In this paper, we examined the unsteady boundary layer flow and heat transfer of a Sisko fluid model over an axisymmetric stretching porous disk in the presence of uniform magnetic field. Mathematical modellingis performed in cylindrical polar coordinates. By means of suitable transformations, the governing time-dependent partial differential equations are reduced to nonlinear coupled ordinary differential equations. Shooting method with Runge–Kutta of order 5 is employed to compute non-dimensional velocity and temperature. The effects ofpertinent parameters are portrayed through graphs. The skin friction coefficient and Nusselt number are tabulated to study the behaviours at the stretching surface.

Steady State Tokamak-2 (SST-2) will be an intermediate fusion machine before Indian DEMOnstration power reactor (DEMO) development to realise the reactor technologies. It is designed for fusion gain Q = 5 andfusion power in the range of 100–300 MW. Nuclear design analyses of SST-2 machine have been carried out to support the conceptual design work. Analyses have been carried out for two breeding blanket concepts: Indian lead–lithium ceramic breeder (LLCB) and helium-cooled ceramic breeder (HCCB). The analyses assess the tritium production and radiation shielding capability of the machine referring to the engineering design parameters. In this study, one-dimensional radiation transport calculations have been performed to assess the SST-2 nuclear responses for 1 full power year (FPY) operation. Nuclear responses such as tritium breeding ratio (TBR), various radiation loads to toroidal field (TF) coil have been calculated to obtain the radial build-up of SST-2 capable of breeding tritium and satisfying the shielding requirements. The assessment has been made using the ANISEN code andFENDL 2.1 cross-section library. It is observed that the TBRs with LLCB and HCCB blankets are 0.85 and 0.94, respectively. Shielding calculations confirm that the radial build is sufficient to protect the superconducting TF coils for 1 FPY.

A simple relation of chemical processes for three-dimensional flow of a cross magnetofluid over bidirectional stretched surface is constructed. The impact of convective heat transport in the manifestation of non-linear thermal radiation and features of heat source–sink are also considered for heat transfer mechanism.Furthermore, in this research paper, the innovative relation between heterogeneous and homogeneous responses with equivalent diffusivities for reactant and autocatalysis is exploited. Apposite alterations are guaranteed to obtain ordinary differential equations (ODEs) with high nonlinearity. Numerically, the bvp4c technique is exploited to the interpret the structure of ODEs. Portrayals of temperature and concentration for cross liquid equivalent to abundant somatic parameters are presented graphically as well as in tabular form. Our results reveal that the temperature of the cross fluid decreases with fluctuation in the heat sink parameter. Furthermore, it is perceived from the figuresthat the concentration of the cross fluid reduces for higher values of chemical reaction parameters.

Nanoliquids possess remarkable features that have fascinated numerous researchers because of their utilisation in nanoscience and nanotechnology. A mathematical relation for the two-dimensional flow of Maxwell nanoliquid over a stretching cylinder is established. Buongiorno’s relation is considered here to visualise the impact of Brownian moment and thermophoresis mechanisms on Maxwell liquid. The convective heat transport is deliberated for heat transfer mechanisms. Transformation procedure yields nonlinear differential system which is then computed through the homotopic approach. The results obtained are studied in detail in relation to somatic parameters. It is notable that the velocity of Maxwell liquid shows conflicting behaviour for curvature parameter $\alpha$ and Deborah number $\beta$. Moreover, the liquid temperature increases for increased values of Brownian motion $N_{b}$ and thermophoresis parameter $N_{t}$ . Additionally, the authentication of numerical consequences is prepared via benchmarking with formerly identified restrictive circumstances and we initiate a splendid communication with these results.

Magnetic resonance imaging (MRI) is used in physics, chemistry, engineering and medicine to study complex materials. In this paper, numerical solution of fractional Bloch equations in MRI is obtained using fractional variation iteration method (FVIM) and fractional homotopy perturbation transform method (FHPTM). Sufficient conditions for the convergence of FVIM and its error estimate are established. The obtained results are comparedwith the existing as well as recently developed methods and with the exact solution. The obtained numerical results for different fractional values of time derivative are discussed with the help of figures and tables. Figures are drawn using the Maple package. Test examples are provided to illustrate the accuracy and competency of the proposed schemes.

