Phase space path integral approach to harmonic oscillator with a time-dependent force constant

The quantum statistical mechanical propagator for a harmonic oscillator with a time-dependent force constant, m omega(2)(t), has been investigated in the past and was found to have only a formal solution in terms of the solutions of certain ordinary differential equations. Such path integrals are frequently encountered in semiclassical path integral evaluations and having exact analytical expressions for such path integrals is of great interest. In a previous work, we had obtained the exact propagator for motion in an arbitrary time-dependent harmonic potential in the overdamped limit of friction using phase space path integrals in the context of Levy flights - a result that can be easily extended to Brownian motion. In this paper, we make a connection between the overdamped Brownian motion and the imaginary time propagator of quantum mechanics and thereby get yet another way to evaluate the latter exactly. We find that explicit analytic solution for the quantum statistical mechanical propagator can be written when the time-dependent force constant has the form omega(2)(t) = lambda(2)(t) - d lambda(t)/dt where lambda(t) is any arbitrary function of t and use it to evaluate path integrals which have not been evaluated previously. We also employ this method to arrive at a formal solution of the propagator for both Levy flights and Brownian subjected to a time-dependent harmonic potential in the underdamped limit of friction. (C) 2015 Elsevier B.V. All rights reserved.

Low-Order Harmonic Suppression for Open-End Winding IM With Dodecagonal Space Vector Using a Single DC-Link Supply

This paper proposes a technique to suppress low-order harmonics for an open-end winding induction motor drive for a full modulation range. One side of the machine is connected to a main inverter with a dc power supply, whereas the other inverter is connected to a capacitor from the other side. Harmonic suppression (with complete elimination of fifth- and seventh-order harmonics) is achieved by realizing dodecagonal space vectors using a combined pulsewidth modulation (PWM) control for the two inverters. The floating capacitor voltage is inherently controlled during the PWM operation. The proposed PWM technique is shown to be valid for the entire modulation range, including overmodulation and six-step mode of operation of the main inverter. Experimental results have been presented to validate the proposed technique.

Harmonic analysis of DC capacitor current in sinusoidal and space-vector modulated neutral-point-clamped inverters

The voltage ripple and power loss in the DC-capacitor of a voltage source inverter depend on the harmonic currents flowing through the capacitor. This paper presents a double Fourier series based analysis of the harmonic contents of the DC capacitor current in a three-level neutral-point clamped (NPC) inverter, modulated with sine-triangle pulse-width modulation (SPWM) or conventional space vector pulse-width modulation (CSVPWM) schemes. The analytical results are validated experimentally on a 3-kVA three-level inverter prototype. The capacitor current in an NPC inverter has a periodicity of 120(a similar to) at the fundamental or modulation frequency. Hence, this current contains third-harmonic and triplen-frequency components, apart from switching frequency components. The harmonic components vary with modulation index and power factor for both PWM schemes. The third harmonic current decreases with increase in modulation index and also decreases with increase in power factor in case of both PWM methods. In general, the third harmonic content is higher with SPWM than with CSVPWM at a given operating condition. Also, power loss and voltage ripple in the DC capacitor are estimated for both the schemes using the current harmonic spectrum and equivalent series resistance (ESR) of the capacitor.

A Mitigation Technique for Harmonic Downconversion in Wideband Spectrum Sensors

The down conversion of radio frequency components around the harmonics of the local oscillator (LO), and its impact on the accuracy of white space detection using integrated spectrum sensors, is studied. We propose an algorithm to mitigate the impact of harmonic downconversion by utilizing multiple parallel downconverters in the system architecture. The proposed algorithm is validated on a test-board using commercially available integrated circuits and a test-chip implemented in a 130-nm CMOS technology. The measured data show that the impact of the harmonic downconversion is closely related to the LO characteristics, and that much of it can be mitigated by the proposed technique.

