Estimation of the degree of asphericity of a glass sphere using a vectorial shearing interferometer

The degree of asphericity is estimated by determining the average radius of curvature in different sections, at various points on the surface of a sphere, and the deviation from it. We employ the vectorial shearing interferometer (VSI) as the instrument to determine the radius of curvature from two subapertures of the transparent glass sphere. We incorporate the sphere as a thick lens into the interferometric setup, illuminating it with an expanded beam. The spherical aberration, introduced by the sphere in the wave front, depends on the local sphere radius, on the refraction index of the glass, and on the cone angle of the source. The wave front aberrated by the sphere impinges on the VSI. Here, the wave front is divided in two in amplitude, it is sheared vectorially, and it is superimposed with itself. The fringe pattern is formed in the intersection of the wave fronts. The shape of the resulting fringe pattern is directly related to spherical aberration. We estimate qualitatively the degree of asphericity, comparing the phase gradients in different sections of the sphere. Here, we report on the experimental setup to test the asphericity, the results with different vectorial shearing (magnitude and direction). Finally, we perform a comparison with the theoretical predictions.     

Determining Type II sensitivity ranges of the fractional assignment problem

This paper proposes iterative labeling algorithms to determine the Type II sensitivity ranges of the fractional assignment problem. Unlike the traditional sensitivity range which keeps the current optimal basis remaining optimal, the Type II sensitivity range is the range that keeps the current optimal assignment remaining optimal. Focusing only on the non-degenerate basic variables makes the Type II sensitivity range more practical. Three cases of perturbation, each with two kinds, are discussed. An example is presented to demonstrate the proposed algorithms.     

Auxiliary probe design adaptable to existing probes for remote detection NMR, MRI, and time-of-flight tracing

A versatile, detection-only probe design is presented that can be adapted to any existing NMR or MRI probe with the purpose of making the remote detection concept generally applicable. Remote detection suggests freeing the NMR experiment from the confinement of using the same radio frequency (RF) coil and magnetic field for both information encoding and signal detection. Information is stored during the encoding step onto a fluid sensor medium whose magnetization is later measured in a different location. The choice of an RF probe and magnetic field for encoding can be made based solely on the size and characteristics of the sample and the desired information quality without considering detection sensitivity, as this aspect is dealt with by a separate detector. While early experiments required building probes that included two resonant circuits, one for encoding and one for detection, a modular approach with a detection-only probe as presented here can be used along with any existing NMR probe of choice for encoding. The design of two different detection-only probes is presented, one with a saddle coil for milliliter-sized detection volumes, and the other one with a microsolenoid coil for sub-microliter fluid quantities. As example applications, we present time-of-flight (TOF) tracing of hyperpolarized (129)Xe spins in a gas mixture through coiled tubing using the microsolenoid coil detector and TOF flow imaging through a nested glass container where the gas flow changes its direction twice between inlet and outlet using the saddle coil detector.     

Optimal strategy policy in batch arrival queue with server breakdowns and multiple vacations

This paper considers a like-queue production system in which server vacations and breakdowns are possible. The decision-maker can turn a single server on at any arrival epoch or off at any service completion. We model the system by an M^[x]/M/1 queueing system with N policy. The server can be turned off and takes a vacation with exponential random length whenever the system is empty. If the number of units waiting in the system at any vacation completion is less than N, the server will take another vacation. If the server returns from a vacation and finds at least N units in the system, he immediately starts to serve the waiting units. It is assumed that the server breaks down according to a Poisson process and the repair time has an exponential distribution. We derive the distribution of the system size through the probability generating function. We further study the steady-state behavior of the system size distribution at random (stationary) point of time as well as the queue size distribution at departure point of time. Other system characteristics are obtained by means of the grand process and the renewal process. Finally, the expected cost per unit time is considered to determine the optimal operating policy at a minimum cost. The sensitivity analysis is also presented through numerical experiments.     

