Dynamic stability of a slender beam under horizontal–vertical excitations

The dynamic stability of a vertically standing cantilevered beam simultaneously excited in both horizontal and vertical directions at its base is studied theoretically. The beam is assumed to be an inextensible Euler–Bernoulli beam. The governing equation of motion is derived using Hamilton's principle and has a nonlinear elastic term and a nonlinear inertia term. A forced horizontal external term is added to the parametrically excited system. Applying Galerkin's method for the first bending mode, the forced Mathieu–Duffing equation is derived. The frequency response is obtained by the harmonic balance method, and its stability is investigated using the phase plane method. Excitation frequencies in the horizontal and vertical directions are taken as 1:2, from which we can investigate the influence of the forced response under horizontal excitation on the parametric instability region under vertical excitation. Three criteria for the instability boundary are proposed. The influences of nonlinearities and damping of the beam on the frequency response and parametric instability region are also investigated. The present analytical results for instability boundaries are compared with those of experiments carried out by one of the authors.     

Dynamic contact analysis of a tensioned beam with a moving mass–spring system

The dynamic contact problem of a tensioned beam with clamped-pinned ends is analyzed when the beam contacts a moving mass–spring system. The contact and contact loss conditions are expressed in terms of constraint equations after considering the dynamic contact between the beam and the moving mass. Using these constraints and equations of motion for the beam and moving mass, dynamic contact equations are derived and then discretized using the finite element method, which is based on the Lagrange multiplier method. The time responses for the contact forces are computed from these discretized equations. The contact force variations and contact loss are investigated for the variations of the moving mass velocity, the beam tension, the moving mass, and the stiffness of the moving mass–spring system. In addition, the possibility of contact loss and safe contact conditions between the moving mass and the tensioned beam are also studied.     

Switching of the polarization of ferroelectric–ferroelastic gadolinium molybdate in a magnetic field

A change in the character of the electric switching of polydomain ferroelectric–ferroelastic gadolinium molybdate in an external magnetic field has been detected. This change has been attributed to a magnetically stimulated increase in the pinning of domain walls. Under certain conditions, the loop of switchable polarization is degenerated into an ellipse characteristic of a linear insulator with leakage current.     

Estimating the probability of P–H bonds breaking in a modified biocomposite after exposure to a pulsed magnetic field

For the successful compaction wood, we miust convert its amorphous component (lignin) from a glassy to a highly elastic state by treating it with, e.g., ammonia. This plasticization of lignin results in the formation of compounds containing bi-coordination phosphorus, increasing its hydrophobicity due to the formation of P–H bonds. In this work, the problem of reducing the number of such bonds after treatment with a pulsed magnetic field is discussed, using the results from studying the IR spectra of modified wood samples.     

Effects of Rashba spin–orbit coupling and a magnetic field on a polygonal quantum ring

Using standard quantum network method, we analytically investigate the effect of Rashba spin–orbit coupling (RSOC) and a magnetic field on the spin transport properties of a polygonal quantum ring. Using Landauer–Büttiker formula, we have found that the polarization direction and phase of transmitted electrons can be controlled by both the magnetic field and RSOC. A device to generate a spin-polarized conductance in a polygon with an arbitrary number of sides is discussed. This device would permit precise control of spin and selectively provide spin filtering for either spin up or spin down simply by interchanging the source and drain.     

Extension of Nelson?s stochastic quantization to finite temperature using thermo field dynamics

We present an extension of Nelson?s stochastic quantum mechanics to finite temperature. Utilizing the formulation of Thermo Field Dynamics (TFD), we can show that Ito?s stochastic equations for tilde and non-tilde particle positions reproduce the TFD-type Schrödinger equation which is equivalent to the Liouville-von Neumann equation. In our formalism, the drift terms in the Ito?s stochastic equation have the temperature dependence and the thermal fluctuation is induced through the correlation of the non-tilde and tilde particles. We show that our formalism satisfies the position-momentum uncertainty relation at finite temperature.     

