Bohr–van Leuween theorem has attracted the notice of physicists for more than 100 years. The theorem states about the absence of magnetisation in classical systems in thermal equilibrium. In this paper, we discuss about fluctuations of magnetic moment in classical systems. In recent years, this topic has been investigated intensivelyand it is not free from controversy.We have considered a system consisting of a single particle moving in a plane. A magnetic field is applied perpendicular to the plane. The system is in contact with a thermal bath.We have considered three cases: (a) particle moving in a homogeneous medium, (b) particle moving in a medium with space-dependent friction and (c) particle moving in a medium with space-dependent temperature. For all the three cases, the averagemagnetic moment and fluctuations in magnetic moment have been calculated. Average magnetic moment saturates to a finite value in the case of free particle but goes to zero when the particle is confined by a 2D harmonic potential. Fluctuations in magnetic moment shows universal features in the presence of arbitrary friction inhomogeneity. For this case, the system reaches equilibrium asymptotically. In the case of space-dependent temperature profile, the stationary distribution is non-Gibbsian and fluctuations deviate from universal value for the bounded system only.

Industrial demand for neutrons constrains careful energy measurements. Elastic scattering of monoenergetic $\alpha$-particles from neutron collision enables neutron energy measurement by calculating the amount of deviation from the position where collision takes place. The neutron numbers with specific energy is obtained by counting the number of $\alpha$-particles in the corresponding location on the charged particle detector. Monte Carlo simulation and COMSOL Multiphysics5.2 are used to account for one-to-one collision of neutrons with $\alpha$-particles.

In this article, a simple autonomous transiently chaotic flow with cubic nonlinearities is proposed. This system represents some unusual features such as having a surface of equilibria. We shall describe some dynamical properties and behaviours of this system in terms of eigenvalue structures, bifurcation diagrams, time series, and phase portraits. Various behaviours of this system such as periodic and transiently chaotic dynamics can be shown by setting special parameters in proper values. Our system belongs to a newly introduced category of transiently chaotic systems: systems with hidden attractors. Transiently chaotic behaviour of our proposed system has beenimplemented and tested by the OrCAD-PSpise software. We have found a proper qualitative similarity between circuit and simulation results.

In this work, the statistical distribution functions for boson, fermions and their mixtures have been derived and it is found that distribution functions follow the symmetry features of $\beta$ distribution. If occupation index is greater than unity, then it is easy in the present approach to visualise condensations in terms of intermediate values of mixing parameters. There are some applications of intermediate values of mixing parameters.

In this paper, we construct a novel 4D autonomous chaotic system with four cross-product nonlinear terms and five equilibria. The multiple coexisting attractors and the multiscroll attractor of the system are numerically investigated. Research results show that the system has various types of multiple attractors, including three strange attractors with a limit cycle, three limit cycles, two strange attractors with a pair of limit cycles, two coexisting strange attractors. By using the passive control theory, a controller is designed for controlling the chaos of the system. Both analytical and numerical studies verify that the designed controller can suppress chaotic motion and stabilise the system at the origin. Moreover, an electronic circuit is presented for implementing the chaotic system.

In this article, we have developed new exact analytical solutions of a nonlinear evolution equation that appear in mathematical physics, a (2 + 1)-dimensional generalised time-fractional Hirota equation, which describes the wave propagation in an erbium-doped nonlinear fibre with higher-order dispersion. By virtue of the tanh-expansion and complete discrimination system by means of fractional complex transform, travelling wave solutions are derived.Wave interaction for the wave propagation strength and angle of field quantity under the long wave limit are analysed: Bell-shape solitons are found and it is found that the complex transform coefficient in thesystem affects the direction of the wave propagation, patterns of the soliton interaction, distance and direction.

The $\alpha$ decay half-lives of hyper and normal isotopes of Po nuclei are studied in the present work. The inclusion of $\Lambda–N$ interaction changes the half-life for $\alpha$ decay. The theoretical predictions on the $\alpha$ decay half-lives of normal Po isotopes are compared with experimental results and are seen to be matching well with each other. The neutron shell closure at $N = 126$ is found to be the same for both normal and hypernuclei. The Geiger–Nuttal (G–N) law for $\alpha$ decay is unaltered in the case of hypernuclei. The hypernuclei will decay into normal nuclei by mesonic or non-mesonic decay modes. Since the half-lives of normal Po nuclei are well within the experimental limits, our theoretical results suggest experimental verification of the $\alpha$ emission from hyper Po nuclei in a cascade process.

Valence universal multireference coupled cluster (VUMRCC) method via eigenvalue independent partitioning has been applied to estimate the effect of three-body transformed Hamiltonian $(\tilde{H}_3)$ on ionisation potentials through full connected triple excitations $S^{(1,0)}_{3}$. $(\tilde{H}_3)$ is constructed using CCSDT1-A model of Bartlett $\it{et al}$ for the ground-state calculation. Contribution of transformed Hamiltonian through full connected triples $\tilde{H}_{3}S^{(1,0)}_{3}$ involves huge amount of computational operations that is time-consuming. Investigation on $\rm{Cl_2}$ and $\rm{F_2}$ molecules using cc-pVDZ and cc-pVTZ basis sets shows that the above effect varies from 0.001 eV to around 0.5 eV, suggesting that inclusion of $\tilde{H}_{3}S^{(1,0)}_{3}$ is essential for highly accurate calculations.

