Narrow Results

In this paper, we consider a model for a nucleon interacting with the ω and σ mesons in the atomic nucleus. The model is relativistic, but we study it in the nuclear physics non-relativistic limit, which is of a very different nature from the one of the atomic physics. Ground states with a given angular momentum are shown to exist for a large class of values for the coupling constants and the mesons' masses. Moreover, we show that, for a good choice of parameters, the very striking shapes of mesonic densities inside and outside the nucleus are well described by the solutions of our model.

In this paper, the heat-transfer enhancement phenomena have been explored for non-axisymmetric Homann stagnation-point flow of Maxwell fluid. Furthermore, Buongiorno’s model for nanofluid is utilized to study remarkable impacts of random (Brownian) motion and thermophoresis of dispersed nanoparticle. The Maxwell nanofluid generates new class of asymmetric stagnation-point flows that depends on ratio $\gamma =b∕a$ ($b$ is shear and $a$ is strain rate) and Deborah number ${\beta }_1$. The numerical and asymptotic consequences of leading equations for current model are obtained using shooting technique. The solution is obtained for diverse values of involved parameters over $\gamma$. The wall shear stress, heat/mass transfer rate, velocities, temperature distributions and nanoparticle concentration compared to their large-$\gamma$ asymptotic behaviors were presented for different values of involved parameters. It is observed that the numerical outcomes of wall shear stress, heat-transfer rate and mass flux best agree with their perturbative solution for large-$\gamma$. Moreover, the wall shears $f^{\prime \prime }(0)$, $g^{\prime \prime }(0)$ grow as viscoelasticity raises. The reduction in heat flux and particles mass diffusion occurs near the wall boundary-layer due to clustering of nanoparticles. However, heated surface during thermophoresis is pushed nanoparticles into Brownian motion which constitute to enhance the heating process.

Micropolar fluid flow studied in this paper is influenced by microstructural slip. The flow is directed by a scheme of Partial Differential Equalities. These Partial Differential Equalities are then converted to nonlinear set of Ordinary Differential Equalities via boundary layer conversions. MATLAB bvp4c built in code is taken into account to resolve the leading set of ODEs, along with the initial-boundary settings. Hydro dynamical and thermal boundary layer outlines are considered and deliberated and the results are confirmed by linking with available literature in the classical case. Microstructural slip effects are shown on the Nusselt number and skin-friction coefficient. This model can better predict the effects and characteristics of rotational slip. Specifically, it is predicted from the tabular and graphical results that the rotational slip affects the boundary layer thickness when second-order translational slip disappears. It is important to mention that augmenting the standards of Prandtl number and radiation constraint declines the fluid temperature in the nonappearance and existence of microstructural slip. Moreover, increasing the values of magnetic parameter enhances the fluid temperature in presence as well as in absence of microstructural slip.

CdMnTe is demonstrated to be a good candidate in the X-ray and $\gamma$-ray detector application, however, there are few reports on theoretical analysis of electron scattering rate in CdMnTe quantum well. Within the framework of effective mass approximation and envelope function approximation, the influence of the Mn alloy composition ($x_{\mathrm{\text{Mn}}})$, the well width ($L_w)$, the electron temperature ($T_e)$ and the electron density ($N_e)$ on the electron–electron scattering rate (1/${\tau }_{22-11})$ in the CdTe/Cd${}_{1-x}$Mn${}_x$Te single quantum well (SQW), are simulated by shooting method and Fermi’s Golden Rule. The results show that 1/${\tau }_{22-11}$ is significant inverse proportional to $x_{\mathrm{\text{Mn}}}$, but positively proportional to $L_w$ and $N_e$. Except for a small peak at 20 K, 1/${\tau }_{22-11}$ is not sensitive to $T_e$. The above differential dependency of 1/${\tau }_{22-11}$ on $x_{\mathrm{\text{Mn}}}$ and $L_w$ can be interpreted by sub-band separation ($E_{21}=E_2-E_1)$, which is proportional to $x_{\mathrm{\text{Mn}}}$ but inversely proportional to $L_w$. When $E_{21}$ decreases gradually, the electron transition becomes easier, which leads to 1/${\tau }_{22-11}$ increases. The dependency of 1/${\tau }_{22-11}$ on $T_e$ can be interpreted by kinetic energy of electrons. The larger the electron kinetic energy is, the more difficult the electron transition from first excited state to ground state is, which leads to 1/${\tau }_{22-11}$ decreasing. The dependency of 1/${\tau }_{22-11}$ on $N_e$ can be interpreted by the Coulomb interaction between electrons, i.e., the increase of electron collision probability caused by the increase of $N_e$.

