Radial motion of a solid spherical body in a magnetic field

The object of the present paper is to investigate the radial motion of a solid spherical body, assumed to be homogeneous, isotropic and elastic, in presence of a magnetic field in the azimuthal direction. The body is assumed to be in a state of initial stress which is hydrostatic in nature. This theory of radial motion of a solid spherical body in a magnetic field has been utilised to find the small radial motion of a solid Earth assumed to be homogeneous isotropic elastic sphere in presence of a magnetic field in the azimuthal direction. Considering the effect of gravity and the initial stress produced by slow process of creep due to extra masses over the surface of the Earth, the fundamental equations of motion are derived which are non-linear in character and are solved. The times of a desired radial displacement are calculated in presence of a magnetic field only and in presence of the same magnetic field, initial stress and gravitational field, which are compared and exhibited numerically.     

Reduction of turbulent boundary layer induced interior noise through active impedance control

The use of a single actuator tuned to an optimum impedance to control the sound power radiated from a turbulent boundary layer (TBL) excited aircraft panel into the aircraft interior is examined. An approach to calculating the optimum impedance is defined and the limitations on the reduction in radiated power by a single actuator tuned to that impedance are examined. It is shown that there are too many degrees of freedom in the TBL and in the radiation modes of the panel to allow a single actuator to control the radiated power. However, if the panel modes are lightly damped and well separated in frequency, significant reductions are possible. The implementation of a controller that presents a desired impedance to a structure is demonstrated in a laboratory experiment, in which the structure is a mass. The performance of such a controller on an aircraft panel is shown to be effective, if the actuator impedance is similar to but not the same as the desired impedance, provided the panel resonances are well separated in frequency and lightly damped.     

The shape gradient of the least-squares objective functional in optimal shape design problems of radiative heat transfer

Optimal shape design problems of steady-state radiative heat transfer are considered. The optimal shape design problem (in the three-dimensional space) is formulated as an inverse one, i.e., in the form of an operator equation of the first kind with respect to a surface to be optimized. The operator equation is reduced to a minimization problem via a least-squares objective functional. The minimization problem has to be solved numerically. Gradient minimization methods need the gradient of a functional to be minimized. In this paper the shape gradient of the least-squares objective functional is derived with the help of the shape sensitivity analysis and adjoint problem method. In practice a surface to be optimized may be (or, most likely, is to be) given in a parametric form by a finite number of parameters. In this case the objective functional is, in fact, a function in a finite-dimensional space and the shape gradient becomes an ordinary gradient. The gradient of the objective functional, in the case that the surface to be optimized is given in a finite-parametric form, is derived from the shape gradient. A particular case, that a surface to be optimized is a “two-dimensional” polyhedral one, is considered. The technique, developed in the paper, is applied to a synthetic problem of designing a “two-dimensional” radiant enclosure.     

Gravitational coupling and dynamical reduction of the cosmological constant

We introduce a dynamical model to reduce a large cosmological constant to a sufficiently small value. The basic ingredient in this model is a distinction which has been made between the two unit systems used in cosmology and particle physics. We have used a conformal invariant gravitational model to define a particular conformal frame in terms of large scale properties of the universe. It is then argued that the contributions of mass scales in particle physics to the vacuum energy density should be considered in a different conformal frame. In this manner, a decaying mechanism is presented in which the conformal factor appears as a dynamical field and plays a key role to relax a large effective cosmological constant. Moreover, we argue that this model also provides a possible explanation for the coincidence problem.     

Manifestation of the stochastic resonance in submerged jets under an acoustic action

A phenomenon that is similar to the well-known stochastic resonance in nonlinear oscillators but is caused by the turbulence in a circular submerged jet under a harmonic acoustic action, rather than by noise, is considered. It is shown that, at a fixed distance from the nozzle, a variation of the initial turbulence level leads to a non-monotonic variation of the wave amplitude at the frequency of the acoustic action, namely, to the appearance of an amplitude maximum at a certain level of the initial turbulence. The qualitative explanation of the phenomenon consists in that the initial turbulence acts on the system in a way similar to that of external noise: it changes the effective parameters of the system and, in particular, shifts the spectral maxima, which is equivalent to a change in a certain “eigenfrequency.” Such a change in the effective parameters of the jet leads to a phenomenon similar to the stochastic resonance.     

