Showing papers in "Pramana in 2021"

Entropy generation of three-dimensional Bödewadt flow of water and hexanol base fluid suspended by $$\hbox {Fe}_{{{3}}}\hbox {O}_{{{4}}}$$ Fe 3 O 4 and $$\hbox {MoS}_{{{2}}}$$ MoS 2 hybrid nanoparticles

Abstract: In this study, three-dimensional Bodewadt hybrid nanofluid flow has been investigated. Base fluids are water and hexanol which contain $$\hbox {Fe}_{3}\hbox {O}_{4}$$ and $$\hbox {MoS}_{2}$$ . The governing nonlinear PDEs are converted into nonlinear ODEs and the nonlinear equations are solved by the homotopy perturbation method (HPM). The effects of nanoparticle volume fraction, Eckert number, base fluid and shape factor on entropy generation, Nusselt number, skin friction coefficient and Bejan number have been studied. Entropy generation is increased with an increment in Eckert number; while, it is decreased by growth in nanoparticle volume fraction and shape factor. In a similar situation, hexanol has higher rate of irreversibility, higher Bejan number and higher Nusselt number than water. The skin friction coefficient is not a function of the Eckert number and shape factor, but it is an increasing function of nanoparticle volume fraction. In this paper, by averaging the differences of Nusselt number and skin friction coefficient between water and hexanol, it can be observed that the Nusselt number and skin friction coefficient for hexanol are 11% and 5% more than water, respectively. Indeed, in a fixed situation, hexanol-based fluid flows have higher heat transfer and drag than water-based fluid flows.

Exploring the impact of magnetic dipole on the radiative nanofluid flow over a stretching sheet by means of KKL model

Abstract: This study mainly focusses on the rheological properties of the nanofluids by using Koo–Kleinstreuer–Li model. The nanofluids have been proposed as viable replacements to traditional fluids due to their increased heat transport capacity. In this regard, the influence of non-uniform heat sink/source and thermal radiation effects on the nanoliquid flow past a stretching sheet is studied in the presence of chemical reaction and magnetic dipole. The defined flow equations are transformed to ordinary differential equations by using appropriate similarity variables and then they are numerically tackled with Runge Kutta Fehlberg-45 (RKF-45) scheme by adopting shooting process. The graphical outcomes of the velocity, thermal, concentration profiles, drag force, Sherwood number and Nusselt number are found to get an obvious insight into the existing boundary layer flow problem. The outcomes reveal that, the gain in values of radiation parameter improves the thermal profile due to the production of inner heat. The rise in Biot number improves the thermal boundary layer region which automatically boosts up the thermal profile. Further, the escalation in space-dependent internal heat sink/source parameter deteriorates the rate of heat transfer.

Lie symmetry analysis, group-invariant solutions and dynamics of solitons to the (2+1)-dimensional Bogoyavlenskii–Schieff equation

Abstract: In the present work, abundant group-invariant solutions of ( $$2+1$$ )-dimensional Bogoyavlenskii–Schieff equation have been investigated using Lie symmetry analysis. The Lie infinitesimal generators, all the geometric vector fields, their commutative and adjoint relations are provided by utilising the Lie symmetry method. The Lie symmetry method depends on the invariance criteria of Lie groups, which results in the reduction of independent variables by one. A repeated process of Lie symmetry reductions, using the double, triple and septuple combinations between the considered vectors, converts the Bogoyavlenskii–Schieff (BS) equation into nonlinear ordinary differential equations (ODEs) which furnish numerous explicit exact solutions with the help of computerised symbolic computation. The obtained group-invariant solutions are entirely new and distinct from the earlier established findings. As far as possible, a comparison of our reported results with the previous findings is given. The dynamical behaviour of solutions is discussed both analytically as well as graphically via their evolutionary wave profiles by considering suitable choices of arbitrary constants and functions. To ensure rich physical structures, the exact closed-form solutions are supplemented via numerical simulation, which produce some bright solitons, doubly solitons, parabolic waves, U-shaped solitons and asymptotic nature.

