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In this article, we aim to analyze electrically induced magnetic incompressible flow and heat transfer through a channel within the framework of micropolar continuum. Finite element method is employed to compute the numerical solution of the governing dynamics formulated in the form of PDEs along with associated boundary conditions on the channel. The weak form is presented and variational problem is implemented in FreeFem++ language. To validate, the correct implementation of the problem and obtained numerical results, a reduced micropolar magnetohydrodynamic model is taken into consideration. The analytical solution is presented. Computed numerical results are compared with the exact solution in case of reduced micropolar model and a good agreement is achieved. An excellent convergence of the numerical solution to the exact solution is shown through Tables where L 2 -norm and H 1 -errors are computed at refined meshes. Effect of different physical parameters such as magnetic Reynolds number ( R m ), Hartmann number (Ha), micorpolar constants (m and l 1 2 ), micropolar coupling number (N), Prandtl number (Pr) and Brinkmann number (Br) are studied and discussed in detail. The development of thermal, translational and micro-rotational velocity profiles over the cross-sectional domain of the channel is shown for varying values of these material parameters. Some interesting and new findings in this investigation are presented and discussed. It is observed that the maximum temperature in the medium shifts from the center of the domain toward the boundaries if the micropolar coupling constant N is increased. Maximum micro-rotations are always found near the channel's boundary where it is evidenced that the particle's micro-rotations have a direct proportionality with the micropolar constant m. Moreover, the counter rotations of the continuum particles are evidenced at the channel's boundary. Furthermore, the micorpolar coupling constant l 1 2 is found to resist the micro motions of the particles in the channel. The successful implementation of one and higher dimensional magnetohydrodynamic model in FreeFEM++ in general and within the context of micorpolar continuum in particular is delineated. This shows that it provides an efficient platform to simulate magnetohydrodynamic problems in higher order continuum which has applications in designing magneto-rheological airbags, aircraft take-off gear, mechanical heart valves and cooling systems. [ABSTRACT FROM AUTHOR]

We study the dynamics of magnetic flows on Heisenberg groups, investigating the extent to which properties of the underlying Riemannian geometry are reflected in the magnetic flow. Much of the analysis, including a calculation of the Mañé critical value, is carried out for (2 n + 1) -dimensional Heisenberg groups endowed with any left invariant metric and any exact, left-invariant magnetic field. In the three-dimensional Heisenberg case, we obtain a complete analysis of left-invariant, exact magnetic flows. This is interesting in and of itself, because of the difficulty of determining geodesic information on manifolds in general. We use this analysis to establish two primary results. We first show that the vectors tangent to periodic magnetic geodesics are dense for sufficiently large energy levels and that the lower bound for these energy levels coincides with the Mañé critical value. We then show that the marked magnetic length spectrum of left-invariant magnetic systems on compact quotients of the Heisenberg group determines the Riemannian metric. Both results confirm that this class of magnetic flows carries significant information about the underlying geometry. Finally, we provide an example to show that extending this analysis of magnetic flows to the Heisenberg-type setting is considerably more difficult. [ABSTRACT FROM AUTHOR]

The important role of electromagnetic induction in neuronal activities has received considerable attention. However, its connection with epilepsy disease is rarely explored, especially the related dynamical mechanisms have not been fully investigated. In this paper, with the help of the magnetic flux variable, an improved Taylor model considering electromagnetic induction is proposed. Based on this model, we separately study the effect of the excitatory projection ( c 3 ) from the pyramidal neuronal population (PY) to the specific relay nucleus (SRN) and the inhibitory projection ( c 9 ) from the thalamic reticular nucleus (TRN) to the specific relay nucleus (SRN) on the epileptogenesis under electromagnetic induction. The results show that electromagnetic induction is a double-edged sword. On the one hand, 2-SWDs are triggered to help expand the seizure area caused by c 3 . On the other hand, it has a certain elimination effect on seizures induced by c 9 . More importantly, the internal bifurcation mechanism of dynamical transitions has been revealed, in which 2-SWDs is induced by fold of cycles or 'ghost' bifurcations, and the expansion of the oscillating (resting) monostable region leads to aggravation (partial elimination) of absence seizures. Our results might contribute to understanding the role of endogenous magnetic fields in epileptic seizures. [ABSTRACT FROM AUTHOR]