A hypothetical model of confinement in a dia-electric medium

The assumption of a perfect color dia-electric vacuum in quantum chromodynamics (QCD) led to a reasonable explanation of quark confinement. Along the same lines, a hypothetical dia-electric medium in electromagnetism is shown to lead to charge confinement; although such a medium does not exist, the analysis of this hypothetical problem illuminates in a very simple and straightforward way how this dia property (negative susceptibility) of a medium leads to confinement. It is shown that adding a dipole (particle-antiparticle) charge distribution to such a dia-electric medium would lead the creation of a cavity surrounding the charges; by a simple analysis, using the image problem along with a series expansion in Legendre polynomials, it is shown that the polarization charge distribution on the cavity's surface would lead to an increase in the dipole energy by a finite amount; on the other hand, the increase in the electric energy of a single charge inserted in such a medium would be infinite. It is thus concluded that in such a dia-electric medium, separating the charges of a dipole would require an infinite amount of energy, and thus illustrating in a simple way the confinement concept.     

The effects of a laser field on phase transitions in liquid crystals

We investigate theoretically some phase transitions in liquid crystals in the presence of a laser beam. We found, in non-absorbing nematics, a laser-induced one-way transition from a paranematic to a nematic phase. In absorbing nematics we found, in addition to this transition, a one-way transition from a nematic to a paranematic phase with increasing laser intensity. Further, we found a reentrant nematic or a reentrant paranematic via paranematic or nematic phase respectively. In the case of smectic A, laser absorption results in a coupling between the positional and orientational orders. As a result, the smectic A to nematic transition can change from second order to first order and the smectic C to smectic A transition can become first-order in the field of a laser.     

On the critical behaviour of a surface interacting linear polymer chain

A method based on a real space renormalization group transformation is developed to describe the critical behaviour of a surface interacting linear flexible polymer chain, represented by a self-avoiding walk. It is shown that a lattice model based on a central rule in which the starting point of the walk and the surface are taken to be in the middle of one cell, provides a suitable framework to study both the penetrable and impenetrable surfaces. In contrast to this, a method based on a corner rule in which the starting point of the walk and the surface are fixed to be one corner of a cell cannot describe the behaviour of a chain interacting with an impenetrable surface. The value of crossover exponent found by us for a square lattice are in agreement with those expected to be exact for both the cases.     

Non-sequential effects in the decay of resonant states

Fano and Prats' treatment of continuum-continuum interaction is used to study the time-dependent behaviour of a system initially in a discrete state coupled to a continuum which is itself coupled to another continuum. This level scheme represents a limiting case in a model which is currently used in the theory of molecular processes, the opposite limit being the sequential scheme which leads to chain-like rate equations. A very different behaviour is obtained in the two limits. In contrast with the results of the sequential model the continuum-continuum coupling produces a change (a decrease) in the decay rate of the discrete state. The two continua are populated in parallel. The calculations provide an explicit example of the influence of higher order terms on a rate constant, a problem which has received attention recently in relation to the evaluation of non-radiative transition rates using approximate molecular wave functions.     

Quasi-pyroelectricity in the TGS crystal

It has been shown that a side electrode perpendicular to the measurement ones can significantly enhance the transverse electric current in TGS. Such a current, measured in a zero external electric field, resembles the classic longitudinal one. However, the amplitude of the transverse current oscillation, observed while cooling and heating the sample, rises much more slowly with the time of the transverse electric field preliminary application. Such exposure to the transverse field is required prior to the measurements for the transverse current to be observed, in a similar way to a longitudinal field that is applied in order to achieve a single domain state before longitudinal pyroelectric current measurements. A huge difference in the time of reaction to the electric fields preliminarily applied in order to achieve the maximum amplitude of the current oscillations in both cases is the evidence that the transverse current cannot be considered to be originated just for geometrical reasons.     

