Volume 71, Issue 3

This is an attempt of a non-technical but conceptually consistent presentation of quantum theory in a historical context. While the first part is written for a general readership, Section 5 may appear a bit provocative to some quantum physicists. I argue that the single-particle wave functions of quantum mechanics have to be correctly interpreted as field modes that are “occupied once” (i.e. first excited states of the corresponding quantum oscillators in the case of boson fields). Multiple excitations lead to apparent many-particle wave functions, while the quantum states proper are defined by wave function(al)s on the “configuration” space of fundamental fields, or on another, as yet elusive, fundamental local basis.

Energy bands and density of states (DOS) of mixed molybdenum dichalcogenides like MoS 2 , MoSeS, MoSe 2 , MoTe 2 , MoTeS, and MoTe 0.5 S 1.5 are reported for the first time using the Tran–Blaha modified Becke–Johnson potential within full potential-linearised augmented plane wave technique. From the partial DOS, a strong hybridisation between the Mo- d and chalcogen- p states is observed below the Fermi energy E F . In addition, the dielectric constants, absorption coefficients, and refractivity spectra of these compounds have also been deduced. The integrated absorption coefficients derived from the frequency-dependent absorption spectra within the energy range of 0–4.5 eV show a possibility of using molybdenum dichalcogenides, particularly MoTe 0.5 S 1.5 , in solar cell applications. Birefringence and degree of anisotropy are also discussed using the data on refractivity and imaginary components of the dielectric constant.

The formation mechanisms and the origin of manganese dendrites on the magnesite ore have been under discussion. The growth process of the manganese dendrites is statistically studied by comparing them to aggregations obtained according to the diffusion limited aggregation (DLA) model via Monte Carlo simulations. In this case, ten manganese dendrite patterns changing from the least dense to the densest aggregations on the surface are separately selected to determine the relationship between real and simulated patterns. The sticking parameter is ranged from 0.05≤ t ≤1. The density–density correlation functions C ( r ) (their critical exponent A ), fractal dimension D f , critical exponent α , and critical exponent β pertaining to the root mean square (rms) thickness have been computed for both the ten manganese dendrites and the simulated aggregations representing them. The results indicate that manganese dendrites may be determined with the general DLA model. Analyses of manganese dendrites, both scaling and simulations, suggest the growth mechanism for the macroscopic expression of crystalline anisotropy for the dendritic patterns. These results are in good agreement with the values in other literature and can be helpful in comparing natural and simulated aggregations (both dendritic and compact deposits).

Nonlocal symmetries are obtained for the coupled integrable dispersionless (CID) equation. The CID equation is proved to be consistent, tanh-expansion solvable. New, exact interaction excitations such as soliton–cnoidal wave solutions, soliton–periodic wave solutions, and multiple resonant soliton solutions are discussed analytically and shown graphically.

In this article, the generalised nonlinear Schrödinger–Maxwell–Bloch system is investigated, which describes the propagation of the optical solitons in an optical fibre doped with two-level resonant impurities like erbium with the fourth-order dispersion taken into account. Bilinear forms are derived via the Hirota method, symbolic computation, and the auxiliary function. Bright solitons can be obtained for the complex envelope of the field and the measure of the polarisation for the resonant medium, while the dark ones have been deduced for the extant population inversion. Propagation of the one and two solitons is analysed with the results that the solitons keep their shapes unchanged after the interaction, except for the phase shifts, which means that the interaction is elastic. Velocities of the solitons decrease when the effect of discreteness and higher-order dispersion increases. For the bound-state solitons, which can be formed among the solitons at the same velocity, the period decreases when the effect of discreteness and higher-order dispersion increases.

The local distortions and electron paramagnetic resonance (EPR) parameters for Cu 2+ in lithium sodium borate (LNB) glasses x Li 2 O·(30– x )·Na 2 O·69.5B 2 O 3 (5≤ x ≤25 mol%) are theoretically studied at various concentrations x in a consistent way. Owing to the Jahn–Teller effect, the [CuO 6 ] 10− clusters are found to experience the significant tetragonal elongations of 16% along C 4 axis. Despite the nearly unchanging observed g factors, measured d–d transition band (or cubic field parameter Dq ) shows remarkable linear increases with concentration x , whose influences on g ‖ and g ⊥ are actually cancelled by the linearly increasing covalency factor N and relative elongation ratio η with x . The almost unvarying hyperfine structure constants are attributed to the fact that the influences of the linearly increasing N and the linearly decreasing core polarisation constant κ largely cancel one another. The microscopic mechanisms of the above concentration dependences for these quantities are illustrated from mixed alkali effect (modification of B 2 O 3 network by transforming some BO 3 units into BO 4 ones with variations in modifier Li 2 O concentration).

The electron paramagnetic resonance (EPR) parameters [i.e. g factors g i ( i = x , y , z ) and hyperfine structure constants A i ] and the local lattice structure for the Cu 2+ centre in Tl 2 Zn(SO 4 ) 2 ·6H 2 O (TZSH) crystal were theoretically investigated by utilising the perturbation formulae of these parameters for a 3d 9 ion under rhombically elongated octahedra. In the calculations, the admixture of d orbitals in the ground state and the ligand orbital and spin-orbit coupling interactions are taken into account based on the cluster approach. The theoretical EPR parameters show good agreement with the observed values, and the Cu 2+ –H 2 O bond lengths are obtained as follows: R x ≈1.98 Å, R y ≈2.09 Å, R z ≈2.32 Å. The results are discussed.

An investigation is made for a three-dimensional unsteady mixed nano-bioconvection flow between two contracting or expanding rotating discs. The passively controlled nanofluid model in which Brownian diffusion and thermophoresis are considered as the two dominant factors for nanoparticle/base-fluid slip mechanisms is introduced for description of this flow problem. A novel similarity transformation is introduced so that the governing equations embodying the conservation of total mass, momentum, thermal energy, nanoparticle volume fraction, and microorganisms are reduced to a set of five fully coupled ordinary differential equations. Exact solutions are then obtained analytically for this complex nonlinear system. Besides, the influences of various physical parameters on distributions of velocity, temperature, nanoparticle volume fraction, and the density of motile microorganisms, along with the local Nusselt number and the local wall motile microorganisms flux, are presented and discussed. It is expected that this study can provide a theoretical base for understanding the transport mechanisms of unsteady bioconvection in nanofluids.

The stagnation-point flow of a second-grade fluid past a power law lubricated surface is considered in this paper. It is assumed that the fluid impinges on the wall obliquely. A suitable choice of similarity transformations reduces the governing partial differential equations into ordinary differential equations. The thin lubrication layer suggests that the interface conditions between the fluid and the lubricant can be imposed on the boundary. An implicit finite difference scheme known as the Keller-Box method is employed to obtain the numerical solutions. The effects of slip parameter and Weissenberg number on the fluid velocity and streamlines is discussed in the graphs. The limiting cases of partial-slip and no-slip can be deduced from the present solutions.

How to construct a variable coefficient integrable coupling equation hierarchy is an important problem. In this paper, we present new Lax pairs with some arbitrary functions and generate a variable coefficient integrable coupling of Ablowitz-Kaup-Newell-Segur hierarchy from a zero-curvature equation. Then the Hamiltonian structure of the variable coefficient coupling equation hierarchy is derived from the variational trace identity. It is also indicated that this method is an efficient and straightforward way to construct the variable coefficient integrable coupling equation hierarchy.