Volume 74, Issue 1

Basically enzymes are biological catalysts that increase the speed of a chemical reaction without undergoing any permanent chemical change. With the application of Euler’s forward scheme, a discrete-time enzyme model is presented. Further investigation related to its qualitative behaviour revealed that discrete-time model shows rich dynamics as compared to its continuous counterpart. It is investigated that discrete-time model has a unique trivial equilibrium point. The local asymptotic behaviour of equilibrium is discussed for discrete-time enzyme model. Furthermore, with the help of the bifurcation theory and centre manifold theorem, explicit parametric conditions for directions and existence of flip and Hopf bifurcations are investigated. Moreover, two existing chaos control methods, that is, Ott, Grebogi and Yorke feedback control and hybrid control strategy, are implemented. In particular, a novel chaos control technique, based on state feedback control is introduced for controlling chaos under the influence of flip and Hopf bifurcations in discrete-time enzyme model. Numerical simulations are provided to illustrate theoretical discussion and effectiveness of newly introduced chaos control method.

The determination of temperature and auxiliary quantities such as local and average Nusselt numbers for thermally developing flow is referred as the Graetz problem. In the classical Graetz problem, the fluid entering the tube or channel is Newtonian in nature. Here, an extension of the classical Graetz problem is presented by assuming that the fluid entering the tube or channel obeys the Ellis constitutive equation. The energy equation for the considered problem is solved using the separation of variables technique supplemented with the MATLAB routine bvp4c for computation of the eigenvalues and numerical solution of the associated Sturm-Liouville boundary value problem. The problem is solved for two types of thermal boundary conditions, namely, uniform surface temperature and uniform surface heat flux for both flat and circular geometries. Expressions for bulk mean temperature and local and average Nusselt numbers are presented and discussed through tables and graphs.

The present study is a report on the asymmetry of dispersed oil phase in vertical upward oil-water two phase flow. The multi-channel signals of the rotating electric field conductance sensor with eight electrodes are collected in a 20-mm inner diameter pipe, and typical images of low pattern are captured using a high speed camera. With the multi-channel rotating electric field conductance signals collected at pipe cross section, multi-scale time asymmetry (MSA) and an algorithm of multi-scale first-order difference scatter plot are employed to uncover the fluid dynamics of oil-water two phase flow. The results indicate that MSA can characterise the non-linear behaviours of oil-water two phase flow. Besides, the MSA analysis also beneficial for understanding the underlying inhomogeneous distribution of the flow pattern in different directions at pipe cross section.

It is known that the principle of minimal coupling in quantum mechanics determines a unique interaction form for a charged particle. By properly redefining the canonical commutation relation between (canonical) conjugate components of position and momentum of the particle, e.g. an electron, we restate the Dirac equation for the hydrogen-like atom problem incorporating a generalized minimal electromagnetic coupling. The corresponding interaction keeps the 1/|q|$1/\left|\mathbf{q}\right|$ dependence in both the scalar potential V(|q|)$V\left({\left|\mathbf{q}\right|}\right)$ and the vector potential A(q)$\mathbf{A}\left(\mathbf{q}\right)$ (|A(q)|∼1/|q|$\left|{\mathbf{A}\left(\mathbf{q}\right)}\right|\sim 1/\left|\mathbf{q}\right|$). This problem turns out to be exactly solvable; moreover, the eigenstates and eigenvalues can be obtained in an elementary fashion. Some feasible models within this approach are discussed. Then we make a few remarks about the breaking of supersymmetry. Finally, we briefly comment on the possible Lie algebra (dynamical symmetry algebra) of these relativistic quantum systems.

For the first time, the formalism of intrinsic loss processes such as below-band gap, thermalisation, angle mismatch, Carnot and emission loss in the intermediate band solar cells (SCs) is obtained by a theoretical framework based on the principle of detailed balance approach, and with the physical origins of losses discussed in terms of photon absorption and emission in the presence of intermediate energy band (IB). Then, the effect of IB position on each intrinsic loss in the intermediate band SCs is investigated. The results show that the introduction of IB reduces the below-band gap loss due to absorption of low energy photons by narrower sub-band gap and reduces the thermalisation loss due to absorption of high energy photons by the band gap of host semiconductor. Furthermore, the thermalisation and angle mismatch losses are dominant fractions of intrinsic loss, while the emission loss presents less than 2.2 % of intrinsic loss.

AgBr crystals containing impurity Rh 2+ with and without a next nearest neighbor silver vacancy (V Ag ) in the [001] axis are theoretically studied. The defect structures, bandgap, Mulliken charge, density of states, ultraviolet-visible (UV-Vis) and electron paramagnetic resonance spectra are analysed for two distinct (i.e. tetragonally elongated and compressed) centres by using density functional theory calculations. The results demonstrate that the structural, photoelectric and spectroscopic properties of AgBr are significantly changed after Rh substitution. The covalency of Rh-Br bonds in the two centres is stronger than that of pure AgBr according to the larger magnitudes of the overlap population. Compared to pure AgBr, Rh doping also results in significantly enhanced red shifts of absorption bands in the UV-Vis region and some new d-d transitions in the visible and near-infrared regions. Meanwhile, the bandgap of Rh-doped AgBr is about 10 % narrower than that of pure AgBr. As a result, the visible light activity may be enhanced in AgBr:Rh systems. Rh dopants can induce the magnetic moments of about 1.73 μ B for both centres. Therefore, transition-metal Rh dopants may effectively modulate the electronic, optical and magnetic properties of AgBr.

In this article, we use first-principles density functional theory (DFT), with plane-wave pseudopotentials, to calculate the structural, mechanical, thermal, electronic, and bonding properties of the cubic perovskite Pb(Mg 1/3 Nb 2/3 )O 3 . The results are compared with those of some isostructural compounds. The optimised lattice constant agrees fairly well with the experimental value. Mechanical stability is verified for this compound. This perovskite is damage-tolerant, as it is ductile according to all indicators. The machinability level of this substance is similar to that of the well-known MAX phases. Low thermal conductivity, better thermal shock resistance, low Debye temperature, and high melting temperature of Pb(Mg 1/3 Nb 2/3 )O 3 should favour its use as thermal barrier coating (TBC) material. Dual characteristics of a weak metal and a semiconductor are expected for this material. Covalent bonding is significant in this cubic perovskite. The Fermi surface is very complex and contains a Fermi pocket around each X-point.

The structural parameters, mechanical, dynamic, and thermodynamic properties of WSi 2 with the C11 b structure under pressure were systematically explored by using first-principles calculations. The results shown that calculated lattice constants and elastic constants of WSi 2 were consistent with previous experimental findings and theoretical values. Our obtained elastic constants revealed that WSi 2 was mechanically stable from 0 to 100 GPa. The values of anisotropic indexes, three-dimensional surface constructions, and two-dimensional projections under pressure indicated that WSi 2 showed mechanical anisotropy. Additionally, the phonon density of state and phonon dispersion curves under pressure were obtained, and all vibration modes were analyzed. Finally, thermodynamic properties were also predicted based on quasi-harmonic approximation.