Steady state genuine multipartite entanglement in harmonic oscillator ensembles with a common environment

Steady state entanglement in ensembles of harmonic oscillators with a common squeezed reservoir is studied. Under certain conditions the ensemble features genuine multipartite entanglement in the steady state. Several analytic results regarding the bipartite and multipartite entanglement properties of the system are derived. We also discuss a possible experimental implementation which may exhibit steady state genuine multipartite entanglement.

Numerical methods for second-order stochastic differential equations

We seek numerical methods for second‐order stochastic differential equations that reproduce the stationary density accurately for all values of damping. A complete analysis is possible for scalar linear second‐order equations (damped harmonic oscillators with additive noise), where the statistics are Gaussian and can be calculated exactly in the continuous‐time and discrete‐time cases. A matrix equation is given for the stationary variances and correlation for methods using one Gaussian random variable per timestep. The only Runge–Kutta method with a nonsingular tableau matrix that gives the exact steady state density for all values of damping is the implicit midpoint rule. Numerical experiments, comparing the implicit midpoint rule with Heun and leapfrog methods on nonlinear equations with additive or multiplicative noise, produce behavior similar to the linear case.

Manufacturing challenges with fabrication of large size mechanical harmonic drives

In truck manufacturing, the exhaust and air inlet pipes are specialized equipment that requires highly skilled, heavy machinery and small batch production methods. This paper describes a project to develop the computer numerically controlled (CNC) pipe bending process for a truck component manufacturer. The company supplies a huge range of heavy duty truck parts to the domestic market and is a significant supplier in Australia. The company has been using traditional methods of machine assisted manual pipe bending techniques. In a drive of continuous improvement, the company has acquired a pre-owned CNC bending machine capable of bending pipes automatically up to 25 bends. However, due to process mismatch, this machine is only used for single bending operation. The researchers studied the bending system and changed the manufacturing process. Using an example exhaust pipe as the benchmark, a significant drop of manufacturing lead time from 70 minutes to 40 minutes for each pipe was demonstrated. There was also a decrease of material cost due to the multiple bends part in one piece without cutting excessive materials for each single bend like it used to be.

Manufacturing challenges with fabrication of large size mechanical harmonic drives

Mechanical harmonic transmissions are relatively new kind of drives having several unusual features. For example, they can provide reduction ratio up to 500:1 in one stage, have very small teeth module compared to conventional drives and very large number of teeth (up to 1000) on a flexible gear. If for conventional drives manufacturing methods are well-developed, fabrication of large size harmonic drives presents a challenge. For example, how to fabricate a thin shell of 1.7m in diameter and wall thickness of 30mm having high precision external teeth at one end and internal splines at the other end? It is so flexible that conventional fabrication methods become unsuitable. In this paper special fabrication methods are discussed that can be used for manufacturing of large size harmonic drive components. They include electro-slag welding and refining, the use of special expandable devices to locate and hold a flexible gear, welding peripheral parts of disks with wear resistant materials with subsequent machining and others. These fabrication methods proved to be effective and harmonic drives built with the use of these innovative technologies have been installed on heavy metallurgical equipment and successfully tested.

Krylov subspace approximations for the exponential Euler method: Error estimates and the harmonic Ritz approximant

We study Krylov subspace methods for approximating the matrix-function vector product φ(tA)b where φ(z) = [exp(z) - 1]/z. This product arises in the numerical integration of large stiff systems of differential equations by the Exponential Euler Method, where A is the Jacobian matrix of the system. Recently, this method has found application in the simulation of transport phenomena in porous media within mathematical models of wood drying and groundwater flow. We develop an a posteriori upper bound on the Krylov subspace approximation error and provide a new interpretation of a previously published error estimate. This leads to an alternative Krylov approximation to φ(tA)b, the so-called Harmonic Ritz approximant, which we find does not exhibit oscillatory behaviour of the residual error.

Mean and variance of estimates of the bispectrum of a harmonic random process-an analysis including leakage effects

Analytical expressions are derived for the mean and variance, of estimates of the bispectrum of a real-time series assuming a cosinusoidal model. The effects of spectral leakage, inherent in discrete Fourier transform operation when the modes present in the signal have a nonintegral number of wavelengths in the record, are included in the analysis. A single phase-coupled triad of modes can cause the bispectrum to have a nonzero mean value over the entire region of computation owing to leakage. The variance of bispectral estimates in the presence of leakage has contributions from individual modes and from triads of phase-coupled modes. Time-domain windowing reduces the leakage. The theoretical expressions for the mean and variance of bispectral estimates are derived in terms of a function dependent on an arbitrary symmetric time-domain window applied to the record. the number of data, and the statistics of the phase coupling among triads of modes. The theoretical results are verified by numerical simulations for simple test cases and applied to laboratory data to examine phase coupling in a hypothesis testing framework

Harmonic elimination technique for a single-phase multilevel converter with unequal DC link voltage levels

Multilevel converters, because of the benefits they attract in generating high quality output voltage, are used in several applications. Various modulation and control techniques are introduced by several researchers to control the output voltage of the multilevel converters like space vector modulation and harmonic elimination (HE) methods. Multilevel converters may have a DC link with equal or unequal DC voltages. In this study a new HE technique based on the HE method is proposed for multilevel converters with unequal DC link voltage. The DC link voltage levels are considered as additional variables for the HE method and the voltage levels are defined based on the HE results. Increasing the number of voltage levels can reduce lower order harmonic content because of the fact that more variables are created. In comparison to previous methods, this new technique has a positive effect on the output voltage quality by reducing its total harmonic distortion, which must take into consideration for some applications such as uninterruptable power supply, motor drive systems and piezoelectric transducer excitation. In order to verify the proposed modulation technique, MATLAB simulations and experimental tests are carried out for a single-phase four-level diode-clamped converter.

