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

There is a famous criterion for objective wave function reduction which is derived by using the Shrödinger–Newton equation [L Diosi, Phys. Lett. A 105(4–5), 199 (1984)]. In this regard, a critical mass for the transition from quantum world to the classical world is determined for a particle or an object. In this paper, we shall derive that criterion by using the concept of Bohmian trajectories. This

In this paper, we developed the fractional-order finance system transmission model. The main objective of this paper is to construct and evaluate a fractional derivative to track the shape of the dynamic chaotic financial system of fractional order. The numerical solution for fractional-order financial system is determined using the Atangana–Baleanu–Caputo (ABC) and Caputo derivatives. Picard–Lindelof’s

We propose Whittaker function approach as a theoretical method for finding exact solutions of a quantum mechanical system placed in the Kratzer potential. We then show that the effect of an external uniform magnetic field on this system can be satisfactorily determined using variational method. By following the one-step treatment suggested in this study, we increase the reliability and the accuracy

In this study, by using full-potential linearised augmented plane wave (FP-LAPW) method with the generalised gradient approximation (GGA) based on density functional theory (DFT), the structural, electronic, elastic and magnetic properties of the Heusler alloys Cr\(_{\mathrm {2}}\)NbSi\(_{{1-x}}\)Ge\(_{x}\) have been evaluated. The AlCu\(_{\mathrm {2}}\)Mnl-type structure is more stable than the CuHg\(_{\mathrm

In this work, we studied the relaxation dynamics of coherences of different orders present in a system of two coupled nuclear spins. We used a previously designed model for intrinsic noise present in such systems which considers the Lindblad master equation for Markovian relaxation. We experimentally created zero-, single- and double-quantum coherences in several two-spin systems and performed a complete

In this paper, the mechanism of system solutions approaching infinity is explored based on a modified Rayleigh–Duffing oscillator with two slow-varying periodic excitations. System solutions approaching infinity is a new novel route to bursting oscillation, and are not reported yet. The system can be separated into a fast subsystem and a slow subsystem according to the slow–fast analysis method. We

In this paper, the single bunch fast transverse instabilities of the electron beam in the ILSF storage ring due to the RF cavity impedance are investigated. We consider Satoh’s formalism (that studied mode coupling instabilities based on the Vlasov equation) and Lindberg’s formalisms (that studied mode coupling instabilities based on the Fokker–Planck equation). The Lindberg formalisms are rewritten

The effect of an external magnetic field on the mixed convection \(\hbox {Fe}_{{3}}\hbox {O}_{{4}}/\)water ferrofluid flow in a horizontal porous channel was studied numerically. The governing equations using the Darcy–Brinkman–Forchheimer formulation were solved by employing the finite volume method. The computations were carried out for a range of volume fractions of nanoparticles \(0\le \varphi

A numerical formula is derived which gives solutions of the fractional Schrödinger equation in time-independent form in the case of Coulomb potential using Riemann–Liouville definition of the fractional derivative and the quadrature methods. The formula is applied for electron in the nucleus field for multiple values of fractional parameter of the space-dependent fractional Schrödinger equation and

The present paper aims at weak non-linear stability analysis followed by linear analysis of finite-amplitude Rayleigh–Benard magnetoconvection problem in an electrically conducting Newtonian liquid with heat source/sink. It is showed that the internal Rayleigh number, thermorheological parameter and Chandrasekhar number influence the onset of stationary convection and Nusselt number. The generalised

A typical axially compact, square window core steering magnet has a very small 2D good field region (GFR) of 18% of the iron core aperture. It is weak with 85% of its dipole in the fringes. Increasing the current fed area (coil) to increase the dipole strength lowers the good field zone. Some novel and simple coil shapes can expand their 2D/3D GFR to 94/40% of the iron aperture. They are axially compact

The radial wave functions of the generalised Woods–Saxon (GWS) potential within the two-body model of \(\left( \mathrm {Core}+n \right) \) have been used to study the ground-state density distributions of protons, neutrons and matter and the associated root mean square (rms) radii of neutron-rich \(^{\mathrm {14}}\hbox {B}\), \(^{\mathrm {22}}\hbox {N}\), \(^{\mathrm {23}}\hbox {O}\) and \(^{\mathrm