Structural evolution and second harmonic properties of lithium niobate-tantalate nanocrystals embedded in a borate glass

Nano-crystals of LiNbxTa1 (-) O-x(3) were evolved by subjecting melt-quenched 1.5Li(2)O-2B(2)O(3)-xNb(2)O(5)-(1 - x)Ta2O5 glasses (where x = 0, 0.25, 0.5, 0.75 and 1.00) to a controlled 3-h isothermal heat treatment between 530 and 560 degrees C. Detailed X-ray diffraction and Raman spectral studies confirmed the formation of nano-crystalline LiNbxTa1 (-) O-x(3) along with a minor phase of ferroelectric and non-linear optic Li2B4O7. The sizes of the nanocrystals evolved in the glass were in the range of 19-37 nm for x = 0-0.75 and 23-45 nm for x = 1.00. Electron microscopic studies confirmed a transformation of the morphology of the nano-crystallites from dendritic star-shaped spherulites for x = 0 to rod-shaped structures for x = 1.00 brought about by a coalescence of crystallites. Broad Maker-fringe patterns (recorded at 532 nm) were obtained by subjecting the heat-treated glass plates to 1064 nm fundamental radiation. However, an effective second order non-linear optic coefficient, d(eff), of 0.45 pm/V, which is nearly 1.2 times the d(36) of KDP single crystal, was obtained for a 560 degrees C/3 h heat-treated glass of the representative composition x = 0.50 comprising 37 nm sized crystallites. (C) 2015 Elsevier B.V. All rights reserved.

Structural evolution and second harmonic properties of lithium niobate-tantalate nanocrystals embedded in a borate glass

Nano-crystals of LiNbxTa1 (-) O-x(3) were evolved by subjecting melt-quenched 1.5Li(2)O-2B(2)O(3)-xNb(2)O(5)-(1 - x)Ta2O5 glasses (where x = 0, 0.25, 0.5, 0.75 and 1.00) to a controlled 3-h isothermal heat treatment between 530 and 560 degrees C. Detailed X-ray diffraction and Raman spectral studies confirmed the formation of nano-crystalline LiNbxTa1 (-) O-x(3) along with a minor phase of ferroelectric and non-linear optic Li2B4O7. The sizes of the nanocrystals evolved in the glass were in the range of 19-37 nm for x = 0-0.75 and 23-45 nm for x = 1.00. Electron microscopic studies confirmed a transformation of the morphology of the nano-crystallites from dendritic star-shaped spherulites for x = 0 to rod-shaped structures for x = 1.00 brought about by a coalescence of crystallites. Broad Maker-fringe patterns (recorded at 532 nm) were obtained by subjecting the heat-treated glass plates to 1064 nm fundamental radiation. However, an effective second order non-linear optic coefficient, d(eff), of 0.45 pm/V, which is nearly 1.2 times the d(36) of KDP single crystal, was obtained for a 560 degrees C/3 h heat-treated glass of the representative composition x = 0.50 comprising 37 nm sized crystallites. (C) 2015 Elsevier B.V. All rights reserved.

Complex patterns arise through spontaneous symmetry breaking in dense homogeneous networks of neural oscillators

There has been much interest in understanding collective dynamics in networks of brain regions due to their role in behavior and cognitive function. Here we show that a simple, homogeneous system of densely connected oscillators, representing the aggregate activity of local brain regions, can exhibit a rich variety of dynamical patterns emerging via spontaneous breaking of permutation or translational symmetries. Upon removing just a few connections, we observe a striking departure from the mean-field limit in terms of the collective dynamics, which implies that the sparsity of these networks may have very important consequences. Our results suggest that the origins of some of the complicated activity patterns seen in the brain may be understood even with simple connection topologies.

