Representation and properties of para-Bose oscillator operators. II. Coherent states and the minimum uncertainty states

The energy, position, and momentum eigenstates of a para-Bose oscillator system were considered in paper I. Here we consider the Bargmann or the analytic function description of the para-Bose system. This brings in, in a natural way, the coherent states ||z;alpha> defined as the eigenstates of the annihilation operator ?. The transformation functions relating this description to the energy, position, and momentum eigenstates are explicitly obtained. Possible resolution of the identity operator using coherent states is examined. A particular resolution contains two integrals, one containing the diagonal basis ||z;alpha><−z;alpha||. We briefly consider the normal and antinormal ordering of the operators and their diagonal and discrete diagonal coherent state approximations. The problem of constructing states with a minimum value of the product of the position and momentum uncertainties and the possible alpha dependence of this minimum value is considered. Journal of Mathematical Physics is copyrighted by The American Institute of Physics.

Proton magnetic resonance study of piezoelectric lithium formate monohydrate

Abstract is not available.

Dissipative dynamics of a harmonic oscillator: A nonperturbative approach

Starting from a microscopic theory, we derive a master equation for a harmonic oscillator coupled to a bath of noninteracting oscillators. We follow a nonperturbative approach, proposed earlier by us for the free Brownian particle. The diffusion constants are calculated analytically and the positivity of the master equation is shown to hold above a critical temperature. We compare the long time behavior of the average kinetic and potential energies with known thermodynamic results. In the limit of vanishing oscillator frequency of the system, we recover the results of the free Brownian particle.

Influence of Temperature and High Electric Field on Power Consumption by Piezoelectric Actuated Integrated Structure

The influence of electric field and temperature on power consumption of piezoelectric actuated integrated structure is studied by using a single degree of freedom mass-spring-damper system model coupled with a piezoactuator. The material lead zirconate titanate, is considered as it is capable of producing relatively high strains (e.g., 3000 mu epsilon). Actuators are often subject to high electric fields to increase the induced strain produced, resulting in field dependant piezoelectric coefficient d(31), dielectric coefficient epsilon(33) and dissipation factor delta. Piezostructures are also likely to be used across a wide range of temperatures in aerospace and undersea operations. Again, the piezoelectric properties can vary with temperature. Recent experimental studies by physics researchers have looked at the effect of high electric field and temperature on piezoelectric properties. These properties are used together with an impedance based power consumption model. Results show that including the nonlinear variation of dielectric permittivity and dissipation factor with electric field is important. Temperature dependence of the dielectric constant also should be considered.

Highly stable oscillator for quartz crystal thickness monitor

A highly stable oscillator used in a quartz crystal thickness monitor for monitoring the rate of evaporation and total thickness of film during thin film deposition is reported. The design aspects of the oscillator and its long term stability, which enhances the reproducibility and the performance of the thickness monitor, are discussed. The stability of the oscillator at defined conditions is tested and compared with the conventional transistorized oscillator and the IC oscillator using inverters. The oscillator is coupled to the crystal monitor and its performance is studied in an evaporation system by evaporating different materials

Time Domain Characteristics of Electrical Measures for a Piezoelectric Thin Film to Identify Defects in the Substrate

A reduced 3D continuum model of dynamic piezoelectricity in a thin-film surface-bonded to the substrate/host is presented in this article. While employing large area flexible thin piezoelectric films for novel applications in device/diagnostics, the feasibility of the proposed model in sensing the surface and/or sub-surface defects is demonstrated through simulations - which involve metallic beams with cracks and composite beam with delaminations of various sizes. We have introduced a set of electrical measures to capture the severity of the damage in the existing structures. Characteristics of these electrical measures in terms of the potential difference and its spatial gradients are illustrated in the time domain. Sensitivity studies of the proposed measures in terms of the defected areas and their region of occurence relative to the sensing film are reported. The simulations' results for electrical measures for damaged hosts/substrates are compared with those due to undamaged hosts/substrates, which show monotonicity with high degree of sensitivity to variations in the damage parameters.