In this paper we report the control and synchronisation of chaos in a memristive Murali–Lakshmanan–Chua (MLC) circuit. This circuit, introduced by the present authors in 2013, is basically a non-smooth system having two discontinuity boundaries by virtue of it having a flux-controlled active memristor as its nonlinear element. While the control of chaos has been effected using state feedback techniques

The effect of diffusive heat conduction and Brownian motion on the enhancement of thermal conductivity in nanofluids is presented here.\({\hbox {Al}}_{2} {\hbox {O}}_{3}\) and \({\hbox {TiO}}_{2}\) nanofluids were prepared at four different wt. fractions of 1%, 0.5%, 0.1% and 0.05% and their thermal conductivity values were measured over temperatures ranging from 25 to \(55^{\circ }\hbox {C}\) for

The influence of excluded volume interactions (EVIs) governs the dynamics of branched polymeric structures. Therefore, we developed a theory with the inclusion of ubiquitous EVIs on average square displacement (ASD) of the centre of mass in layered random flow (LRF). The mean-field approach is used to account for effective EVIs between non-bonded monomers of generalised Gaussian structures. The effect

In this paper, the Dirac equation in the presence of some scalar potentials based on sl(2) Lie algebra is solved by quasi-exact solvability theory. The configuration of the classes III and VI potentials in the Turbiner’s classification is constructed. Then, the Bethe ansatz equations are calculated so that the energy eigenvalues and eigenfunctions are obtained. Also, we study the problem by using asymptotic

The present article deals with the study of interacting and non-interacting dark energy (DE) and dark matter (DM) in the spatially homogeneous and anisotropic Bianchi I space–time within the framework of Brans–Dicke (BD) scalar–tensor theory of gravitation. As the set of field equations is not closed, exact solutions are obtained using power-law relation and assuming a linearly varying deceleration

Recent advances in laser-plasma accelerators have made possible the production of high-power beams with very low divergence. In this paper, the carbon heavy-ion beam was used to provide optimal conditions for the ignition of P–\(^{\mathrm {11}}\)B clean fuel pellets using the Deira-4 simulation code. The calculations showed that generating maximum ion heating of about 140 keV requires a laser with

The purpose of this paper is to suggest a numerical technique to solve fractional variational problems (FVPs). These problems are based on Caputo fractional derivatives. Rayleigh–Ritz method is used in this technique. First we approximate the objective function by the trapezoidal rule. Then, the unknown function is expanded in terms of the Bernstein polynomials. By this method, a system of algebraic

In this work, efficient amplitude-apodization pupils have been presented for tailoring the point spread function (PSF), which results in a decreased full-width at half-maximum (FWHM) and suppressed sidelobes. Comparison of PSF intensity profiles for both the unapodized and apodized cases have been reported. By analysing the resulting PSFs, the well-known effects induced by monochromatic aberrations

In this paper, we investigate the effects of gravitational field on the dynamical behaviour of nonlinear atom–field interaction. We consider a moving tripod-type four-level atom interacting with a single mode field in the presence of a classical homogeneous gravitational field. The analytical solution of the model is calculated by using the Schrödinger equation for a coherent electromagnetic field

Exact analytical expression of the Fredholm determinant with outgoing wave boundary condition for motion in Hulthén-distorted non-local separable potential is constructed and expressed in the maximum reduced form. Using boundary conditions (regular and irregular), two approximate energy-dependent interactions corresponding to the parent non-local potential are also constructed. The phase shifts for

The influence of a point heat source and Hall current on the laminar hydromagnetic free convective flow of an incompressible and electrically conducting viscous liquid between two vertical walls has been studied. A wavelet function is utilised to mathematically formulate the point or line heat source. The incidental equations on the flow have been processed subject to the Boussinesq approximation.