On the basis of finite element analysis, an eigenvalue problem is performed to examine the vibrational characteristics of a hetero-nanotube made of carbon (C) and boron nitride (BN) nanotubes in magnetic and thermal environment. By incorporating the assumption of nonlocal elasticity theory, the size-dependent behavior of the considered structure is also taken into account. The obtained results demonstrate that the onset of the divergence and flutter instabilities may be postponed by exploiting a hetero-nanotube rather than a uniform one composed of carbon nanotube. Moreover, it is exhibited that, in the presence of fluid flow, the mode shape configuration of nanotubes may be different from those of classical modes and therefore the later one should not be utilized in the dynamic analysis of fluid-conveying tubes. Finally, it is shown that, as the temperature decreases, the natural frequencies of the system decrease in high temperature conditions and increase for the case of room temperature. [ABSTRACT FROM AUTHOR]

We study magnetic trajectories in Lie groups equipped with bi‐invariant Riemannian metric. We define the Lorentz force of a magnetic field in a Lie group G, and then, we give the Lorentz force equation for the associated magnetic trajectories that are curves in G. When the manifold is a Lie group G equipped with bi‐invariant Riemannian metric, we derive differential equation system that characterizes magnetic flow associated with the Killing magnetic curves with regard to the Lie reduction of the curve γ in G. [ABSTRACT FROM AUTHOR]

Based on the high attitude platform of building slabstone-installing robot with independent development,research was carried out about multi-DIM vibration. The paper firstly constructs the system with two degrees of freedom parallel mechanism as the main body and rotating MR damper as actuator. The dynamics equation of the vibration system is established by using Lagrange equation. The paper analyzes the vibration characteristics and designs a kind of rotary MR damper based on a shear mode of magneto rheological fluid. The mechanical characteristics of MR damper is analyzed. The kinematics and kinetic analysis of parallel mechanism is done. The multi-DIM vibration suppression works quickly based on the position of platform according to the kinematics equation. Finally the simulation experiment of this system of multi-DIM vibration suppression is introduced with the aid of to calculate and analysis whether the model is effective and feasible.

This paper documents the incompressible hydro-magnetic flow and heat transfer analysis of water–Graphene oxide (GO) nanofluid. More exactly, the nanofluid flow occurs along a thin needle moving axially. Despite the fact that there seems to be various works on the subject in the existing literature, however, very few studies have been carried out to investigate the dual numerical solution for such flow. Consequently, the inspiration here is to look for dual numerical solutions for such a non-linear phenomenon along with the stability analysis of computed solutions. The governing coupled equations representing the mathematical formulation of the current physical problem were obtained from the equation of motion and the mass and the energy conservations by taking steady and incompressible flow. The numerical solution of governing set of simultaneous ordinary differential equations is computed with the assistance of Matlab solver bvp4c. This research aimed at revealing the conceivable impacts of existing fluid interaction parameters on non-dimensional velocity and temperature distributions. These computations exhibits that more than one solution is possible only in case of flow over shrinking needle for certain combinations of the parameters. The result shows that the skin friction coefficient increases in both solutions with higher nanoparticles volume fraction. Furthermore, an enhancement in local Nusselt number is noted as the thermal radiation parameter increases. • We simulate the fluid flow over a past a continuously moving thin needle immersed in a nanofluid. • Dual branch of solutions are possible for a certain range of parameter. • A stability analysis is carried out to examine which solution stable and physically realizable. • The bvp4c collocation formula is employed to get the solution for governing problem. [ABSTRACT FROM AUTHOR]

Breathing is a complex rhythmic movement. The dynamics of neuron firing activity has important implications in understanding the causes of pathological respiratory rhythm. Studies on electrophysiology have shown that the internal and external bioelectricity of nervous system may play important roles on firing activities of neuron. In this paper, the magnetic flow is added as a new variable to the Butera model to investigate the effect of electromagnetic induction on neuronal activities. The effect of magnetic flow on membrane potential is described by imposing additive memristive current on the membrane variable. The memristive current depends on the variation of magnetic flow. Direct and alternating currents of external stimulus are also added to the membrane potential. Dynamics of this modified model is discussed to consider the influence of magnetic flux on the membrane potential under different conditions of direct and alternating currents. The results show that the magnetic flux makes the pre-BötC neuron oscillate under a lower value of the direct current. Regular bursting and the mixed modes bursting types can be observed by changing the external condition and stimulus. Further studies on the combination effects of the parameter k1 and the direct and alternating currents are performed by two-parameter bifurcation analysis. [ABSTRACT FROM AUTHOR]