Experimental Demonstration of H{infty} Control based Active Vibration Suppression in Composite Fin-tip of Aircraft using Optimally Placed Piezoelectric Patch Actuators

The goal of this study is the multi-mode structural vibration control in the composite fin-tip of an aircraft. Structural model of the composite fin-tip with surface bonded piezoelectric actuators is developed using the finite element method. The finite element model is updated experimentally to reflect the natural frequencies and mode shapes accurately. A model order reduction technique is employed for reducing the finite element structural matrices before developing the controller. Particle swarm based evolutionary optimization technique is used for optimal placement of piezoelectric patch actuators and accelerometer sensors to suppress vibration. H{infty} based active vibration controllers are designed directly in the discrete domain and implemented using dSpace® (DS-1005) electronic signal processing boards. Significant vibration suppression in the multiple bending modes of interest is experimentally demonstrated for sinusoidal and band limited white noise forcing functions.

Modeling and analysis of a tunable piezoelectric structure for transverse shear wave generation

An analytical investigation of the transverse shear wave mode tuning with a resonator mass (packing mass) on a Lead Zirconium Titanate (PZT) crystal bonded together with a host plate and its equivalent electric circuit parameters are presented. The energy transfer into the structure for this type of wave modes are much higher in this new design. The novelty of the approach here is the tuning of a single wave mode in the thickness direction using a resonator mass. First, a one-dimensional constitutive model assuming the strain induced only in the thickness direction is considered. As the input voltage is applied to the PZT crystal in the thickness direction, the transverse normal stress distribution induced into the plate is assumed to have parabolic distribution, which is presumed as a function of the geometries of the PZT crystal, packing mass, substrate and the wave penetration depth of the generated wave. For the PZT crystal, the harmonic wave guide solution is assumed for the mechanical displacement and electric fields, while for the packing mass, the former is solved using the boundary conditions. The electromechanical characteristics in terms of the stress transfer, mechanical impedance, electrical displacement, velocity and electric field are analyzed. The analytical solutions for the aforementioned entities are presented on the basis of varying the thickness of the PZT crystal and the packing mass. The results show that for a 25% increase in the thickness of the PZT crystal, there is ~38% decrease in the first resonant frequency, while for the same change in the thickness of the packing mass, the decrease in the resonant frequency is observed as ~35%. Most importantly the tuning of the generated wave can be accomplished with the packing mass at lower frequencies easily. To the end, an equivalent electric circuit, for tuning the transverse shear wave mode is analyzed.

Piezoelectric zinc oxide thin film for MEMS application: A comparative study

We report here, the study carried out on piezoelectric thin film for MEMS/Microsensor applications. The study includes characterization of sputtered thin film using indirect methods and comparison of behavior using cantilever technique for the confirmation of piezoelectric property. A suitable experimental setup was designed and fabricated for subjecting the cantilever to vibrate. The data was recorded for piezoelectric thin films deposited with different compositions. It is clearly evident that the direct method is inexpensive and easier for determining the quality of the deposited piezoelectric thin film.

Simulation and implementation of a tunable C-band dielectric resonator oscillator

Microwave sources used in present day applications are either multiplied source derived from basic quartz crystals, or frequency synthesizers. The frequency multiplication method increases FM noise power considerably, and has very low efficiency in addition to being very complex and expensive. The complexity and cost involved demands a simple, compact and tunable microwave source. A tunable dielectric resonator oscillator(DRO) is an ideal choice for such applications. In this paper, the simulation, design and realization of a tunable DRO with a center frequency of 6250 MHz is presented. Simulation has been carried out on HP-Ees of CAD software. Mechanical and electronic tuning features are provided. The DRO operates over a frequency range of 6235 MHz to 6375 MHz. The output power is +5.33 dBm at centre frequency. The performance of the DRO is as per design with respect to phase noise, harmonic levels and tunability. and hence, can conveniently be used for the intended applications.