We show that the theory of self-adjoint differential equations can be used to provide a satisfactory solution of the inverse variational problem in classical mechanics. A Newtonian equation, when transformed to the self-adjoint form, allows one to find an appropriate Lagrangian representation (direct analytic representation) for it. On the other hand, the same Newtonian equation in conjunction with

We construct infinitely many conservation laws of the generalised short pulse equation with the help of its Lax pairs. By a reciprocal transformation, the generalised short pulse equation was transformed to the first negative flow of Sawada–Kotera hierarchy. On the basis of Darboux and reciprocal transformations, we obtain some exact solutions of the generalised short pulse equation.

The optical solitons for the complex Ginzburg–Landau model with Kerr law, quadratic–cubic law and parabolic law are obtained via the \(\hbox {exp}(-\Phi (\zeta ))\) expansion method. Many abundant solutions such as complex dark-singular, complex periodic-singular and plane-wave solutions are derived for this model. These complex solutions are useful for understanding the physical properties for this

We consider a deformed fifth-order Korteweg–de Vries (D5oKdV) equation and investigated its integrability and group theoretical aspects. By extending the well-known Lax pair technique, we show that the D5oKdV equation admits a Lax representation provided that the deformed function satisfies certain differential constraint. It is observed that the D5oKdV equation admits the same differential constraint

This study deals with the generalised Kudryashov method (GKM) for the time-fractional generalised Burgers–Fisher equation (TF-GBF). Using the transformation of travelling wave, the TF-GBF is transformed into a non-linear ordinary differential equation (NLODE). Later, GKM has been applied in the resultant equation which is a novel technique to obtain exact solutions. These exact solutions are plotted

We have measured the \(\beta \)-particle-induced bremsstrahlung energy yield and photon yield in the energy range 0.1668–2.274 MeV using beta sources such as \(^{\mathrm {35}}\hbox {S}\) (0.1668), \(^{\mathrm {99}}\hbox {Tc}\) (0.293), \(^{\mathrm {147}}\hbox {Pm}\) (0.225), \(^{\mathrm {90}}\hbox {Sr}\) (0.5462), \(^{\mathrm {204}}\hbox {Tl}\) (0.76), \(^{\mathrm {91}}\hbox {Y}\) (1.5), \(^{\mathrm

In this paper, we propose that the late-time acceleration of the Universe is due to bulk viscous fluid and trace of energy–momentum tensor T in f(R, T) theory of gravity. We assume that \(f(R,T) = f(R) + 2f(T)\) with \(f(R) = R\) and \(f(T) = \lambda T\) where \(\lambda \) is a constant, R and T are the Ricci scalar and trace of energy–momentum tensor. First, we obtain an exact solution of the bulk

In this article, generalised Kudryashov technique has been implemented to construct new soliton solutions of modified Benjamin–Bona–Mahony (mBBM) equation. Also, the optimal homotopy asymptotic method (OHAM) has been employed to estimate the numerical solution. The solutions thus acquired by the above methods are illustrated graphically. The techniques considered here are efficacious, plausible and

We consider models of light dark matter coupled to quarks through a vector current interaction. For low energies, these models must be treated through the effective couplings to mesons, which are implemented here through the chiral Lagrangian. We find the signals of dark matter annihilation and decay to the light mesons, and find the expected photon spectrum from the decay of the hadrons. We compare

This paper reports a modified 2D periodically forced oscillator. Numerical simulation results using the phase portrait and Lyapunov exponents’ spectrum say that the proposed oscillator depicts megastability. Offset boosting in the new system is shown using the variable boostable phenomenon. Very limited research is available on such type of oscillator. Further, in this paper, a controller based on

A broadband polarisation-insensitive terahertz (THz) metamaterial absorber (MMA) is presented in this paper. The MMA consists of a simple planar structure as a unit cell and an optically transparent indium tin oxide (ITO) ground plane, both are separated by a \(50\, \mu \hbox {m}\) dielectric substrate. We designed three combinations of MMA here, which are ITO–polyimide–ITO, ITO–polyethylene terephthalate

In this work, influence of hybrid nanofluids on heat transfer flow of a viscous fluid due to pressure gradient is discussed with innovative constant proportional Caputo fractional derivative. For this purpose, we consider an infinite vertical wall which is exponentially moving in the x-direction with variable temperature. Nanosized particles of Cu and \(\hbox {Al}_{2}\hbox {O}_{3}\) are suspended in