非完整映射理论与刚体定点转动的几何描述

利用非完整映射方法,从一个已知Riemann空间构造一个嵌入其中的Riemann-Cartan空间.作为特例,研究从Euclidean空间构造Weitzenbock空间的方法.基于dAlembert-Lagrange原理和非完整映射,将一个Riemann空间的测地线对应于另一个Riemann-Cartan空间的自平行线.把这种非完整映射理论应用到刚体定点转动问题上,得到了刚体运动的欧拉方程是欧拉角描述的Riemann位形空间的测地线方程,而在刚体角速度对应的准坐标空间上是常挠率Riemann-Cartan空间的自平行线方程的结论. 关键词： 欧拉角 非完整映射 Riemann-Cartan空间 自平行线     

Vowel errors in noise and in reverberation by hearing-impaired listeners

The effects of noise and reverberation on the identification of monophthongs and diphthongs were evaluated for ten subjects with moderate sensorineural hearing losses. Stimuli were 15 English vowels spoken in a /b-t/ context, in a carrier sentence. The original tape was recorded without reverberation, in a quiet condition. This test tape was degraded either by recording in a room with reverberation time of 1.2 s, or by adding a babble of 12 voices at a speech-to-noise ratio of 0 dB. Both types of degradation caused statistically significant reductions of mean identification scores as compared to the quiet condition. Although the mean identification scores for the noise and reverberant conditions were not significantly different, the patterns of errors for these two conditions were different. Errors for monophthongs in reverberation but not in noise seemed to be related to an overestimation of vowel duration, and there was a tendency to weight the formant frequencies differently in the reverberation and quiet conditions. Errors for monophthongs in noise seemed to be related to spectral proximity of formant frequencies for confused pairs. For the diphthongs in both noise and reverberation, there was a tendency to judge a diphthong as the beginning monophthong. This may have been due to temporal smearing in the reverberation condition, and to a higher masked threshold for changing compared to stationary formant frequencies in the noise condition.     

Fourth order correction to a Gaussian beam focused with a parabolic index lens

We formulate the fourth order correction to a paraxial Gaussian beam propagated along the axis of symmetry of a parabolic index lens. First we examine the evolution of a complex-source-point spherical wave (equivalent paraxially to a Gaussian beam) through the lens in a two-dimensional xz plane. Taking into account the terms of up to fourth order in aperture variables, we find a ray-optical solution to the exit beam that is represented in terms of aberration function. We also analyze the effect of the lens aberration exerted on the degradation in the quality of a Gaussian beam. The fourth order-corrected wave function derived here may be used to evaluate the quality of a Gaussian beam focused with a parabolic index lens. Further it may be applied to the case of an orthogonal system in which the index variations are different in the xz and yz planes.     

Development of a self-oscillating ultrasonic micro-motor and its application to a watch

We have developed an ultrasonic micro-motor for use as a micro-actuator in place of an electromagnetic motor. This ultrasonic micro-motor, which can be driven by a single signal and in which the change of the direction of the rotor movement can be made easily by selecting the electrode to apply the driving signal, can easily construct a self-oscillating circuit and simplify the driving circuit. We have also simplified the motor structure, which is easy to miniaturize and mass-produce. We applied a version of this motor with a diameter of 8 mm to a vibration alarm, and one with a diameter of 4.5 mm to a driving source of a calendar mechanism in a watch. This ultrasonic micro-motor is expected to be of use as a new driving source in a broad range of fields.     