In this paper,we discuss a new fractional-order memristor-based three-dimensional chaotic system with a stable equilibrium point. The proposed system belongs to the category of hidden attractors dynamical system. The system is new in the sense that it is a fractional-order memristor-based chaotic system and exhibits hidden attractors. The chaotic behaviour of the system is accessed by various numerical techniques such as Lyapunovexponents, bifurcation diagrams, instantaneous phase plot, attractor analyses and frequency spectrum plots. Afractional-order proportional integral (PI)-based sliding mode control is designed for chaos suppression of the proposed system. Further, the switching synchronisation of the new system in the form of the master and the slave systems is presented.

A transportable, trolley-mounted stand-off explosive material detection system based on the time-gated Raman spectroscopy was developed and tested in our laboratory. This system is capable of identifying the explosives and improvised explosive materials located up to a distance of 30 m. A frequency tripled Nd:YAG, nanosecond pulsed laser (355 nm, 6 ns) operated at 10 Hz was used as an excitation source to induce Raman spectra of explosive materials under investigation. A reflected type 200 mm aperture telescope designed using Zemax opticaldesign software was used to collect the backscattered Raman signals. Raman signals were recorded using the gated intensified charge coupled device (ICCD) spectrograph. A LabVIEW-based data acquisition and analysis software for real-time identification of materials was developed and used. It gives audio as well as text alarm to the operatorabout threat identification.

The current review proclaims the forced convective flow and heat–mass transfer characteristics of cross nanofluid past a bidirectional stretched surface. The most significant aim of the current review is to incorporatethe features of Buongiorno relation, activation energy, nonlinear thermal radiation and heat sink–source for a three-dimensional flow of the cross fluid. Appropriate transformations are employed to transform the modelledpartial differential equations (PDEs) of momentum, temperature and concentration into coupled nonlinear ordinary differential equations (ODEs). The governing boundary value problem is numerically integrated with the help of bvp4c scheme. The obtained numerical data are plotted for the temperature and concentration profiles of nanofluid for various converging values of physical parameters. The dependence of increasing thermophysical parameters on temperature and concentration profiles of the cross nanofluid is graphically demonstrated. Furthermore, detailedstudy reveals that the concentration of the cross nanofluid decreases for increasing values of Brownian motion parameter. It is also perceived from the sketches that the concentration of the cross nanofluid decreases for higher values of chemical reaction parameter. The validity of the achieved numerical outcomes is ensured by making a comparison with the existing work as special cases.

The current study deals with the influence of a uniform electric field on a cylindrical streaming sheet.This paper investigates a few representatives of porous media. These media are considered to be uniform, homogeneous and isotropic. The analysis is based on viscous potential theory, which assumes that the viscous forces affect only the interface between the fluids. The mathematical treatment is based on the normal modes analysis. For convenience, cylindrical coordinates are used. The boundary-value problem yields coupled second-order and damped differential equations with complex coefficients. These equations are combined with a single equation under the concepts of the symmetric and antisymmetric deformations. The Routh–Hurwitz criterion is adopted to govern the stability of the system. Several special cases are recovered upon appropriate data choices. The effects of various parameters on the interfacial stability are theoretically presented and illustrated graphically through some sets of figures. These parameters are the Darcy’s coefficients, basic velocities, dielectric constants, viscosity and thickness of the inner cylinder. We have found that the thickness of the inner cylinder plays a dual role on the stability picture. Also, the Darcy’s coefficient and dielectric constants have stabilising influence and the dynamic viscosity has a destabilising effect.

In this paper, we employ the improved homoclinic test technique and the extended homoclinic test technique. With the help of the symbolic calculation and applying the improved methods, we solve the (3 + 1)- dimensional potential-Yu–Toda–Sasa–Fukuyama (YTSF) equation to obtain some newperiodic kink-wave, periodic soliton and periodic wave solutions.

In this paper, we study the exact solutions of non-local Boussinesq equation (nlBq) which appears in many scientific fields. We generate dark solitons, singular solitons, a new family of solitons and combo dark–singular soliton-type solutions of nlBq by the extended Kudryashov’s algorithm. Additional solutions such as singular periodic solutions also fall out of this integration scheme. Also, one-soliton, two-soliton and three-soliton type solutions are presented using multiple exp-function algorithm. Lastly, Lie symmetry analysis with the new similarity reductions is also examined.