Here, unsteady boundary layer flow under the action of magnetic effect over a moving stagnation surface has been investigated numerically. This study examines non-Newtonian fluid flow with respect to combined effect of magnetic field, movement of surface and time. Governing equations are dimensionless by applying nondimensional quantities. Then system of coupled ordinary differential equations are obtained by appropriate similarly transformations, in terms of the governing parameter including unsteady parameter ($k)$, magnetic number ($M)$, power-law index ($n)$ and three-dimensional parameter ($\alpha )$. Thus, the obtained modelled equations are solved numerically by the shooting technique. The problem’s parameters are thoroughly discussed and verified physically and graphically. The obtained results validate to literature result. The two relevant flows’ velocity profile’s numerical results have been examined.

In this paper, the effects of heat transfer and Hall current on the sinusoidal motion of solid particles through a planar channel has been discussed. The walls of the channel are considered as compliant under the effects of magnetohydrodynamics. The mathematical formulation has been performed using energy equation, momentum equation, and Ohm’s law. The modeled equations are further modified by taking the assumption of a zero Reynolds number and long wavelength. Numerical shooting technique has been employed to solve the nonlinear differential equations. The impact of all the emerging parameters such as wall rigidity, wall tension, mass characterization, Hall parameter, Hartmann number, Weissenberg number, particle volume fraction, Prandtl number, and Eckert number, respectively. Particularly, we discussed their effects on velocity and temperature profile.

Increasingly sophisticated techniques are being developed for the manufacture of functional nanomaterials. A growing interest is also developing in magnetic nanofluid coatings which contain magnetite nanoparticles suspended in a base fluid and are responsive to external magnetic fields. These nanomaterials are “smart” and their synthesis features high-temperature environments in which radiative heat transfer is present. Diffusion processes in the extruded nanomaterial sheet also feature Soret and Dufour (cross) diffusion effects. Filtration media are also utilized to control the heat, mass and momentum characteristics of extruded nanomaterials and porous media impedance effects arise. Magnetite nanofluids have also been shown to exhibit hydrodynamic wall slip which can arise due to non-adherence of the nanofluid to the boundary. Motivated by the multi-physical nature of magnetic nanomaterial manufacturing transport phenomena, in this paper, we develop a mathematical model to analyze the collective influence of hydrodynamic slip, radiative heat flux and cross-diffusion effects on transport phenomena in ferric oxide (${\mathrm{\text{Fe}}}_3{\mathrm{\text{O}}}_4$-water) magnetic nanofluid flow from a nonlinear stretching porous sheet in porous media. Hydrodynamic slip is included. Porous media drag is simulated with the Darcy model. Viscous magnetohydrodynamic theory is used to simulate Lorentzian magnetic drag effects. The Rosseland diffusion flux model is employed for thermal radiative effects. A set of appropriate similarity transformation variables are deployed to convert the original partial differential boundary value problem into an ordinary differential boundary value problem. The numerical solution of the coupled, multi-degree, nonlinear problem is achieved with an efficient shooting technique in MATLAB symbolic software. The physical influences of Hartmann (magnetic) number, Prandtl number, Richardson number, Soret (thermo-diffusive) number, permeability parameter, concentration buoyancy ratio, radiation parameter, Dufour (diffuso-thermal) parameter, momentum slip parameter and Schmidt number on transport characteristics (e.g. velocity, nanoparticle concentration and temperature profiles) are investigated, visualized and presented graphically. Flow deceleration is induced with increasing Hartmann number and wall slip, whereas flow acceleration is generated with greater Richardson number and buoyancy ratio parameter. Temperatures are elevated with increasing Dufour number and radiative parameter. Concentration magnitudes are enhanced with Soret number, whereas they are depleted with greater Schmidt number. Validation of the MATLAB computations with special cases of the general model is included. Further validation with generalized differential quadrature (GDQ) is also included.