Complex anatomical and physiological structure of an excitable tissue (e.g., cardiac tissue) in the body can represent different electrical activities through normal or abnormal behavior. Abnormalities of the excitable tissue coming from different biological reasons can lead to formation of some defects. Such defects can cause some successive waves that may end up to some additional reorganizing beating behaviors like spiral waves or target waves. In this study, formation of defects and the resulting emitted waves in an excitable tissue are investigated. We have considered a square array network of neurons with nearest-neighbor connections to describe the excitable tissue. Fundamentally, electrophysiological properties of ion currents in the body are responsible for exhibition of electrical spatiotemporal patterns. More precisely, fluctuation of accumulated ions inside and outside of cell causes variable electrical and magnetic field. Considering undeniable mutual effects of electrical field and magnetic field, we have proposed the new Hindmarsh-Rose (HR) neuronal model for the local dynamics of each individual neuron in the network. In this new neuronal model, the influence of magnetic flow on membrane potential is defined. This improved model holds more bifurcation parameters. Moreover, the dynamical behavior of the tissue is investigated in different states of quiescent, spiking, bursting and even chaotic state. The resulting spatiotemporal patterns are represented and the time series of some sampled neurons are displayed, as well. [ABSTRACT FROM AUTHOR]

To investigate the effect of electromagnetic induction on the electrical activity of neuron, the variable for magnetic flow is used to improve Hindmarsh–Rose neuron model. Simultaneously, due to the existence of time-delay when signals are propagated between neurons or even in one neuron, it is important to study the role of time-delay in regulating the electrical activity of the neuron. For this end, a four-variable neuron model is proposed to investigate the effects of electromagnetic induction and time-delay. Simulation results suggest that the proposed neuron model can show multiple modes of electrical activity, which is dependent on the time-delay and external forcing current. It means that suitable discharge mode can be obtained by selecting the time-delay or external forcing current, which could be helpful for further investigation of electromagnetic radiation on biological neuronal system.

The Hindmarsh-Rose (HR) neuron model has been improved to investigate the complex electrophysiological and various physical phenomena at the level of single cell, for example, time-varying action potential can be induced by the exchange of ion currents and the fluctuation of ions concentration in the cell. When the magnetic flux is considered as a new variable associated to magnetic field, the improved HR neuron model can describe the effects of electromagnetic induction and radiation on membrane potential, where a memristor is used to bridge the membrane potential and the magnetic flux. In this paper, considering the magnetic flux driven, respectively, by the periodic high and low frequency electromagnetic radiation and the Gaussian white noise, the improved HR neuron model is employed to study the modes transition in electrical activities of neuron. The thought-provoking phenomena are detected and discussed by using bifurcation analysis on sampled time series of membrane potential. It is found that the electrical modes of HR neuron model under various parameters have different responses to the periodic high-low frequency electromagnetic radiation and the Gaussian white noise. [ABSTRACT FROM AUTHOR]

The electric activities of neurons are dependent on the complex electrophysiological condition in neuronal system, and it indicates that the complex distribution of electromagnetic field could be detected in the neuronal system. According to the Maxwell electromagnetic induction theorem, the dynamical behavior in electric activity in each neuron can be changed due to the effect of internal bioelectricity of nervous system (e.g., fluctuation of ion concentration inside and outside of cell). As a result, internal fluctuation of electromagnetic field is established and the effect of magnetic flux across the membrane should be considered during the emergence of collective electrical activities and signals propagation among a large set of neurons. In this paper, the variable for magnetic flow is proposed to improve the previous Hindmarsh-Rose neuron model; thus, a four-variable neuron model is designed to describe the effect of electromagnetic induction on neuronal activities. Within the new neuron model, the effect of magnetic flow on membrane potential is described by imposing additive memristive current on the membrane variable, and the memristive current is dependent on the variation of magnetic flow. The dynamics of this modified model is discussed, and multiple modes of electric activities can be observed by changing the initial state, which indicates memory effect of neuronal system. Furthermore, a practical circuit is designed for this improved neuron model, and this model could be suitable for further investigation of electromagnetic radiation on biological neuronal system. [ABSTRACT FROM AUTHOR]