Effects of magnetic field on shape evolution of Fe–Co particles in a Cu matrix

The effects of magnetic field on the shape evolution of ferromagnetic fcc Fe–Co particles in Cu–0.83 at.% Fe–1.37 at.% Co alloy single crystals were examined using magnetic anisotropy measurements. The Cu–Fe–Co single crystals were aged at 993 K for 2 h to 24 h under a magnetic field of 10 T parallel to either the [001] or [011] direction. The magnetic anisotropy was examined by measuring magnetic torque around the (100) plane. It was found that the fcc Fe–Co particles are elongated in the direction parallel to the magnetic field. Furthermore, the elongation along [001] is more remarkable than that along [011]. The results are explained quantitatively by considering the minimization of the sum of the interface energy, elastic strain energy and magnetostatic energy of spheroidal particles.     

Geometric phase of spin-1 in a rotating magnetic field

The quantum phase and the related fields have attracted considerable attention. The geometric phase of spin-1/2 particle in the magnetic field has been discussed comprehensively, but few of spin-1. In this paper, the exact solution of spin-1 was obtained by using rotational frame method. The problems of the Rabi oscillation, dynamical phase, and geometric phase were solved.     

Cholesteric–nematic transitions induced by a shear flow and a magnetic field

The untwisting of the helical structure of a cholesteric liquid crystal under the action of a magnetic field and a shear flow has been studied theoretically. Both factors can induce the cholesteric–nematic transition independently; however, the difference in the orienting actions of the magnetic field and the shear flow leads to competition between magnetic and hydrodynamic mechanisms of influence on the cholesteric liquid crystal. We have analyzed different orientations of the magnetic field relative to the direction of the flow in the shear plane. In a number of limiting cases, the analytic dependences are obtained for the pitch of the cholesteric helix deformed by the shear flow. The phase diagrams of the cholesteric–nematic transitions and the pitch of the cholesteric helix are calculated for different values of the magnetic field strength and the angle of orientation, the flow velocity gradient, and the reactive parameter. It is shown that the magnetic field stabilizes the orientation of the director in the shear flow and expands the boundaries of orientability of cholesterics. It has been established that the shear flow shifts the critical magnetic field strength of the transition. It is shown that a sequence of reentrant orientational cholesteric–nematic–cholesteric transitions can be induced by rotating the magnetic field in certain intervals of its strength and shear flow velocity gradients.     

Vectorial structure of the far field of an elegant Hermite–Gaussian beam

Based on the vector angular spectrum method and the method of stationary phase, an analytical expression for the vectorial structure of the far field of an elegant Hermite–Gaussian beam is derived. The analytical formulae of the energy flux distributions of the TE term, the TM term, and the whole beam are presented in the far field. Analytical expressions for the ratios of the powers of the TE and TM terms to those of the elegant Hermite–Gaussian beam are obtained without any approximation. The physical pictures of the far field of an elegant Hermite–Gaussian beam are demonstrated and compared with those of the far field of the corresponding standard Hermite–Gaussian beam. This research reveals the internal vectorial structure of the far field of an elegant Hermite–Gaussian beam from an alternative viewpoint.     

Influence of the in-plane magnetic field on the Andreev conductance of a superconductor–insulator–normal metal structure

Pronounced conductance due to electrons experiencing Andreev reflection from a superconducting condensate has been observed in superconductor (aluminum)–insulator (aluminum oxide)–normal metal (copper) tunnel junctions at low voltages, along with single-electron tunneling. It has been discovered experimentally that the collective current is suppressed in the magnetic field parallel to the tunnel junction plane and the Andreev conductance decreases nearly twofold in a field of ～20–30 mT.     