Evaluation and Minimization of Low-Order Harmonic Torque in Low-Switching-Frequency Inverter-Fed Induction Motor Drives

A low-order harmonic pulsating torque is a major concern in high-power drives, high-speed drives, and motor drives operating in an overmodulation region. This paper attempts to minimize the low-order harmonic torques in induction motor drives, operated at a low pulse number (i.e., a low ratio of switching frequency to fundamental frequency), through a frequency domain (FD) approach as well as a synchronous reference frame (SRF) based approach. This paper first investigates FD-based approximate elimination of harmonic torque as suggested by classical works. This is then extended into a procedure for minimization of low-order pulsating torque components in the FD, which is independent of machine parameters and mechanical load. Furthermore, an SRF-based optimal pulse width modulation (PWM) method is proposed to minimize the low-order harmonic torques, considering the motor parameters and load torque. The two optimal methods are evaluated and compared with sine-triangle (ST) PWM and selective harmonic elimination (SHE) PWM through simulations and experimental studies on a 3.7-kW induction motor drive. The SRF-based optimal PWM results in marginally better performance than the FD-based one. However, the selection of optimal switching angle for any modulation index (M) takes much longer in case of SRF than in case of the FD-based approach. The FD-based optimal solutions can be used as good starting solutions and/or to reasonably restrict the search space for optimal solutions in the SRF-based approach. Both of the FD-based and SRF-based optimal PWM methods reduce the low-order pulsating torque significantly, compared to ST PWM and SHE PWM, as shown by the simulation and experimental results.

Anharmonic surface interactions for biomolecular screening and characterization.

The acoustic response of conventional mechanical oscillators, such as a piezoelectric crystal, is predominantly harmonic at modest amplitudes. However, here, we observe from the electrical response that significant motional anharmonicity is introduced in the presence of attached analyte. Experiments were conducted with streptavidin-coated polystyrene microbeads of various sizes attached to a quartz crystal resonator via specific and nonspecific molecular tethers in liquid. Quantitative analysis reveals that the deviation of odd Fourier harmonics of the response caused by introduction of microbeads as a function of oscillation amplitude presents a unique signature of the molecular tether. Hence, the described anharmonic detection technique (ADT) based on this function allows screening of biomolecules and provides an additional level of selectivity in receptor-based detection that is often associated with nonspecific interactions. We also propose methods to extract mechanical force-extension characteristics of the molecular tether and activation energy using this technique.

The ensemble statistics of the energy of a random system subjected to harmonic excitation

This paper is concerned with the ensemble statistics of the response to harmonic excitation of a single dynamic system such as a plate or an acoustic volume. Random point process theory is employed, and various statistical assumptions regarding the system natural frequencies are compared, namely: (i) Poisson natural frequency spacings, (ii) statistically independent Rayleigh natural frequency spacings, and (iii) natural frequency spacings conforming to the Gaussian orthogonal ensemble (GOE). The GOE is found to be the most realistic assumption, and simple formulae are derived for the variance of the energy of the system under either point loading or rain-on-the-roof excitation. The theoretical results are compared favourably with numerical simulations and experimental data for the case of a mass loaded plate. © 2003 Elsevier Ltd. All rights reserved.

Noise and stability in giant-chirp oscillators mode-locked with a nanotube-based saturable absorber

We compare experimental results showing stable dissipative-soliton solutions exist in mode-locked lasers with ultra-large normal dispersion (as large as 21.5 ps2), with both the analytic framework provided by Haus' master-equation and full numerical simulations. © 2010 Optical Society of America.

Dynamical symmetry of screened Coulomb potential and isotropic harmonic oscillator

It is shown that for the screened Coulomb potential and isotropic harmonic oscillator, there exists an infinite number of closed orbits for suitable angular momentum values. At the aphelion (perihelion) points of classical orbits, an extended Runge-Lenz vector for the screened Coulomb potential and an extended quadrupole tensor for the screened isotropic harmonic oscillator are still conserved. For the screened two-dimensional (2D) Coulomb potential and isotropic harmonic oscillator, the dynamical symmetries SO3 and SU(2) are still preserved at the aphelion (perihelion) points of classical orbits, respectively. For the screened 3D Coulomb potential, the dynamical symmetry SO4 is also preserved at the aphelion (perihelion) points of classical orbits. But for the screened 3D isotropic harmonic oscillator, the dynamical symmetry SU(2) is only preserved at the aphelion (perihelion) points of classical orbits in the eigencoordinate system. For the screened Coulomb potential and isotropic harmonic oscillator, only the energy (but not angular momentum) raising and lowering operators can be constructed from a factorization of the radial Schrodinger equation.