Some new families of exact solitary wave solutions of the Klein–Gordon–Zakharov equations in plasma physics

Abstract: The prime objective of this paper is to obtain some new families of exact solitary wave solutions of the Klein–Gordon–Zakharov (KGZ) equations via computerised symbolic computation on Wolfram Mathematica. By applying the generalised exponential rational function method, numerous exact soliton solutions are constructed for the KGZ equations, which provide a model of the interaction between the Langmuir wave and the ion-acoustic wave in high-frequency plasma. Consequently, the exact solitary wave solutions are obtained in different forms of dynamical wave structures of solitons including multisolitons, lump-type solitons, travelling waves, kink waves, also trigonometric and hyperbolic function solutions, and rational function solutions. Moreover, the dynamical behaviour of the resulting multiple soliton solutions is discussed both analytically and graphically by using suitable values of free parameters through numerical simulation. The reported results have rich physical structures that are helpful to explain the nonlinear wave phenomena in plasma physics and soliton theory.

Bilinear form, bilinear auto-Bäcklund transformation, breather and lump solutions for a (3 $$+$$ + 1)-dimensional generalised Yu–Toda–Sasa–Fukuyama equation in a two-layer liquid or a lattice

Abstract: Two-layer fluids are seen in fluid mechanics, thermodynamics and medical sciences. Lattices are seen in solid-state physics. In a two-layer liquid or a lattice, a ( $$3+1$$ )-dimensional generalised Yu–Toda–Sasa–Fukuyama equation is hereby studied with symbolic computation. Via the Hirota method, bilinear form and bilinear auto-Backlund transformation under certain coefficient constraints are obtained. Breather solutions are worked out based on the Hirota method and extended homoclinic test approach. Considering that the periods of breather solutions tend to infinity, we derive the lump solutions under a limit procedure. We observe that the amplitudes of the breather and lump remain unchanged during the propagation. Furthermore, we graphically present the breathers and lumps under the influence of different coefficients in the equation.

Analytical solution of the steady-state atmospheric fractional diffusion equation in a finite domain

Abstract: In this work, an analytical solution for the steady-state fractional advection-diffusion equation was investigated to simulate the dispersion of air pollutants in a finite media. The authors propose a method that uses classic integral transform technique (CITT) to solve the transformed problem with a fractional derivative, resulting in a more general solution. We compare the solutions with data from real experiment. Physical consequences are discussed with the connections to generalised diffusion equations. In the wake of these analysis, the results indicate that the present solutions are in good agreement with those obtained in the literature. This report demonstrates that fractional equations have come of age as a decisive tool to describe anomalous transport processes.

Lie symmetry analysis, abundant exact solutions and dynamics of multisolitons to the (2 +1 ) -dimensional KP-BBM equation

Abstract: In the present article, our main aim is to construct abundant exact solutions for the $$(2+1)$$ -dimensional Kadomtsev–Petviashvili-Benjamin–Bona–Mahony (KP-BBM) equation by using two powerful techniques, the Lie symmetry method and the generalised exponential rational function (GERF) method with the help of symbolic computations via Mathematica. Firstly, we have derived infinitesimals, geometric vector fields, commutation relations and optimal system. Therefore, the KP-BBM equation is reduced into several nonlinear ODEs under two stages of symmetry reductions. Furthermore, abundant solutions are obtained in different shapes of single solitons, solitary wave solutions, quasiperiodic wave solitons, elastic multisolitons, dark solitons and bright solitons, which are more relevant, meaningful and useful to describe physical phenomena due to the existence of free parameters and constants. All these generated exact soliton solutions are new and completely different from the previous findings. Moreover, the dynamical behaviour of the obtained exact closed-form solutions is analysed graphically by their 3D, 2D-wave profiles and the corresponding density plots by using the mathematical software, which will be comprehensively used to explain complex physical phenomena in the fields of nonlinear physics, plasma physics, optical physics, mathematical physics, nonlinear dynamics, etc.