Role of incoherent pumping field on absorption–dispersion properties of probe pulse in a graphene nanostructure under external magnetic field

The optical properties of weak probe light based on quantum coherence and interference in Landau-quantized graphene nanostructure driven by two coherent fields and incoherent pumping field is investigated. The linear dynamical properties of the graphene by means of density matrix method and perturbation theory are discussed. It is found that under certain condition and for appropriate choosing the parameters of the medium, the absorption, dispersion, group index of the weak probe light can be controlled. Moreover, it is shown that by means of incoherent pumping field the superluminal light propagation in the system is accompanied by amplification to make sure that the probe field is amplified as it passes through the system. Moreover, it is observed that the probe amplification can be obtained in the presence or absence of population inversion by properly choosing of system’s parameters. We hope that these results may have useful in the future quantum communicational system and networks.     

Equivalent circuit model including magnetic and thermo sources for the thermo–magneto–electric coupling effect in magnetoelectric laminates

The nonlinear thermo–magneto–mechanical magnetostrictive constitutive and the linear thermo–mechanical-electric piezoelectric constitutive are adopted in this paper. The bias magnetic field and ambient temperature are equivalent to a magnetic source and a thermo source, respectively. An equivalent circuit, which contains a magnetic source and a thermo source at the input, for the thermo–magneto–electric coupling effect in magnetoelectric(ME) laminates, is established. The theoretical models of the output voltage and static ME coefficient for ME laminates can be derived from this equivalent circuit model. The predicted static ME coefficient versus temperature curves are in excellent agreement with the experimental data available both qualitatively and quantitatively. It confirms the validity of the proposed model. Then the models are adopted to predict variations in the output voltages and ME coefficients in the laminates under different ambient temperatures, bias magnetic fields, and the volume ratios of magnetostrictive phases. This shows that the output voltage increases with both increasing temperature and increasing volume ratio of magnetostrictive phases; the ME coefficient decreases with increasing temperature; the ME coefficient shows an initial sharp increase and then decreases slowly with the increase in the bias magnetic field, and there is an optimum volume ratio of magnetostrictive phases that maximize the ME coefficient.This paper can not only provide a new idea for the study of the thermo–magneto–electric coupling characteristics of ME laminates, but also provide a theoretical basis for the design and application of ME laminates, operating under different sensors.     

Propagation of a Hermite–Laguerre–Gaussian beam in a turbulent atmosphere

The propagation and spreading of a Hermite–Laguerre–Gaussian (HLG) beam in a turbulent atmosphere has been investigated. Based on the extended Huygens–Fresnel integral and some mathematical techniques, analytical expressions for the average intensity, the effective beam size, and the kurtosis parameter of an HLG beam in a turbulent atmosphere are derived, respectively. The average intensity distribution and the spreading properties of HLG beams in a turbulent atmosphere are numerically demonstrated. Upon propagation in a turbulent atmosphere, the central lobes in the beam spot of the HLG beam will evolve into the dominant lobes, and the peripheral lobes around the central lobes will evolve into the subdominant lobes. The influences of the additional angle parameter and the transversal mode numbers on the propagation of HLG beams in a turbulent atmosphere are also discussed. As the coherence length of the turbulence is determined by the propagation distance, the effect of the additional angle parameter on the effective beam size is related to the propagation distance. The kurtosis parameter generally increases with increasing the additional angle parameter. The influence of the transversal mode numbers on the kurtosis parameter is related to the additional angle parameter and the propagation distance. According to the practical need of free-space optical communications and remote sensing, the HLG beam in a turbulent atmosphere can be controlled by choice of the additional angle parameter and the transversal mode numbers.     

Dynamic Mach–Zehnder interferometer based on a Michelson configuration and a cube beam splitter system

We developed simultaneous phase-shifting system based on a Mach–Zehnder interferometer and a replicating system integrated by a Michelson configuration and a cube beam splitter. The system is capable to obtain four simultaneous interferograms in a single capture, and the phase shifts are controlled by placing a linear polarizer in each replica obtained. The system retrieves four interferograms with a relative phase shift of π/2 and the optical phase map is calculated using the four-step algorithm. In addition, the configuration presents potential capabilities for generating spiral interference patterns. To show the advantage of the technique, experimental results are presented for static and dynamic samples.