In this paper, the mechanisms of excitation and propagation of nonlinear Rossby waves are investigated by the approach of topographic balance under the beta approximation for the first time. Using time-space elongation transformation and perturbation expansion method, a Korteweg–de Vries model equation for topographic Rossby wave amplitude is derived. The influences of topography parameters on Rossby solitary waves are discussed through qualitative and quantitative analysis.

In this paper, a special nonsmooth transformation of time is combined with the shooting algorithm for visualization of the manifolds of periodic solutions and their bifurcations. The general class of nonlinear oscillators under smooth, nonsmooth, and impulsive loadings is considered. The corresponding boundary value problems with no singularities are obtained by introducing the periodic piecewise-linear (sawtooth) temporal argument. The Ueda circuit, that is Duffing's oscillator with no linear stiffness, is considered for illustration. It is shown that the temporal mode shape of the input can be responsible for qualitative features of the dynamics, such as transitions between the regular and random motions. The important role of unstable periodic orbits and their links with strange attractors are discussed.

As a consequence of a rather complete analysis of the qualitative properties of the solutions of the Ginzburg–Landau equations, we prove, in this paper, both the continuity of a fundamental map σ, called response map in the physical literature on superconductors, and the convergence of an efficient algorithm for the computation of the graph of σ. The response map σ gives the intensity h of the external magnetic field for which the Ginzburg–Landau equations (in a half-space) have a solution such that the parameter order has a prescribed value at the boundary of the sample. Our study involves a shooting method on either one or the other unknown of the system; our algorithm has been introduced in Bolley–Helffer for small values of the Ginzburg–Landau parameter κ and extended in Bolley to any value of κ. Our preceding mathematical studies were not sufficient to prove the convergence, but a recent result (in Ref. 3) on the monotonicity of the solutions with respect to h, combined with a more extensive use of the properties of the solutions of the Ginzburg–Landau system, allow us to complete the proof and to get, as a by-product, the continuity of σ.

By using a shooting technique, we prove that the quasilinear boundary value problem

In this technical note, the post-buckling behavior of a simply supported elastic column with various rotational end conditions of the supports is investigated. The compressive force is applied at the tip of the column. The characteristic equation for solving the critical loads is obtained from the boundary value problem of linear systems. In the post-buckling state, a set of nonlinear differential equations with boundary conditions is established and numerically solved by the shooting method. The interesting features associated with this problem such as the limit load point, snap-through phenomenon and the secondary bifurcation point will be highlighted herein.

This paper considers the behavior of a spatial elastica in a gravitational field. The slenderness of the system considered is such that the weight becomes an important consideration in determining elastic equilibrium configurations. Both ends of the elastica are clamped in an initially (planar) horizontal orientation at a fixed distance apart. However, one of the ends allows an increase in arc-length, that is, it is a sleeve joint. Thus, the total arc-length is the primary control parameter. This kind of elastica typically loses stability, resulting in out-of-plane deflections, when the total arc-length is increased beyond a critical value. A small mid-length torque can used to perturb a planar equilibrium configuration in order to test for stability. The aim of this study is to assess the effect of self-weight of the elastica (which is typically ignored) on promoting or delaying the loss of stability. To this end, it is useful to compare and contrast the results of orientation, that is, the system is configured in both an initial "upright" orientation and then in an "upside-down" orientation to highlight the influence of gravity. The results of the weightless elastica are used as a reference. Analysis is based on Kirchhoff's rod theory and Euler parameters, and the resulting set of governing differential equations are solved using a shooting method. The results from an experimental system using a slender superelastic wire made from Nitinol (Nickel Titanium Naval Ordnance Laboratory) exhibit close agreement with the analytical results.