In this paper, we perform a theoretical investigation of the plasmon coupling in silver (Ag) nanocube–nanosphere dimer using finite difference time domain (FDTD) technique. Due to plasmonic Fano resonance, we observe a pronounced dip in the absorption spectrum, which is induced by the destructive interference between the bright dipole mode from the Ag nanocube and the dark quadrupole mode from the

In this paper, the dissipative mechanism (bulk viscosity and matter creation) is introduced to describe the effects of cosmic non-perfect fluid on the Ricci dark energy (RDE) model. We consider matter creation and bulk viscosity as two independent irreversible processes. Assuming suitable forms of the bulk viscous coefficient and matter creation rate, we find the exact solution of the field equations

In this paper, a new concentric Hamming linear aperture is suggested. The point spread function (PSF) is computed for concentric Hamming linear aperture and it is compared with the corresponding circular, conventional Hamming and obstructed Hamming apertures. In addition, the autocorrelation corresponding to the aperture under consideration is computed and plotted. Application of the Hamming linear

Quantum entanglement and its paradoxical properties are of paramount importance in quantum information theory. In recent years, there has been an increasing interest in the studies of high-dimensional quantum states and their impact on quantum communication as it can encode and process more data. Photonic entanglement is usually an evanescent property as it is destroyed easily by its interaction with

This article studies the effect of suction/blowing, inclined magnetic field, and chemical reaction on heat-absorbing unsteady radiative Casson fluid past a semi-infinite flat plate in porous medium incorporating the oscillatory plate movement as a linear combination of ‘cosine’ and ‘sine’ functions in time. Further, the mass and heat transfer characteristics are examined under the influence of conjugate

This paper presents the design and development of stretchable and deformable broadband antenna using low-cost silicone rubber-based dielectric substrate. A slot is introduced in the substrate to improve the stretchable behaviour. The dielectric properties of the substrate are measured using suspended ring resonator method. The proposed antenna uses silver elastomeric Lycra fabric as the conductive

In this paper, the Riemann–Hilbert problem of the modified Korteweg–de Vries (mKdV) equation is studied, from which a new combined soliton solution is obtained. In addition, to illustrate the dynamics of the new combined soliton solution, an algebra technique is developed to demonstrate the soliton interactions using Mathematica symbolic computations. The proposed method is effective in deriving and

In the case of technologically important quaternary alloys, structural and optoelectronic properties have been calculated with density functional theory (DFT)-based full-potential linearised augmented plane-wave (FP-LAPW) approach. The Perdew–Burke–Ernzerhof generalised gradient approximation (PBE-GGA) for structural properties and both the modified-Becke–Johnson (mBJ) and Engel and Vosko GGA (EV-GGA)

We present analytical results of the equation of state (EOS) described by a model of thermal quark mass and magnetic potential term introduced in Polyakov–Nambu–Jona–Lasinio (PNJL) model for two-flavour quarks. Under the influence of thermal quark mass and magnetic field term in the potential, the calculated results of EOS using the model are enhanced in a good pattern up to the temperature \(T=2.2T_{c}

This study attempts to answer the question of what space is made of and explores in this objective the analogy between the Einstein’s gravitational geometrical theory in one- and two-dimensional linear deformations and a possible space material based on strain measures done on the Ligo or Virgo interferometers. It draws an analogy between the Einstein’s gravitational constant \(\kappa \) and the Young’s

In this study, we present a new method for assessing the functional connectivity between the drive and the noisy response chaotic oscillators with significant frequency mismatch. This method is based on the footprint of the drive oscillator on the response oscillator. Specifically, we calculate the magnitude squared coherence between the intrinsic frequency of the drive oscillator and the oscillation

The iron calorimeter (ICAL) at India-based neutrino observatory (INO) is designed to mainly observe the muons produced in the charged current interactions of atmospheric muon neutrinos and antineutrinos. The track of the muon is reconstructed using the hits they produce in the detector. From this track, the charge, the energy and the direction of the muon are estimated, which are used to do oscillation