Identification of magnet and superconductor contributions to the ac loss in a magnet-superconductor levitation system

By measuring the quality factor of the mechanical oscillator with an attached magnet we investigated the amplitude dependence of the energy loss in a permanent magnet-YBCO superconductor system. When a non-conducting ferrite magnet is used the energy loss is proportional to the amplitude to the 2.79 power. This value is close to the value of 3 expected for the hysteretic motion of flux lines from the Bean model. When a conducting magnet is used the exponent decreased to the value of 2.5. This reflects the contribution of eddy current dissipation in a conducting magnet to the overall loss. We identified a novel mechanism of ac loss in the magnet-superconductor system. According to this mechanism the eddy current in a magnet is induced by the ac field generated by the ac supercurrent in response to the motion of a magnet. This mechanism would take place in a rotary bearing if circumferential inhomogeneity of the rotor magnetization occurred.     

Synthesis of magnetic systems producing field with maximal scalar characteristics

A method of synthesis of the magnetic systems (MSs) consisting of uniformly magnetized blocks is proposed. This method allows to synthesize MSs providing maximum value of any magnetic field scalar characteristic. In particular, it is possible to synthesize the MSs providing the maximum of a field projection on a given vector, a gradient of a field modulus and a gradient of a field energy on a given directing vector, a field magnitude, a magnetic flux through a given surface, a scalar product of a field or a force by a directing function given in some area of space, etc. The synthesized MSs provide maximal efficiency of permanent magnets utilization. The usage of the proposed method of MSs synthesis allows to change a procedure of projecting in principal, namely, to execute it according to the following scheme: (a) to choose the sizes, a form and a number of blocks of a system proceeding from technological (economical) reasons; (b) using the proposed synthesis method, to find an orientation of site magnetization providing maximum possible effect of magnet utilization in a system obtained in (a). Such approach considerably reduces a time of MSs projecting and guarantees maximal possible efficiency of magnets utilization. Besides it provides absolute assurance in “ideality” of a MS design and allows to obtain an exact estimate of the limit parameters of a field in a working area of a projected MS.The method is applicable to a system containing the components from soft magnetic material with linear magnetic properties.     

Point-like structure and off-shell dual strings

We argue that in a consistent off-shell dual formalism the amplitude for the emission of a scalar off-shell state by a string consists of two components. One of these contains the particle poles in the off-shell leg and the other is intimately related to the insertion of a point-like energy density on the string. As a result, the amplitude for a string to emit a zero momentum scalar state into the vacuum (which may be relevant for spontaneous symmetry breaking) is described by the amplitude for a finite fraction of the energy in the string to collapse to a spatial point at some time (this fraction and its space-time position being integrated over). The off-shell amplitudes have an elegant formulation in terms of a set of “confined modes” which can be assigned quark flavour quantum numbers to reproduce the Chan-Paton scheme.We suggest the dual model be modified by allowing for the coupling of scalar closed strings to the vacuum and the resulting effect on the space-time structure of dual Green functions is described.We find that even the emission of a single zero-momentum closed string modifies the elastic amplitude in a significant manner, leading to a power-behaved fixed-angle cross section in contrast to the usual exponential decrease of the dual model. This arises from point-like scattering between energy densities accumulating in the colliding strings. The relationship between the fixed angle and Regge limits is discussed. The fixed angle behaviour is found to be the asymptotic limit in momentum transfer of a fixed pole that arises in the Regge limit.     

Dynamic reflection and refraction of neutrons at the boundaries of matter characterized by a variable magnetic induction

Optical phenomena that arise in the interaction of a neutron wave with matter characterized by a variable interaction potential are considered. The time dependence of the potential is assumed to be due to a change in the magnetization vector in matter with time. Since the interaction in question is time-dependent, the neutron energy is not conserved. If a neutron interacts with a sample that has a plane boundary, only the neutron-velocity component orthogonal to the matter boundary changes. Thus, reflected waves are characterized by a reflection angle that is different from the angle of incidence. Waves transmitted through a plane sample can also change direction. The changes in the neutron energy and in the neutron-velocity direction are closely related to the reversal of the neutron-spin projection. The question of whether a slab featuring a rotating magnetization vector can be used as a spin flipper or as a coherent wave splitter is considered.