Based on density functional theory, we perform first-principles investigations to study the optical properties of the O-, F- and H-terminated SiC nanoribbons with armchair edges (ASiCNRs). By irradiating with an external electromagnetic field, we calculate the dielectric function, reflection spectra, energy loss coefficientand the real part of the conductance. It is demonstrated that the optical constants are sensitive to the low-energy range, different terminal atoms do not make much difference in the shape of the curves of the optical constants for the same-width ASiCNR, and the optical constants of wider nanoribbons usually have higher peaks than that of the narrower ones in low energy range. We hope that our study helps in experimental technology of fabricating high-quality SiC-based nanoscale photoelectric device.

Quantum chemical calculations have been employed to study the molecular effects produced by $\rm{Cr_{2}O_{3}/SnO_{2}}$ optimised structure. The theoretical parameters of the transparent conducting metal oxides were calculated using DFT/B3LYP/LANL2DZ method. The optimised bond parameters such as bond lengths, bond angles and dihedral angles were calculated using the same theory. The non-linear optical property of the title compound was calculated using first-order hyperpolarisability calculation. The calculated HOMO–LUMO analysis explains the charge transfer interaction between the molecule. In addition, MEP and Mulliken atomic charges werealso calculated and analysed.

Continuous energy supply is critical and important to support oscillating behaviour; otherwise, the oscillator will die. For nonlinear and chaotic circuits, enough energy supply is also important to keep electric devices working. In this paper, Hamilton energy is calculated for dimensionless dynamical system (e.g., the chaotic Lorenz system) using Helmholtz’s theorem.The Hamilton energy is considered as a new variable and then the dynamical system is controlled by using the scheme of energy feedback. It is found that chaos can be suppressed even when intermittentfeedback scheme is applied. This scheme is effective to control chaos and to stabilise other dynamical systems.

We calculate the electronic band dispersion of graphene monolayer on a two-dimensional transition metal dichalcogenide substrate (GrTMD) around $\bf{K}$ and $\bf{K'}$ points by taking into account the interplay of the ferromagnetic impurities and the substrate-induced interactions. The latter are (strongly enhanced) intrinsic spin–orbit interaction (SOI), the extrinsic Rashba spin–orbit interaction (RSOI) and the one related to the transfer of the electronic charge from graphene to substrate. We introduce exchange field $(M)$ in the Hamiltonian to take into account the deposition of magnetic impurities on the graphene surface. The cavalcade of the perturbations yield particle–hole symmetric band dispersion with an effective Zeeman field due to the interplay of the substrate-induced interactions with RSOI as the prime player. Our graphical analysis with extremely low-lying states strongly suggests the following: The GrTMDs, such as graphene on $\rm{WY_2}$, exhibit (direct) band-gap narrowing/widening (Moss–Burstein (MB) gap shift) including the increase in spin polarisation $(P)$ at low temperature due to the increase in the exchange field $(M)$ at the Dirac points. The polarisation is found to be electric field tunable as well. Finally, there is anticrossing of non-parabolic bands with opposite spins, the gap closing with same spins, etc. around the Dirac points. A direct electric field control of magnetism at the nanoscale is needed here. The magnetic multiferroics, like $\rm{BiFeO_{3}}$ (BFO), are useful for this purpose due to the coupling between the magnetic and electric order parameters.

Excitation functions for α-induced reactions on natural vanadium were measured in the energy range up to 20 MeV. The stacked-foil activation technique was used. The experimental results were compared with the theoretical calculations using EMPIRE-3.1, EMPIRE-3.2.2 and TENDL 2015, and with earlier experimental results. Thick target yields were calculated for the production of $^{54}\rm{Mn}$ and for the associated impurity $^{52}\rm{Mn}$.

Using quantum hydrodynamic (QHD) model and standard reductive perturbation method, we have investigated the formation and characteristics of space-charge solitary waves and double layers in n-type compensated drifting semiconductor plasma with varying doping profiles. Through numerical analysis, it is shown that thestructures of space-charge solitary waves and double layers depend significantly on electron drift and compensation parameter which measures a comparative proportion of the donor, acceptor and intrinsic ion concentrations.

A specific class of singularity-free cosmological model has recently been considered in light of different observational data such as observed Hubble data, BAO data from luminous red galaxy survey by Slowan digital sky survey (SDSS) and CMB data from WMAP. However, it is observed that only 12–14 data points are used to study the viability of the model in late time. In this paper, we discuss the viability of all the models belonging to the same class of EU in light of union compilation data (SNIa) which consists of over a hundred data points, thus getting a more robust test for viability. More importantly, it is crucial that we can distinguish between the various models proposed in the class of solution obtained. We discuss here why with the present observational data it is difficult to distinguish between all of them. We show that the late-time behaviour of the model is typical to any asymptotically de Sitter model.