Amplitude-modulated electron-acoustic waves with bipolar ions and kappa-distributed positrons and warm electrons

Abstract: In this paper, we have meticulously studied the amplitude modulation of electron-acoustic waves and the formation and properties of envelope solitons in a five-component complex plasma containing statistically kappa-distributed warm and cold electrons, kappa-distributed positrons and Boltzmann-distributed positive and negative ions. The picture considered here is very similar to solar atmosphere and planetary environments. The parametric dependence of modulational instability on kappa index, positron and electron densities, ion and reciprocal of positron temperatures has been studied in detail and the findings obtained here will be beneficial for further astrophysical investigations.

Numerical solution of time-fractional coupled Korteweg–de Vries and Klein–Gordon equations by local meshless method

Abstract: This article provides numerical simulations of the time-fractional coupled Korteweg–de Vries and Klein–Gordon equations via the local meshless collocation method (LMCM) utilising the radial basis functions. The recommended local meshless technique is utilised for the space derivatives of the models whereas Caputo fractional definition is used for time-fractional derivative. Numerical experiments are performed for one-dimensional coupled Korteweg–de Vries and two-dimensional Klein–Gordon equations. In order to verify the efficiency and accuracy of the proposed meshless method, numerical results are compared with exact and numerical techniques reported in recent literature which reveals that the method is computationally attractive and produces better results.

Effects of exchange symmetry and quantum diffraction on amplitude-modulated electrostatic waves in quantum magnetoplasma

Abstract: In this paper we have made use of reductive perturbation technique (RPT) and carried out homotopy analysis method (HAM) to investigate the effect of exchange correlation and quantum diffraction on the electrostatic waves in quantum magnetoplasma. We have derived a nonlinear Schrodinger equation (NLSE) by using RPT that describes the spatiotemporal evolution of an initial waveform. Apart from this technique, we have made use of HAM to second our initial findings. It has been shown that both quantum diffraction H and parameter streaming velocity $$u_0$$ have significant effects in determining the stability criteria and the growth or decay of any instability created therein. The stable parametric regimes are crucial from the experimental point of view as well.

Exact and numerical solutions for the nanosoliton of ionic waves propagating through microtubules in living cells

Abstract: In this article, the Paul–Painleve approach (PPA) which was formulated recently and built on the balance role has been used perfectly to achieve new impressive solitary wave solutions to the nanosoliton of ionic waves (NSOIW) propagating along the microtubules in the living cells. In addition, variational iteration method (VIM) has been applied in the same vein and parallel to establish numerical solutions of this model.

Rheological effects on boundary layer flow of ferrofluid with forced convective heat transfer over an infinite rotating disk

Abstract: A study in nonlinear mechanical sciences on modelling has been carried out to analyse the combined effect of rotation and Darcy parameter with forced convective heat transfer on the steady flow of magnetic nanofluid over a rotating disk. The basic idea of the Neuringer–Rosensweig (NR) model has been used for the equations of motion and the governing nonlinear time-independent coupled partial differential equations together with the boundary conditions in cylindrical coordinates are transformed to a system of ordinary differential equations, via appropriate transformations. Further, the modelled system is solved by the MATLAB routine bvp4c solver package with suitable initial guesses. Besides calculating numerically, the velocity and temperature profiles with the variation of similarity parameter $$\eta $$ , the effects of several non-dimensional motivating parameters, such as Prandtl number Pr, Darcy parameter $$\beta $$ and ferrohydrodynamic (FHD) interaction parameter B, the heat transfer rate from the surface of the disk and skin frictions are also discussed. The results for these emerging parameters are found numerically and discussed with plots.