In the present article, Lie group of point transformations method is successfully applied to study the invariance properties of the \((2+1)\)-dimensional Pavlov equation. Applying the Lie symmetry method, we strictly obtain the infinitesimals, vector fields, commutation relation and several interesting symmetry reductions of the equation. The explicit exact solutions are derived under some limiting

The phenomenon of heat conduction is important in semiconductor devices. This property is investigated on the basis of modified Callway model. The formalism was carried out using Hamiltonian, phonon Green’s function and equation of motion techniques for various scattering events. It was found that every scattering mechanism is independent of each other and does not affect the others. The thermal conductivity

Sotalol hydrochloride (STHCl) is a cardiovascular agent, specifically an antiarrhythmic and beta-blocker, that can be used regularly for an extended period. However, it may have side effects, such as weakness and slow heart rate (bradycardia). Currently, techniques such as capillary zone electrophoresis and high-performance liquid chromatography have been widely used for the determination of sotalol

The current work deals with the nonlinear azimuthal stability analysis of coupled interfaces between three magnetic fluids. The considered system consists of three incompressible rotating magnetic fluids throughout the porous media. Additionally, the system is pervaded by a uniform azimuthal magnetic field. Therefore, for simplicity, the problem is considered in a planar configuration. The adopted

In this article, we study thermal entanglement between two-coupled two-level atoms interacting with a single-mode cavity field. The cavity mode is assumed to be initially in the vacuum state and the detuning parameter is large. The thermal entanglement in this two-qubit system is quantified in terms of the concurrence, as a proper measure for two-qubit mixed states. We investigate how the thermal entanglement

We performed an investigation on the behaviour of the electrical parameters of ultrathin Cu(In,Ga)Se\(_{\mathrm {2}}\) (CIGS) solar cells buffered with Zn(O,S). Using one-dimensional simulations and by defining a new structure, we achieved a significant reduction of the absorber and the buffer layers to evaluate the changes in the cell’s performance. The simulation results revealed that a good optimisation

In the present work, dye-sensitised solar cell (DSSC) is fabricated using natural dye (Tecoma Stans)-sensitised \(\hbox {TiO}_{\mathrm {2\, }}\) as the photoanode, platinum as the counter electrode and lithium iodide and iodine as the electrolyte. Initially, \(\hbox {TiO}_{\mathrm {2\, }}\) nanoparticles are synthesised by the sol–gel technique using glacial acetic acid as the hydrolysing agent. The

Boron carbide (\(\hbox {B}_{\mathrm {4}}\hbox {C}\)) has been widely used in nuclear reactors and nuclear applications. In this work, the high-purity (99.9%) \(\hbox {B}_{\mathrm {4}}\hbox {C}\) samples were irradiated using a gamma source (\(^{\mathrm {60}}\hbox {Co}\)) with a dose rate (D) of 0.27 Gy/s at different gamma irradiation doses at room temperature. Phase and microstructural characterisation

Due to the exponential attenuation of photons in materials, thick samples will attenuate a large portion of photons. This is a source of error in methods such as neutron activation analysis, which use gamma spectroscopy to characterise a radioactive source. A method is developed to quantify the magnitude of self-shielding with the help of MCNP6. Then the mass of an unknown sample is determined by comparing

In this analysis, the mixed convection boundary layer MHD flow of non-Newtonian Carreau fluid subjected to Soret and Dufour effects over a moving vertical plate is studied. The governing flow equations are converted into a set of non-linear ordinary differential equations using suitable transformations. For numerical computations, bvp4c in MATLAB package is used to solve the resulting equations. Impacts

In this work, we have investigated the structural, electronic and thermodynamic properties of GaP\(_{1-x}\)Sb\(_{x}\) and AlP\(_{1-x}\)Sb\(_{x}\) ternary alloys for a number of ordered structures and compositions in a series of first-principles calculations within the density functional theory, using full potential-linearised augmented plane-wave (FP-LAPW) method, as implemented in the WIEN2k code

We explain how the invariant subspace method can be extended to a scalar and coupled system of time-space fractional partial differential equations. The effectiveness and applicability of the method have been illustrated using time-space (i) fractional diffusion-convection equation, (ii) fractional reaction-diffusion equation, (iii) fractional diffusion equation with source term, (iv) two-coupled system