In this investigation, we employ the generalised $(G'/G)$-expansion method to test its efficiency in extracting travelling wave solutions of nonlinear evolution equations (NLEEs). As test cases, the modifiedKuramoto–Sivashinsky (mK-S) and the modified Burgers–Korteweg–de Vries (mB-KdV) equations are considered because of their importance in soliton theory. The general solutions are obtained in hyperbolic, trigonometric and rational function forms for both the equations. Taking specific parametric values in the corresponding general solutions, some new exact travelling waves in trigonometric and hyperbolic forms and only in hyperbolic form are obtained for the mK-S and mB-KdV equations, respectively. The obtained results are checked to see whether the criticism made by Parkes (Comput. Fluids 42, 108 (2011)), that the so-called ‘new’ solutions derived by the $(G'/G)$-expansion method are often erroneous and are merely disguised versions of previously known solutions, is justified also for the generalised $(G'/G)$-expansion method. The solutions were checked with Maple by putting them back into their corresponding equations. With specific values of parameters, some of our obtained solutions satisfied directly and some solutions never satisfied the considered NLEEs. Among the satisfactory solutions, some are found to be in disguised versions of some results obtained in this study.

Quantum processors are potentially superior to their classical counterparts for many computational tasks including factorisation. Circuit methods as well as adiabatic methods have already been proposed and implemented for finding the factors of a given composite number. The main challenge in scaling it to larger numbers is the unavailability of large number of qubits. Here, we propose a hybrid scheme that involves both classical and quantum computation, based on the previous work of Peng et al, Phys. Rev. Lett. 101(22), 220405 (2008), which reduces the number of qubits required for factorisation. The classical part involves setting up and partially simplifying a set of bit-wise factoring equations and the quantum part involves solving these coupled equations using a quantum adiabatic process. We demonstrate the hybrid scheme by factoring 551 using a 3-qubit NMR quantum register.

A new expression for the dielectric function is suggested here, which is the Mermin–Belkacem-Sigmund(MBS) model derived from the Belkacem–Sigmund (BS) model based on the conservation of a local particle number in the Mermin model. The energy loss function expressions are reviewed analytically for both models, and thesedielectric functions were used to calculate the Bethe sum rule, the energy loss function (ELF), as well as the differential inelastic inverse mean free path (DIIMP) for $\rm{H_{2}O}$. The indication from the results is that, compared to the BS dielectric function, the MBS dielectric function is more compatible in its consistency with the exact Bethe sum rule. The ELF for the MBS type is compatible relatively in high and low momentum transfers, while the ELF forthe BS type is suitable for high-$k$. The two models of ELF were also applied to evaluate DIIMP for electron kinetic energy 1 keV, and these were compared with the results predicted in several ways via the SESINIPAC program, using the Mermin dielectric function and the extended Drude and Monte–Carlo method. These predicted results are in reasonable agreement with those estimated from other methods at the range of energy transfer (0–50) eV.

We propose a pseudopotential of Kumar form with two parameters, the core radius $(r_{c})$ and the model radius $(r_{m})$, which in practice is reduced to a single-parameter potential taking rm as the experimental atomic radius. The validity of the presently used pseudopotential is verified by carrying out a detailed study of transport properties of 16 liquid metals. The results of the liquid metal resistivities using the nearly free electron (NFE) Ziman’s approach and the single-site t-matrix approach are presented and compared with the experimental as well as other theoretical findings. Such comparative study confirms that the t-matrix approach is more appropriate and physically sound for a theoretical understanding of liquid metal resistivity, particularly in the case of transition metals. Furthermore, thermoelectric powers are also calculated using the present method and compared with the available experimental and theoretical results.

In this paper, a passive control scheme based on the fractional-order calculus is proposed.We study the modified complex projective synchronisation between two identical fractional-order complex chaotic systems, and its application in the secure communication. The fractional-order complex chaotic Lorenz system is employed to encrypt the emitted signal. In the transmitter module, the information signal is modulated into one parameter of the Lorenz system. It is assumed that the same parameter is unknown in the receiver module. In order to synchronise two systems with different initial conditions, the controllers and an appropriate parameter update rule are designed. Theoretical analysis and numerical simulations show that this method is feasible and robust to some extent in thepresence of channel noise.