Computing wave solutions and conservation laws of conformable time-fractional Gardner and Benjamin–Ono equations

Abstract: This paper presents travelling wave solutions for the nonlinear time-fractional Gardner and Benjamin–Ono equations via the exp( $$- \Phi ( \varepsilon ))$$ -expansion approach. Specifically, both the models are studied in the sense of conformable fractional derivative. The obtained travelling wave solutions are structured in rational, trigonometric (periodic solutions) and hyperbolic functions. Further, the investigation of symmetry analysis and nonlinear self-adjointness for the governing equations are discussed. The exact derived solutions could be very significant in elaborating physical aspects of real-world phenomena. We have 2D and 3D illustrations for free choices of the physical parameter to understand the physical explanation of the problems. Moreover, the underlying equations with conformable derivative have been investigated using the new conservation theorem.

Two-dimensional ion-acoustic solitary waves obliquely propagating in a relativistic rotating magnetised electron–positron–ion plasma in the presence of external periodic force

Abstract: The characteristics of ion-acoustic solitary waves in rotating, weakly relativistic, magnetised and collisionless plasma system comprising electron, positron and ion (EPI) under a periodic external force, whose constituents electron and positron obey Boltzmann distribution, are investigated by deriving forced Zakharov–Kuznetsov (FZK) equation. FZK equation is constructed using reductive perturbation technique (RPT) which is based on multiple-scale analysis of dependent variables. The effects of physical parameters such as the ratio of temperature of electron and positron, the strength of external periodic force, positron concentration in electron background, ion temperature and magnetic field on the analytical solitary wave solution of FZK equation are observed. It is seen that the behaviours of ion-acoustic wave are significantly affected due to the presence of positron and the periodic external forces. The results of this work may be applied when the above-mentioned plasma environment is found in laboratory as well as in space.

Entropy generation analysis of Falkner–Skan flow of Maxwell nanofluid in porous medium with temperature-dependent viscosity

Abstract: Entropy generation analysis in steady two-dimensional, viscous, incompressible forced convective Falkner–Skan flow of Maxwell nanofluid over a static wedge embedded in a porous medium with temperature-dependent viscosity is examined. The Buongiorno’s model has been utilised, to get the flow governing higher-order coupled nonlinear partial differential equations (PDEs) from mass, momentum, energy and concentration conservations. Suitable transformations have been done to convert governing PDEs into the coupled non-linear ODEs along with no-slip boundary conditions, which are then solved using the MATLAB programme bvp4c. The influences of diverse flow governing parameters on various flow properties and quantities of physical interest are displayed in graphical mode and discussed. It is found that entropy generation reduces only with Eckert number (Ec), while more entropy is generated for pressure gradient parameter (m), local Deborah number ( $$\beta )$$ , variable viscosity parameter ( $$\delta $$ ) and permeability parameter (K). Entropy generation due to heat transfer irreversibility is prominent with increase in m and $$\delta $$ , but it is not so for other parameters. The drag force on the wedge surface become stronger with $$\beta $$ and m, but it reduces with $$\delta $$ . Rates of heat transfer and mass transfer enhance with m and $$\delta $$ . In addition, surface drag force and heat transfer rate diminish with Brownian motion parameter (Nb) and thermophoresis parameter (Nt).

Dynamical structures of interaction wave solutions for the two extended higher-order KdV equations

Abstract: In this paper, we investigate two extended higher-order KdV models (i.e., the extended Sawada–Kotera equation and the extended Lax equation), which can successfully describe propagation of dimly nonlinear long waves in fluids and ion-acoustic waves in harmonic sparklers. First, we present a general formula of multisoliton solutions of the two models. We then build the interaction solutions in terms of hyperbolic and sinusoidal functions by using multisoliton solutions with appropriate complex conjugate parameters controlling the phase shifts, propagation direction and energies of the waves. In particular, we present their collision solutions in the identical plane with different parametric constraints, which degenerate to the line rogue waves, x-shaped rogue waves, cnoidal periodic waves, interactions of rogue and bell waves, line breather and double breather waves. The dynamical characteristics of the wave solutions are shown graphically by choosing some special parameter values.

