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.     

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.     

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.     

Trapped electron coupled to superconducting devices

We propose to couple a trapped single electron to superconducting structures located at a variable distance from the electron. The electron is captured in a cryogenic Penning trap using electric fields and a static magnetic field in the tesla range. Measurements on the electron will allow investigating the properties of the superconductor such as vortex structure, damping and decoherence. We propose to couple a superconducting microwave resonator to the electron in order to realize a circuit QED-like experiment, as well as to couple superconducting Josephson junctions or superconducting quantum interferometers (SQUIDs) to the electron. The electron may also be coupled to a vortex which is situated in a double well potential, realized by nearby pinning centers in the superconductor, acting as a quantum mechanical two level system that can be controlled by a transport current tilting the double well potential. The electron may also be coupled to a single vortex, thus hybridizing an elementary excitation of a superconductor and an elementary particle.     

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.     

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.     

Fast Rydberg gates without dipole blockade via quantum control

We propose a scheme for controlling interactions between Rydberg-excited neutral atoms in order to perform a fast high-fidelity quantum gate. Unlike dipole-blockade mechanisms already found in the literature, we drive resonantly the atoms with a state-dependent excitation to Rydberg levels, and we exploit the resulting dipole-dipole interaction to induce a controlled atomic motion in the trap, in a similar way as discussed in recent ion-trap quantum computing proposals. This leads atoms to gain the required gate phase, which turns out to be a combination of a dynamic and a geometrical contribution. The fidelity of this scheme is studied including small anharmonicity and temperature effects, with promising results for reasonably achievable experimental parameters.     

Particle velocity field measurement using an ultra-light membrane

The aim of this paper, is to present an innovative experimental approach to assess images of the acoustic particle velocity field using a laser vibrometer scanning an ultra-light membrane. Firstly, a theoretical part is devoted to the infinite membrane governing equations, and to its response to an acoustic incident plane wave. An impedance of the membrane is defined, and a mass correction factor is obtained for a plane wave in normal incidence, allowing to assess the particle velocity of the acoustic field without membrane from the measured velocity of the membrane. The practical realization of a finite membrane is reported in a second section, showing difficulties linked to membrane modes generated by an uncontrolled residual tension, also showing how those difficulties are overcome by weighing down the membrane and by applying the mass correction. Third and fourth parts of the article are dedicated to two-dimension applications, illustrating the implementation of the membrane approach in the case of a plate excited by a shaker, and in the case of a loudspeaker driven with a white noise. Results are encouraging, showing that a “heavy” membrane should be used in low frequency to avoid difficulties due to membrane modes, and a light one in high frequency to minimize the mass effect (that can be corrected only for plane wave in normal incidence) and to avoid potential interactions between the membrane and the air gap between the membrane and the source, when the membrane is placed in the near field.     

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.     

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.     

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.     

Magneto-optical polar Kerr effect in a film-substrate system

The problem of electromagnetic reflection at an arbitrary angle of incidence in a system consisting of an isotropic ambient, a magnetic film and a thick magnetic substrate is studied. The magnetizations in both the film and substrate are assumed normal to the planar interfaces. The results are expressed in terms of the reflection matrix which is directly connected to the experimentally observed quantities: ellipsometric ratio and magneto-optical rotation and ellipticity. The general condition for guided wave propagation in the system is obtained. The theory is applied to the special cases of (a) normal incidence, (b) oblique incidence on a uniaxial film on a uniaxial substrate, both optical axes being normal to the interfaces, and (c) oblique incidence on a system consisting of an isotropic ambient, a magnetic film and a thick magnetic substrate assuming the diagonal elements of the permittivity tensor in a particular magnetic medium (film or substrate) equal to each other and the corresponding off-diagonal elements much smaller with respect to them. The possible practical applications of the present analysis are in the optimum design of film-substrate structures in magneto-optic devices and in the optical studies of the surface effects in magnetic materials.     

Loschmidt echo near a dynamical phase transition in a Bose-Einstein condensate

We show that the quantum Loschmidt echo can be employed to characterize the dynamical phase transition, from a tunnelling phase to a self-trapping phase, of a Bose-Einstein condensate in a double-well potential. The echo is found to have a relatively fast decay in the transition region, with a Gaussian decay in the self-trapping phase and a stretched exponential decay in the tunnelling phase.     