On the study of a third-order mechanical oscillator

In this paper, the study of a third-order mechanical oscillator is presented by demonstrating its equivalence to the well-known R.C. multivibrator with two additional reactive elements. The conditions for the oscillator's possession of periodic solutions are presented. It is also shown that under certain conditions, the study of the given third-order autonomous system can be reduced to the study of an equivalent second-order, non-autonomous system.

Crystallographic Evolution, Dielectric, and Piezoelectric Properties of Bi4Ti3O12:W/Cr Ceramics

W/Cr codoped Bi4Ti3O12 ceramics, Bi4Ti3-xWxO12+x+0.2 wt%Cr2O3 (BITWC, x=0-0.15), were prepared using a solid-state reaction method. The crystallographic evolution and phase analysis were distinctly determined focusing on the X-ray diffraction peak changes in (020)/(200) and (220)/(1115) diffraction planes, by which the lattice parameters, a, b, and c can be refined. The thermal variations of permittivity, dielectric loss (tan delta), impedance, and electrical conductivity properties were characterized. A decrease in the values of Curie temperature from 675 degrees to 640 degrees C and an increase in the values of the dielectric constant due to an increase of W6+/Cr3+ content were observed. The highest piezoelectric constant, d(33) of 22 pC/N, was achieved with the composition of Bi4Ti2.975W0.025O12.025+0.2 wt% Cr2O3. Also, this composition had a lower electrical conductivity than the other investigated compositions.

Coupling of surface acoustic waves propagating in two separated piezoelectric media

The coupling of surface acoustic waves propagating in two separated piezoelectric media is studied using the perturbation theory of Auld. The results of the analysis are applied to two configurations using Bi12GeO20 and CdS crystals. It is found that the loss due to coupling is about 7 dB at 50 MHz in the cases of (111)-cut, [110]-prop. Bi12GeO20 and Y-cut, 60°-X prop. CdS combination. On étudie le couplage des ondes acoustiques de surface se propageant sur deux milieux piezo-eléctriques par la théorie de perturbation de Auld. Les resultats d'analyse sont appliqué's aux deux configurations des cristanx Bi12GeO20 et CdS. On trouve que la perte par couplage est environ de 7 dB a 50 MHz dans le cas de combination de (111)-coupe, [110]-prop. Bi12GeO20 et Y-coupe, 60°-X prop. CdS.

Exact path-integral evaluation of the heat distribution function of a trapped Brownian oscillator

Using path integrals, we derive an exact expression-valid at all times t-for the distribution P(Q,t) of the heat fluctuations Q of a Brownian particle trapped in a stationary harmonic well. We find that P(Q, t) can be expressed in terms of a modified Bessel function of zeroth order that in the limit t > infinity exactly recovers the heat distribution function obtained recently by Imparato et al. Phys. Rev. E 76, 050101(R) (2007)] from the approximate solution to a Fokker-Planck equation. This long-time result is in very good agreement with experimental measurements carried out by the same group on the heat effects produced by single micron-sized polystyrene beads in a stationary optical trap. An earlier exact calculation of the heat distribution function of a trapped particle moving at a constant speed v was carried out by van Zon and Cohen Phys. Rev. E 69, 056121 (2004)]; however, this calculation does not provide an expression for P(Q, t) itself, but only its Fourier transform (which cannot be analytically inverted), nor can it be used to obtain P(Q, t) for the case v=0.

Tuning and stability of a singly resonant continuous-wave optical parametric oscillator close to degeneracy

Wavelength tuning and stability characteristics of a singly resonant continuous-wave optical parametric oscillator (cw OPO) in the proximity of signal-idler degeneracy have been studied. The OPO is made singly resonant by using a Bragg grating as a spectral filter in the OPO cavity. The signal-idler frequency difference can be tuned from 0.5 to 7 THz, which makes the OPO suitable for cw THz generation by optical heterodyning. The operation of the OPO within this singly-resonant regime is characterized by a strong self-stabilization effect. A gradual transition to an unstable, doubly-resonant regime is observed for a signal-idler detuning smaller than ~ 0.5 THz.