Generalised exponential rational function method for obtaining numerous exact soliton solutions to a ( $$3+1$$ 3 + 1 )-dimensional Jimbo–Miwa equation

Abstract: In this work, we apply the generalised exponential rational function (GERF) method on an extended ( $$3+1$$ )-dimensional Jimbo–Miwa (JM) equation which describes the modelling of water waves of long wavelength with weakly nonlinear restoring forces and frequency dispersion. This JM equation is also used to construct modelling waves in ferromagnetic media and two-dimensional matter-wave pulses in Bose–Einstein condensates. The main purpose is to construct analytical wave solutions for the ( $$3+1$$ )-dimensional JM equation by utilising the GERF method with the help of symbolic computations. We have also presented three-dimensional plots to observe the dynamics of obtained results. To understand physical phenomenon through different shapes of solitary waves, we discussed solitons, the interaction of multiwave solitons, lump-type solitons and kink-type solutions.

Boundary layer flow of non-Newtonian Eyring–Powell nanofluid over a moving flat plate in Darcy porous medium with a parallel free-stream: Multiple solutions and stability analysis

Abstract: Two-dimensional forced convective steady boundary layer flow of non-Newtonian Eyring–Powell nanofluid over a moving plate in a porous medium in the presence of a parallel free-stream is investigated. The governing coupled non-linear partial differential equations (PDEs) along with boundary conditions are transformed into a set of non-linear coupled ordinary differential equations (ODEs) by using appropriate transformations. The obtained non-linear ODEs with modified boundary conditions are converted into a system of first-order ODEs which are solved using the classical and efficient shooting method. Dual solutions for velocity, temperature and nanoparticle concentration distributions for Eying–Powell fluids similar to Newtonian fluid in some special flow situations are obtained, when the plate and free-stream are moving along mutually opposite directions. The stability analysis of the obtained solutions is performed and it is found that the upper branch solutions are physically stable, while lower branch solutions are unstable. The impacts of different dimensionless physical parameters on velocity, temperature and nanoparticle concentration are reported in the form of graphs and tables. An important result is obtained and it reveals that the ‘dual solutions’ character has been destroyed if resistance due to the porous medium is raised up to a definite level (i.e., permeability parameter $$K > 0.07979$$ ), though the range of existence of unique solution becomes larger with further increase of resistance due to porous medium. It is also observed that heat transfer rate diminishes with increasing thermophoresis parameter, Brownian diffusion parameter and Lewis number in all the cases, whereas mass transfer rate enhances with thermophoresis parameter (for dual solutions), Brownian diffusion parameter (for unique solutions) and Lewis number (for unique solutions). Further, skin-friction coefficient, i.e., the surface drag force, increases with permeability parameter, suction/injection parameter and decreases with Eyring–Powell fluid parameter. Also, increments in permeability parameter and the suction/injection parameter lead to the delay in the boundary layer separation. The critical values of velocity ratio parameter beyond which the boundary layer separation appears are − 0.5476432, − 0.5987132, − 0.704862, − 0.816944, − 0.9365732, − 0.96179102, − 1.057104, − 1.062004, − 1.09222, − 1.115824, − 1.193413, − 1.591023 and − 1.898366 for $$K = 0$$ , 0.01, 0.03, 0.05, 0.07, 0.074, 0.08, 0.082, 0.085, 0.09, 0.1, 0.15 and 0.2, respectively.