Dipolar Waves as NMR maps of helices in proteins

Dipolar Waves describe the periodic variation in the magnitudes of dipolar couplings in the backbone of a protein as a function of residue number. They provide a direct link between experimental measurements of dipolar couplings in aligned samples and the periodicity inherent in regular secondary structure elements. It is possible to identify the residues in a helix and the type of helix, deviations from ideality, and to orient the helices relative to an external axis in completely aligned samples and relative to each other in a common frame in weakly aligned samples with Dipolar Waves. They provide a tool for accurately describing helices and a step towards high throughput structure determination of proteins.     

Escape Through a Small Opening: Receptor Trafficking in a Synaptic Membrane

We model the motion of a receptor on the membrane surface of a synapse as free Brownian motion in a planar domain with intermittent trappings in and escapes out of corrals with narrow openings. We compute the mean confinement time of the Brownian particle in the asymptotic limit of a narrow opening and calculate the probability to exit through a given small opening, when the boundary contains more than one. Using this approach, it is possible to describe the Brownian motion of a random particle in an environment containing domains with small openings by a coarse grained diffusion process. We use the results to estimate the confinement time as a function of the parameters and also the time it takes for a diffusing receptor to be anchored at its final destination on the postsynaptic membrane, after it is inserted in the membrane. This approach provides a framework for the theoretical study of receptor trafficking on membranes. This process underlies synaptic plasticity, which relates to learning and memory. In particular, it is believed that the memory state in the brain is stored primarily in the pattern of synaptic weight values, which are controlled by neuronal activity. At a molecular level, the synaptic weight is determined by the number and properties of protein channels (receptors) on the synapse. The synaptic receptors are trafficked in and out of synapses by a diffusion process. Following their synthesis in the endoplasmic reticulum, receptors are trafficked to their postsynaptic sites on dendrites and axons. In this model the receptors are first inserted into the extrasynaptic plasma membrane and then random walk in and out of corrals through narrow openings on their way to their final destination.     

Unified Solution of the Expected Maximum of a Discrete Time Random Walk and the Discrete Flux to a Spherical Trap

Two random-walk related problems which have been studied independently in the past, the expected maximum of a random walker in one dimension and the flux to a spherical trap of particles undergoing discrete jumps in three dimensions, are shown to be closely related to each other and are studied using a unified approach as a solution to a Wiener-Hopf problem. For the flux problem, this work shows that a constant c = 0.29795219 which appeared in the context of the boundary extrapolation length, and was previously found only numerically, can be derived analytically. The same constant enters in higher-order corrections to the expected-maximum asymptotics. As a byproduct, we also prove a new universal result in the context of the flux problem which is an analogue of the Sparre Andersen theorem proved in the context of the random walker's maximum.     

One-dimensional single and multipulse simulations of the ON/OFFvoltages and the bistable margin for He, Xe, and He/Xe filled plasmadisplay pixels

A one-dimensional plasma model developed for AC plasma display pixels is used to perform multipulse and single-pulse simulations to model the maximum sustain voltages, the minimum sustain voltages, and the voltage margins for 100% helium, 100% xenon, and for 2% xenon in helium and a 400 torr pressure (p) and a gap (L) of 100 μm. The multipulse simulations describe the growth in wall voltage at the so-called ON voltage and the decay in wall voltage at the so-called OFF voltage. For square wave forms, the ON voltage is the voltage at which a pixel attains to a stable operation in which a discharge occurs in each succeeding pulse and the wall voltage equal to the applied voltage. The OFF voltage is the voltage at which a pixel that is ON goes off and no further discharges occur. Experimental data for helium show the hysteresis in the discharge current observed when the voltage is increased to turn ON pixels and then reduced to turn OFF-pixels in a panel. Simulations which match the helium data are also shown. The difference between the ON and OFF voltages defines the bistable margin. For the helium-xenon Penning mixture, the ON and OFF voltages determined by multipulse simulations are almost identical to the values obtained from the wall voltage transfer curve method. In the helium-xenon Penning mixture, the ionization rate for xenon ground state increases dramatically compared to its ionization rate in pure xenon due to the modification in the electron velocity distribution function in the mixture. This feature provides enhanced volumetric ionization in the discharge and hence a rapid growth rate of the wall voltage which is desirable for a sharp transition from OFF to ON in a pixel