Abstract: We consider the problem of sound propagation in a wind. We note that the rays, as in the absence of a wind, are given by Fermat’s principle and show how to map them to the trajectories of a charged particle moving in a magnetic field on a curved space. For the specific case of sound propagating in a stratified atmosphere with a small wind speed, we show that the corresponding particle moves in a constant magnetic field on the hyperbolic plane. In this way, we give a simple ‘straightedge and compass’ method to estimate the intensity of sound upwind and downwind. We construct Mach envelopes for moving sources. Finally, we relate the problem to that of finding null geodesics in a squashed anti-de Sitter spacetime and discuss the symmetry of the problem from this point of view. [Copyright &y& Elsevier]

In this paper we study semi-conjugacy of Kähler magnetic flows for a product of complex space forms. [Copyright &y& Elsevier]

We introduce the Hofer–Zehnder Γ-semicapacity $c_{\rm HZ}^\Gamma (M, \omega)$ of a symplectic manifold (M,ω) (or Γ-sensitive Hofer–Zehnder capacity) with respect to a subset Γ⊂π1(M) $(c_{\rm HZ}(M, \omega)\le c^\Gamma_{\rm HZ}(M, \omega))$ and prove that given a geometrically bounded symplectic manifold (M,ω) and an open subset N⊂M admitting a Hamiltonian free circle action with order greater than two then N has bounded Hofer–Zehnder Γ-semicapacity, where Γ⊂π1(N) is the subgroup generated by the orbits of the action. We give several applications of this result. Using Biran's decomposition theorem, we prove the following: let (M2n,Ω) be a closed Kähler manifold (n>2) with [Ω]∈H2(M,ℤ) and Σ a complex hypersurface representing the Poincaré dual of k[Ω], for some k∈ℕ. Suppose either that Ω vanishes on π2(M) or that k>2. Then there exists a decomposition of M into an open dense subset E such that E\Σ has finite Hofer–Zehnder Γ-semicapacity and an isotropic CW-complex, where Γ⊂π1(E\Σ) is the subgroup generated by the obvious circle action on the normal bundle of Σ. Moreover, we prove that if (M,Σ) is subcritical then M\Σ has finite Hofer–Zehnder Γ-semicapacity. We also show that given a hyperbolic surface M and TM endowed with the twisted symplectic form ω0+π*Ω, where Ω is the Kähler form on M, then the Hofer–Zehnder Γ-semicapacity of the domain Uk bounded by the hypersurface of kinetic energy k minus the zero section M0 is finite if k<1/2, where Γ⊂π1(Uk) is the subgroup generated by the fibers of SM. Finally, we consider the problem of the existence of periodic orbits on prescribed energy levels for magnetic flows. We prove that given any weakly exact magnetic field Ω on any compact Riemannian manifold M there exists a sequence of contractible periodic orbits of arbitrarily small energy, extending a previous result of Polterovich. [ABSTRACT FROM AUTHOR]

Displacements of miscible magnetic fluids in a capillary tube under a moving ring-shaped magnet are studied numerically. The magnet is adjusted dynamically to maintain a constant distance from the mixing tip on the centerline. Control parameters, such as magnetic pulling force, effective viscosity variation due to magnetization and the position of the magnet, are analyzed systematically. Mass transfer performance is evaluated by several quantitative measurements. In general, a stronger magnetic effect leads to a better performance, except for the global amount of transferred mass that varies insignificantly. An asymptotic tip velocity is reached if the magnetic strength is beyond a certain value. A less effective viscosity leads to a higher finger velocity but a shorter transferable distance. Unlike the monotonic influences of magnetic pulling force and effective viscosity variation, there exists a potential optimal magnet position for the best effective mass transfer. [Copyright &y& Elsevier]