Dynamic response of the e-HR neuron model under electromagnetic induction

Abstract: Due to the fluctuation of membrane potential of neuron, there are complex time-varying electromagnetic fields in nervous systems, and the exciting electromagnetic field will further regulate the discharge activities of neurons. In this paper, the coupling of magnetic flux variables to the membrane potential is realised by using a magnetron memristor, and then a 5D extended Hindmarsh–Rose (e-HR) neuron model is established. With the help of Matcont software, the distribution and bifurcation properties of the equilibrium point in the e-HR model is analysed. It is found that there are subcritical Hopf bifurcation, coexisting oscillation modes and hidden limit cycle attractors with period 1 and period 2. In addition, by applying the washout controller, the subcritical Hopf bifurcation point can be transformed into the supercritical Hopf bifurcation point. Thus, the hidden oscillation behaviour of the model can be effectively eliminated. In order to analyse the influence of various parameters on the bifurcation behaviour, numerical simulation of two-parameter bifurcation, single-parameter bifurcation, maximum Lyapunov exponential and time response are given. It is found that the e-HR neuron has a complex bifurcation structure, i.e., the bifurcation structure with period-doubling bifurcations, inverse period-doubling bifurcations, period-adding bifurcations with and without chaos. At the same time, the study also finds that the coexistence behaviour of the periodic cluster discharge and the mixed-mode oscillations (MMOs) can be observed from the bifurcation structure with unique ‘periodic dislocation layer’ on the two-parameter plane. Interestingly, the bursting mode of the system is converted into MMOs when the system parameters are randomly perturbed. The results of this study provide useful insights into the complex discharge patterns and hidden discharge behaviours of neurons under electromagnetic induction.

Generalised charged anisotropic quark star models

Abstract: We find new stellar models to the field equations for charged anisotropic spheres. We use linear quark equation of state for strange quark matter. We choose a new form of pressure anisotropy as a rational function. In our model, we regain previous isotropic and anisotropic stellar models as specific cases. Isotropic models regained are those found by Komathiraj and Maharaj, Mak and Harko, and Misner and Zapolsky. Anisotropic models regained include the performance by Maharaj, Sunzu and Ray; and Sunzu and Danford. We indicate that our model meets the stability and energy conditions. We also generate stellar masses consistent with observations.

Second law analysis of MHD third-grade fluid flow through the microchannel

Abstract: The present study analyses the phenomena of entropy generation of magneto third-grade fluid flow through the microchannel. The significance of Joule heating, viscous heating and internal heat source is also scrutinised. The non-dimensional forms of the corresponding governing equations of the physical phenomenon with the associated boundary conditions for third-grade fluid flow and heat transfer has been solved using finite element method. The impact of various parameters on the flow and heat transfer behaviour, entropy generation and Bejan number is explained using graphs. The obtained results are examined through the plots. The results showed that an increase in the fluid parameter reduces the activity of the fluid flow and, as a result, the temperature is diminished. An enhancement in fluid motion and temperature is obtained by increasing the viscosity index. We noted that the effect of Hartmann number on the rate of local entropy generation and Bejan number is sinusoidal in nature.

Evaluating the performance of new mass flux theory on Carreau nanofluid using the thermal aspects of convective heat transport

Abstract: Nanofluids can be engineered as per requirements and have applications in microelectronic, therapeutic activities, hybrid-mechanical machineries, aeronautics zones, thermonuclear storehouses, shielding of miscellaneous engines etc. Here, the aspects of new mass flux theory in magneto Carreau nanofluid with convective and variable connectivity have been studied. Additionally, nonlinear properties of mixed convection are examined. The shear thinning–thickening properties are analysed by utilising bvp4c algorithm for influential variables. The fluid temperature increases with thermophoresis and variable conductivity parameters. The outcomes of thermophoresis and Brownian motion parameters have conflicting influences on concentration field.

An optimised stability model for the magnetohydrodynamic fluid

Abstract: Magnetohydrodynamics (MHD) is a very challenging problem which affects the stability of Poiseuille flow. Therefore, in this work we investigate the instability of an electrically conductive fluid between two parallel plates under the influence of a transverse magnetic field. We apply the Chebyshev collocation method to solve the generalised Orr–Summerfield equations to determine wave number, growth rates and spatial modes of the eigenmodes. To get the neutral curves of MHD instability, the QZ method is used. It is observed that the magnetic field has a stabilising effect on the flow and the stability increases as we increase the Hartmann number and for various wave numbers, magnetic field put down the growth of perturbation. It is concluded that effect of perturbations is little in span-wise direction for different Hartmann numbers that increase the critical values of Reynolds numbers.