This paper investigates the behavior of a pre-stressed arch under a sliding load, where the initial configuration can be obtained from the buckling of a straight column. The shape of the pre-stressed arch can be varied by increasing the end shortening. Subsequently, a sliding load is applied at a certain height level. The orientation of the applied load maintains the right angle with respect to the tangential line of the arch. By moving the load horizontally, the behavior of the arch can be explored. The governing differential equations of the problem can be obtained by equilibrium equations, constitutive relation, and nonlinear geometric expressions. The exact closed-form solutions can be derived in terms of elliptic integrals of the first and second kinds. In this problem, the arch can be divided into two segments where each segment is a part of a buckled hinged-hinged column mounted on an inclined support. The shooting method is employed to solve the numerical solutions for comparing with the elliptic integral method. The stability of the pre-stressed arch is evaluated from vibration analysis, where the shooting method is again utilized for solving the natural frequencies in terms of a square function. A simple experiment is set up to explore the equilibrium shapes. Poly-carbonate sheet is utilized as the pre-stressed arch. From the results, it is found that the results obtained from elliptic integral method are in excellent agreement with those obtained from shooting method. The equilibrium shapes from the theoretical results can also compare with those from the experiment. The pre-stressed arch can lose its stability and snap into an upside-down (inverted) configuration depending on the ratio of rise to span-length and loading height. The instability of the arch is not only detected during the pushing of the sliding load but a pulling load can also cause unstable behavior of the arch.

The buckling and postbuckling behaviors of functionally graded graphene platelets-reinforced composite (FG-GPLRC) circular plates are studied based on the classical nonlinear von Karman plate theory. The effective Young’s modulus of the composite is estimated using the modified Halpin–Tsai micromechanical model, and the effective Poisson’s ratio is estimated by the rule of mixtures. Governing equations of the problem are derived based on the Hamilton principle and the numerical solutions of critical loads and postbuckling deflection–load relationships are calculated using the shooting method. Different from the existing linear buckling analysis based on the Terriftz criterion, the study with considering the global deformation of the plates, we analyze the influencing factors of the critical buckling loads and postbuckling paths of the FG-GPLRC circular plates subjected to uniformly distributed radial pressure. The results show that the content, geometric parameters and distribution pattern of GPL have great influences on the critical buckling loads and the post-buckling bearing capacities of the circular FG-GPLRC plates.

This paper is concerned with thermal post-buckling of uniform isotropic beams with axially immovable spring-hinged ends. The ends of the beam with elastic rotational restraints represent the actual practical support conditions and the classical hinged and clamped conditions can be achieved as the limiting cases of the rotational spring stiffness. The governing differential–integral equation is solved by assuming suitable admissible function for lateral displacement and by employing the Galerkin method. A brief and explicit analytical approximate formulation is established to predict the thermal post-buckling behavior of the beam. The present analytical approximate expressions show excellent agreement with the corresponding numerical solutions based on the shooting method. This confirms the effectiveness and verifies the accuracy of the formulas established.

This paper presents the postbuckled configurations of simply supported and clamped-pinned nanorods under self-weight based on elastica theory. Numerical solution is considered in this work since closed-form solution of postbuckling analysis under self-weight cannot be obtained. The set of nonlinear differential equations of a nanorod including the effect of nonlocal elasticity are investigated. The constraint equation at boundary condition technique is introduced for the solution of postbuckling analysis. In order to solve the set of nonlinear differential equations, the shooting method is utilized, where the set of these equations along with boundary conditions are integrated by the fourth-order Runge-Kutta algorithm. Numerical results are obtained and the highlighting influences of the nonlocal elasticity on postbuckling behavior of nanorods are discussed. The obtained results indicate that the rotation angle and the postbuckled configurations of nanorods are varied by changing the nonlocal elasticity parameter. The effect of nonlocal elasticity shows the softening behavior in comparison with the Euler beam. The present formulation together with constraint boundary condition technique is an effective solution for postbuckling analysis of a nanorod under self-weight including the effect of nonlocal elasticity.

Compared with the clearance-sealed pistonphone, the membrane-sealed pistonphone can realize the sound pressure at very low frequency and very high sound pressure for its lower leakage. However, the membrane-sealed pistonphone also brings the problem that the compressed volume cannot be decided precisely because of the deformation of the membrane, which results in the inaccurate calculation for the sound pressure in the chamber. In this paper, a sound pressure formula for the membrane-sealed pistonphone is derived according to an analysis of the characteristics of the ideal membrane. The static and the dynamic deformation of the membrane are studied. Then, the effects of the thickness, the sealed width, the extension ratio, and the modal vibration of the membrane are studied through the finite element method. The results show that the deviation of the sound pressure level obtained from the ideal sound pressure formula can be reduced to less than 0.1dB when the sound pressure level is lower than 174dB and the membrane is specially designed, which indicates that the influence of the membrane on the sound pressure is almost negligible.