Harmonic quality of multilevel cascade inverters with random carrier phase pulse width modulation

The output harmonic quality of N series connected full-bridge dc-ac inverters is investigated. The inverters are pulse width modulated using a common reference signal but randomly phased carrier signals. Through analysis and simulation, probability distributions for inverter output harmonics and vector representations of N carrier phases are combined and assessed. It is concluded that a low total harmonic distortion is most likely to occur and will decrease further as N increases.

Harmonic quality of multilevel cascade inverters with random carrier phase pulse width modulation

The output harmonic quality of N series connected full-bridge dc-ac inverters is investigated. The inverters are pulse width modulated using a common reference signal but randomly phased carrier signals. Through analysis and simulation, probability distributions for inverter output harmonics and vector representations of N carrier phases are combined and assessed. It is concluded that a low total harmonic distortion is most likely to occur and will decrease further as N increases.

Higher harmonic large-amplitude fourier transformed alternating current voltammetry : analytical attributes derived from studies of the oxidation of ferrocenemethanol and uric acid at a glassy carbon electrode

An analytical evaluation of the higher ac harmonic components derived from large amplitude Fourier transformed voltammetry is provided for the reversible oxidation of ferrocenemethanol (FcMeOH) and oxidation of uric acid by an EEC mechanism in a pH 7.4 phosphate buffer at a glassy carbon (GC) electrode. The small background current in the analytically optimal fifth harmonic is predominantly attributed to faradaic current associated with the presence of electroactive functional groups on the GC electrode surface, rather than to capacitive current which dominates the background in the dc, and the initial three ac harmonics. The detection limits for the dc and the first to fifth harmonic ac components are 1.9, 5.89, 2.1, 2.5, 0.8, and 0.5 µM for FcMeOH, respectively, using a sine wave modulation of 100 mV at 21.46 Hz and a dc sweep rate of 111.76 mV s−1. Analytical performance then progressively deteriorates in the sixth and higher harmonics. For the determination of uric acid, the capacitive background current was enhanced and the reproducibility lowered by the presence of surface active uric acid, but the rapid overall 2e− rather than 1e– electron transfer process gives rise to a significantly enhanced fifth harmonic faradaic current which enabled a detection limit of 0.3 µM to be achieved which is similar to that reported using chemically modified electrodes. Resolution of overlapping voltammetric signals for a mixture of uric acid and dopamine is also achieved using higher fourth or fifth harmonic components, under very low background current conditions. The use of higher fourth and fifth harmonics exhibiting highly favorable faradaic to background (noise) current ratios should therefore be considered in analytical applications under circumstances where the electron transfer rate is fast.

Probing second harmonic components of pH-sensitive Redox processes in a mesoporous TiO2-Nafion film electrode with Fourier-transformed large-amplitude sinusoidally modulated voltammetry

Electrochemical processes in mesoporous TiO2-Nafion thin films deposited on indium tin oxide (ITO) electrodes are inherently complex and affected by capacitance, Ohmic iR-drop, RC-time constant phenomena, and by potential and pH-dependent conductivity. In this study, large-amplitude sinusoidally modulated voltammetry (LASMV) is employed to provide access to almost purely Faradaic-based current data from second harmonic components, as well as capacitance and potential domain information from the fundamental harmonic for mesoporous TiO2-Nafion film electrodes. The LASMV response has been investigated with and without an immobilized one-electron redox system, ferrocenylmethyltrimethylammonium+. Results clearly demonstrate that the electron transfer associated with the immobilized ferrocene derivative follows two independent pathways i) electron hopping within the Nafion network and ii) conduction through the TiO2 backbone. The pH effect on the voltammetric response for the TiO2 reduction pathway (ii) can be clearly identified in the 2nd harmonic LASMV response with the diffusion controlled ferrocene response (i) acting as a pH independent reference. Application of second harmonic data derived from LASMV measurement, because of the minimal contribution from capacitance currents, may lead to reference-free pH sensing with systems like that found for ferrocene derivatives.

Second harmonic generation and multiphoton microscopic detection of collagen without the need for species specific antibodies

High-resolution, high-contrast, three-dimensional images of live cell and tissue architecture can be obtained using second harmonic generation (SHG), which comprises non-absorptive frequency changes in an excitation laser line. SHG does not require any exogenous antibody or fluorophore labeling, and can generate images from unstained sections of several key endogenous biomolecules, in a wide variety of species and from different types of processed tissue. Here, we examined normal control human skin sections and human burn scar tissues using SHG on a multi-photon microscope (MPM). Examination and comparison of normal human skin and burn scar tissue demonstrated a clear arrangement of fibers in the dermis, similar to dermal collagen fiber signals. Fluorescence-staining confirmed the MPM-SHG collagen colocalization with antibody staining for dermal collagen type-I but not fibronectin or elastin. Furthermore, we were able to detect collagen MPM-SHG signal in human frozen sections as well as in unstained paraffin embedded tissue sections that were then compared with hematoxylin and eosin staining in the identical sections. This same approach was also successful in localizing collagen in porcine and ovine skin samples, and may be particularly important when species-specific antibodies may not be available. Collectively, our results demonstrate that MPM SHG-detection is a useful tool for high resolution examination of collagen architecture in both normal and wounded human, porcine and ovine dermal tissue.