Impact of metal oxide nanoparticles on unsteady stagnation point flow of the hybrid base fluid along a flat surface

Abstract: This paper deals with a detailed investigation of the effects of various metal oxide nanoparticles on unsteady stagnation point flow of a hybrid base fluid impinging on a flat surface. The ‘single-phase’ nanofluid model, i.e., the Tiwari and Das model, is considered for the study. We consider water and ethylene glycol in 1:1 ratio as the base fluid and four different types of metal oxides, namely, CuO, TiO $$_{\mathrm {2}}$$ , ZnO and MgO as the nanoparticles. Using similarity transformations, the conservation equations are transformed into self-similar ordinary differential equations. Dual and unique similarity solutions are obtained for certain set of values of parameters. The analysis explores many important findings. Dual self-similar solutions exist up to a certain critical value of the decelerating unsteady parameter and the critical value is independent of the type of metal oxide nanoparticles considered. The strongest surface drag force is observed for the nanofluid with CuO nanoparticles, while the weakest is for the nanofluid with MgO nanoparticles. The heat transfer rate is highest for the nanofluid with CuO nanoparticles and lowest for the nanofluid with TiO $$_{\mathrm {2}}$$ nanoparticles. Also, the boundary layer is thickest for the nanofluid with MgO nanoparticles.

Resonance synchronisation between memristive oscillators and network without variable coupling

Abstract: Continuous energy pumping and exchange along the coupling channel can balance the energy release between nonlinear oscillators for reaching complete synchronisation. When external stimulus is applied, energy is injected and encoded for regulating the dynamics of nonlinear oscillators and circuits. In this paper, the synchronisation between memristive Rossler oscillators is investigated by reactivating one memristive variable, and external stimuli are changed to detect the occurrence of synchronisation without direct variable coupling. In the presence of periodical stimulus, stochastic switch and feedback on the memristive variable can induce synchronisation between two memristive oscillators and chain network composed of memristive oscillators. In the presence of noise, stochastic feedback and disturbance on the memristive variable can keep synchronisation stable between two oscillators, and complete synchronisation is realised. In addition, the synchronisation factor and spatial patterns are calculated to confirm the occurrence of synchronisation between more chaotic oscillators when memristive function is activated even when no coupling channels are switched on.

Mixed convection MHD nanofluid flow over a wedge with temperature-dependent heat source

Abstract: The present work investigates the transfer of heat, mass and fluid flow at the boundary layer of a nanofluid past a wedge in the presence of a variable magnetic field, temperature-dependent heat source and chemical reaction. The study is entirely theoretical and the proposed model describes the influence of Brownian motion and thermophoresis in the case of nanofluids. This study also includes the impact of thermal radiation. The partial differential equations relating to the flow are nonlinear and hence are numerically solved after transforming them into ordinary differential equations with similar variables. The outcome of the present study is given in tabular form and depicted graphically. It is found that the nanofluid flow along the wedge is accelerated by enhancing the Falkner–Skan parameter. The study further reveals that the magnetic field has an improved effect on the velocity. The Brownian motion parameter raises the profile of temperature but decreases the profile of volume fractions. Thermal radiation decreases the energy transport rate to the fluid and hence reduces the degree of heat present in the fluid. It is also observed that heat sink blankets the surface with a layer of cold fluid.

New stochastic solutions for a new extension of nonlinear Schrödinger equation

Abstract: In this article, we applied the unified solver method to extract stochastic solutions of a new stochastic extension of nonlinear Schrodinger equation. This solver gives the closed formula in explicit form. The acquired stochastic solutions may be applicable for explaining some phenomena in many fields of applied sciences. The presented results illustrate that the proposed solver is efficient and adequate. Moreover, the constraint conditions are utilised to verify the existence of solutions. Chi-square statistical distribution is chosen to represent the dispersion random input. In order to illustrate the dynamical behaviour of random solutions, the expectation value and their variance are depicted graphically using suitable parameters.

