible background to several searches of beyond Standard Model physics and hence the rates at LHC energies need to be measured accurately. In the present study, the methods for measurement of the Drell–Yan mass spectrum and the estimation of the cross-section have been developed for LHC operation at the centre-of-mass energy of 10 TeV and an integrated luminosity of 100 pb^-1 in the context of CMS experiment

Decay of neutron-deficient ^128−137Gd parents emitting ⁴He to ³²S clusters are studied within the Coulomb and proximity potential model. The predicted half-lives are compared with other models and most of the values are well within the present experimental limit for measurements ($T_{1/2}$ < $10^{30} s$). The lowest $T_{1/2}$ value for ²⁸Si emission from ¹²⁸Gd indicates the role of doubly magic ¹⁰⁰Sn daughter in cluster decay process. It is also found that neutron excess in the parent nuclei slows down the cluster decay process. Geiger–Nuttal plots for all clusters are found to be linear with different slopes and intercepts. The 𝛼-decay half-lives of ${}^{148−152}$Gd parents are computed and are in agreement with experimental data. The role of doubly magic ¹³²Sn daughter in cluster decay process is also examined for various neutron-rich Ba, Ce, Nd, Sm and Gd parents emitting clusters ranging from ⁴He to ³²Si. Alpha-like structures are most probable in the decays leading to ¹⁰⁰Sn, while non-𝛼-like structures are probable in the decays leading to ¹³²Sn. The neutron–proton asymmetry in parent and daughter nuclei is responsible for the reduced decay rate in the decay leading to ¹³²Sn.

We present cluster-decay studies of ⁵⁶Ni^∗ formed in heavy-ion collisions using different Skyrme forces. Our study reveals that different Skyrme forces do not alter the transfer structure of fractional yields significantly. The cluster decay half-lives of different clusters lie within $\pm 10%$ for preformed cluster models (PCM) and $\pm 15%$ for unified fission models (UFM)

The neutron skin effect has been investigated for even isotopes of molybdenum at 25.6 MeV ${}^{94−100}$Mo($p, xn$) reaction using the geometry-dependent hybrid model of pre-equilibrium nuclear reactions. Here the initial neutron/proton exciton numbers were calculated from the neutron/proton densities obtained from an effective nucleon–nucleon interaction of the Skyrme type. Initial exciton numbers from different radii of even Mo isotopes were used to obtain the corresponding neutron emission spectra. In this investigation the calculated results are compared with the experimental data as also with each other. The results using central densities in the geometry-dependent hybrid model are in better agreement with the experimental data.

We have calculated the excitation energies ($\Delta E$) and optical oscillator strengths (OOS), of both length ($f_L$) and velocity ($f_V$) forms, for the $1s^2 2s^2 2p^6 3s^2 3p^6 3d {}^2 D^e \to 1s^2 2s^2 2p^6 3s^2 3p^5 3d^2 {}^2P^o, {}^2D^o, {}^2F^o$ transitions in V⁴⁺ ion of the potassium isoelectronic sequence by employing multiconfiguration Hartree–Fock (MCHF) method exactly in the same way as we did in our earlier work (Tiwary et al, Pramana – J. Phys. 46, 381 (1996)). We have compared the available relevant experimental data and our earlier theoretical results obtained by employing the configuration interaction (CI) method (Tiwary et al, J. Phys. B: At. Mol. Phys. 16, 2457 (1983)). Our present investigation clearly demonstrates that the MCHF method is more accurate than the CI method.

In this paper we report our calculations on several important total cross-sections (TCS$_s$) of positron impact on isoelectronic N₂ and CO molecules, treated in the complex spherical potential formalism. Basically the total (complete) cross-section $Q_T$ consists of elastic and inelastic contributions. Our total inelastic cross-section ($Q_{\text{inel}}$) contains ionization and electronic excitations together with positronium formation. Our goal here is to bifurcate $Q_{\text{inel}}$ further to deduce total ionization cross-section, using the `complex scattering potential–ionization contribution’ (CSP-ic) method of electron–atom/molecule scattering. The present range of positron energy is 15–2000 eV. All the resulting cross-sections are in a good general accord with the existing data. This work highlights the importance of various scattering channels in $e^+ - N_2$ and $e^+ - CO$ interactions at intermediate and high energies.

Self-field effects, induced by charge and current densities of the electron beam, on gain in two-stage free-electron laser with nonuniform guide magnetic field is presented. The gain equation for small-signal has been derived analytically. The results of numerical calculations show a gain decrement for group I orbits and a gain enhancement for group II orbits, due to the self-field effects. The wiggler-induced self-magnetic field has a diamagnetic effect for group I orbits, whereas for group II, it has a paramagnetic effect. It is also found that using a nonuniform guide field, rather than a uniform one, causes the gain to increase.

Performance of the backward wave oscillator (BWO) is greatly enhanced with the introduction of plasma. Linear theory of the dispersion relation and the growth rate have been derived and analysed numerically for plasma-filled rippled wall rectangular waveguide driven by sheet electron beam. To see the effect of plasma on the TM₀₁ cold wave structure mode and on the generated frequency, the parameters used are: relativistic factor $\gamma = 1.5$ (i.e. $v/c = 0.741$), average waveguide height $y_0 = 1.445$ cm, axial corrugation period $z_0 = 1.67$ cm, and corrugation amplitude $\epsilon = 0.225$ cm. The plasma density is varied from zero to $2\times 10^{12}$ cm^-3. The presence of plasma tends to raise the TM₀₁ mode cut-off frequency (14 GH$_z$ at $2 \times 10^{12}$ cm^-3 plasma density) relative to the vacuum cut-off frequency (5 GH$_z$) which also causes a decrease in the group velocity everywhere, resulting in a flattening of the dispersion relation. With the introduction of plasma, an enhancement in absolute instability was observed.

The nonlinear dust acoustic waves in dusty plasmas with negative as well as positive ions and the combined effects of bounded spherical geometry and the transverse perturbation and the size distribution of dust grains are studied. Using the perturbation method, a spherical Kadomtsev–Petviashvili (SKP) equation that describes the dust acoustic waves is deduced.

Three demonstration samples of intrinsic hydrogenated amorphous silicon (a-Si:H) films were deposited using hot wire–chemical vapour deposition (HW–CVD) technique. The optical parameters and the thickness were determined from the extremes of the interference fringes of transmission spectrum in the range of 400–2500 nm using the envelope method. The calculated values of the refractive index (𝑛) were fitted using the two-term Cauchy dispersion relation and the static refractive index values ($n_0$) obtained were 2.799, 2.629 and 3.043 which were in the range of the reported values. The calculated thicknesses for all samples were cross-checked with Taly-Step profilometer and found to be almost equal. Detailed analysis was carried out to obtain the optical band gap ($E_g$) using Tauc’s method and the estimated values were 1.99, 2.01 and 1.75 eV. The optical band gap values were correlated with the hydrogen content ($C_H$) in the samples calculated from Fourier transform infrared (FTIR) analysis. An attempt was made to apply Wemple–DiDomenico single-effective oscillator model to the a-Si:H samples to calculate the optical parameters. The optical band gap obtained by Tauc’s method and the static refractive index calculated from Cauchy fitting are in good agreement with those obtained by the single-effective oscillator model. The real and the imaginary parts of dielectric constant ($\epsilon_r, \epsilon_i$), and the optical conductivity (𝜎) were also calculated.