SQP-methods for solving optimal control problems with control and state constraints: adjoint variables, sensitivity analysis and real-time control

Parametric nonlinear optimal control problems subject to control and state constraints are studied. Two discretization methods are discussed that transcribe optimal control problems into nonlinear programming problems for which SQP-methods provide efficient solution methods. It is shown that SQP-methods can be used also for a check of second-order sufficient conditions and for a postoptimal calculation of adjoint variables. In addition, SQP-methods lead to a robust computation of sensitivity differentials of optimal solutions with respect to perturbation parameters. Numerical sensitivity analysis is the basis for real-time control approximations of perturbed solutions which are obtained by evaluating a first-order Taylor expansion with respect to the parameter. The proposed numerical methods are illustrated by the optimal control of a low-thrust satellite transfer to geosynchronous orbit and a complex control problem from aquanautics. The examples illustrate the robustness, accuracy and efficiency of the proposed numerical algorithms.     

Multiple-detector responses or multiple-retention times: what is more informative for gas chromatography peak identification?

Multiple-separation and -detection are two approaches applied at the identification of analytes in chromatography. Using them depends on the physico-chemical properties and elemental content of the analytes. When physico-chemical properties are similar multiple-separation gives better opportunities for the identification. In this case, the efficiency of the columns is very important. When analytes contain some characteristic groups as--NO2, halogen, or nitrogen atoms then multiple-detection will be more useful. The sensitivity and/or selectivity of the detectors increase reliability of identification significantly.     

Transfer functions of US transducers for harmonic imaging and bubble responses

Current medical diagnostic echo systems are mostly using harmonic imaging. This means that a fundamental frequency (e.g., 2 MHz) is transmitted and the reflected and scattered higher harmonics (e.g., 4 and 6 MHz), produced by nonlinear propagation, are recorded. The signal level of these harmonics is usually low and a well-defined transfer function of the receiving transducer is required. Studying the acoustic response of a single contrast bubble, which has an amplitude in the order of a few Pascal, is another area where an optimal receive transfer function is important.

We have developed three methods to determine the absolute transfer function of a transducer. The first is based on a well-defined wave generated by a calibrated source in the far field. The receiving transducer receives the calibrated wave and from this the transfer functions can be calculated. The second and third methods are based on the reciprocity of the transducer. The second utilizes a calibrated hydrophone to measure the transmitted field. In the third method, a pulse is transmitted by the transducer, which impinges on a reflector and is received again by the same transducer. In both methods, the response combined with the transducer impedance and beam profiles enables the calculation of the transfer function.

The proposed methods are useful to select the optimal piezoelectric material (PZT, single crystal) for transducers used in reception only, such as in certain 3D scanning designs and superharmonic imaging, and for selected experiments like single bubble behavior.

We tested and compared these methods on two unfocused single element transducers, one commercially available (radius 6.35 mm, centre frequency 2.25 MHz) the other custom built (radius 0.75 mm, centre frequency 4.3 MHz). The methods were accurate to within 15%.     

Detection of NMR signals with a radio-frequency atomic magnetometer

We demonstrate detection of proton NMR signals with a radio-frequency (rf) atomic magnetometer tuned to the NMR frequency of 62 kHz. High-frequency operation of the atomic magnetometer makes it relatively insensitive to ambient magnetic field noise. We obtain magnetic field sensitivity of 7 fT/Hz1/2 using only a thin aluminum shield. We also derive an expression for the fundamental sensitivity limit of a surface inductive pick-up coil as a function of frequency and find that an atomic rf magnetometer is intrinsically more sensitive than a coil of comparable size for frequencies below about 50 MHz.     

Spectral editing in solid-state MAS NMR of quadrupolar nuclei using selective satellite inversion

A sensitivity enhancement method based on selective adiabatic inversion of a satellite transition has been employed in a (pi/2)CT-(pi)ST1-(pi/2)CT spectral editing sequence to both enhance and resolve multisite NMR spectra of quadrupolar nuclei. In addition to a total enhancement of 2.5 times for spin 3/2 nuclei, enhancements up to 2.0 times is reported for the edited sites in a mixture of rubidium salts.     

Sensitivity analysis of composite piecewise smooth equations

This paper is a contribution to the sensitivity analysis of piecewise smooth equations. A piecewise smooth function is a Lipschitzian homeomorphism near a given point if and only if it is coherently oriented and has an invertible B-derivative at this point. We emphasise the role of functions of the typef=g °h whereg is piecewise smooth andh is smooth and present verifiable conditions which ensure that the functionf=g ° is a Lipschitzian homeomorphism near a given point for every sufficiently close toh with respect to theC ¹-topology. Revised version of part of the paper “Sensitivity analysis and Newton’s method for composite piecewise smooth equations”.