Cross-correlated sine-Wiener bounded noises-induced logical stochastic resonance

Abstract: Noise improves the reliability of logic operations if noise parameter is in certain proper region (reliable region), which is known as logical stochastic resonance (LSR). LSR attracts much attention due to its potential application in new-style logic devices. However, nothing is reported about the effect of cross-correlated sine-Wiener (CCSW) bounded noises on the reliability and agility of logic operations. Here we explicitly demonstrate that in certain proper parameter regions of amplitude and correlation time of CCSW noises, CCSW noises can induce LSR. In addition, cross-correlation intensity of CCSW noises can drastically influence the range of reliable region. By comparison, moderate cross-correlation intensity can drastically destroy the reliability of the logic system, and strongly shrink the optimal parameter ranges, depending on cross-correlation time and amplitude. Moreover, for given amplitudes and cross-correlation time, a little faster logic operation can be obtained with increasing cross-correlation intensity.

Cluster pre-formation probabilities and decay half-lives for trans-lead nuclei using modified generalised liquid drop model (MGLDM)

Abstract: Cluster decay half-lives of trans-lead nuclei emitting clusters like C, N, O, F, Ne, Mg and Si are studied by incorporating various cluster pre-formation probabilities to the modified generalised liquid drop model (MGLDM). MGLDM is a method in which generalised liquid drop model (GLDM) is modified using proximity 77 potential. In this approach, we make the assumption that the cluster is pre-born inside the parent nuclei and the pre-formation factor that depends on Q value, size of the cluster and product of atomic number of the cluster and the daughter nuclei are formulated and added to MGLDM. Calculated half-lives using three formulae are cross checked with experimentally detected values from various isotopes of Fr, Ra, Ac, Th, U, Pa, Np, Pu and Am parent nuclei and the results match exactly. Standard deviations of logarithmic half-lives using pre-formation factors which depend on Q values, cluster size and product of atomic number of the cluster and the daughter nuclei, are 1.08, 0.995 and 1.07 respectively. Hence, we formulate a pre-formation factor that depends on all the three parameters together in an equation and the standard deviation is found to be 0.885. Again, the four formulae proved its applicability in the case of alpha decay from the parent nuclei of atomic numbers 85–102.

Shear viscosity and electrical conductivity of the relativistic fluid in the presence of a magnetic field: A massless case

Abstract: We have explored the shear viscosity and electrical conductivity calculations for bosonic and fermionic media, without and with presence of an external magnetic field. For numerical visualisation, we have dealt with their simplified massless expressions. In the presence of a magnetic field, five independent velocity gradient tensors can be designed, and so their corresponding proportional coefficients, connected with the viscous stress tensor, provide us five components of the shear viscosity coefficient. In the existing literature, two sets of viscous stress tensors are available. Starting from them, the present work has obtained expressions for two sets of five shear viscosity coefficients, which can be ultimately classified into three basic components – parallel, perpendicular and Hall components as one get similar expression for the electrical conductivity at the finite magnetic field. Our calculations are based on the kinetic theory approach in relaxation time approximation. Repeating the same mathematical steps under finite magnetic field, which is traditionally practiced in the absence of magnetic field, we have obtained two sets of five shear viscosity components, whose final expressions are in good agreements with earlier references, although a difference in methodology or steps can be noticed. In this context, the present work, for the first time, addresses a detailed calculation of relaxation time approximation (RTA)-based kinetic theory calculations of the second set of five shear viscosity components, which was previously done by Denicol et al (Phys. Rev. D 98, 076009 (2018)) in moment method technique. Realising the massless results of viscosity and conductivity for Maxwell–Boltzmann, Fermi–Dirac and Bose–Einstein distribution functions, we have applied them for massless quark gluon plasma and hadronic matter phases, which can provide us a rough order of strength, within which actual results will vary during quark–hadron phase transition. The present work also indicates that the magnetic field might have some role in building perfect fluid nature in RHIC or LHC matter. The lower bound expectation of shear viscosity to entropy density ratio is also discussed. Here, for the first time, we are addressing an analytic expression of temperature- and magnetic field-dependent relaxation time of the massless fluid, for which perpendicular component of shear viscosity to entropy density ratio can reach its lower bound.