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[en] We provide a Biot–Savart inversion scheme that, for any two-dimensional, or bulk with planar crystallization, high-temperature superconducting (HTS) sample, determines current density maps with a higher resolution and accuracy than previous procedures and at a fraction of its computational cost. The starting point of our scheme is a Hall scanning microscopy map of the out-of-plane component of the magnetic field generated by the current. Such maps are noisy in scans of real samples with commercial-grade equipment, and their error is the limiting factor in any Biot–Savart inversion scheme. The main innovation of our proposed scheme is a singular spectrum analysis (SSA) filtering of the Hall probe maps, which cancels measurement errors such as noise or drifts without introducing any artifacts in the field map. The SSA filtering of the Hall probe data is so successful in this task that the resulting magnetic field map does not require an overdetermined QR inversion, allowing Fourier inversion of the Biot–Savart problem. Our implementation of SSA filtering of the Hall scan measurements, followed by Biot–Savart inversion using the fast Fourier transform (FFT), is applied to both simulations and real samples of HTS tape stacks. The algorithm works in cases where ill conditioning ruled out the application of Fourier inversion, and achieves a finer resolution for a fraction of the cost of the QR inversion used to date. The computation passes physical and statistical validity tests in all cases, and in three-dimensional samples it is shown to yield the average, with a depth-dependent weight, of the current density circulating in the different layers of the sample. (paper)
[en] The conference includes discussions of several areas in modern optics where the space-time or space-frequency descriptions of optical fields are finding growing theoretical and practical applications. Topics covered include space-time optics, phase conjugation, phase-space methods, holography, coding and encoding of optical signals, and optical reconstruction
[en] The dynamics of a one-dimensional weak-link superconductor connecting two stronger superconductors is investigated by means of the time-dependent Ginzburg--Landau theory. It is shown that the singularities along the length of the weak link where the order parameter tends to zero, otherwise called phase-slip centers, are at the zeros of a theta function and the points where the total current is made up entirely of the supercurrent are at the zeros of another theta function. From the properties of these theta functions the step structure of the pair electrochemical potential is analytically derived
[en] We present an implementation of matched filtering comprised three basic steps: (1) compute a fast Fourier transform (FFT) of the data, (2) map the FFT to a (data independent) one-dimensional track in a multi-dimensional space, and (3) take an inverse multi-dimensional Fourier transform. In contrast to the standard approach, this method does not require the explicit use of template waveforms. This implementation was found as a byproduct of an exploration of sampling theory in the context of the template placement problem. We show that the latter problem can be completely mapped, in all its details, onto that of sampling an analog multi-dimensional random field, including the use of anti-aliasing before the acquisition of samples. The last point is non-trivial since the analog signal in question, namely the output of a template bank, does not physically exist unless it is computed
[en] The flow induced in a quiescent micropolar fluid by a doubly infinite plate accelerated suddenly from rest to a constant velocity is investigated in the present paper. The local balance equations according to Eringen's model are non-dimensionalized and solved in the Laplace transform domain. The Laplace transforms for velocity and microrotation are then inverted in some special cases analytically and in the general case numerically, by applying the Valko-Abate procedure. Comparing to the monotonically decaying error-function velocity profile of the Newtonian case, in a micropolar fluid also non-monotonic behavior with backflow may occur. In the case of microrotation, in addition to the monotonic decay, some special features, such as the inversion and overshoot phenomena, have been found.
[en] Any bipartite nonlocal unitary operation can be carried out by teleporting a quantum state from one party to the other, performing the unitary gate locally, and teleporting a state back again. This paper investigates unitaries which can be carried out using less prior entanglement and classical communication than are needed for teleportation. Large families of such unitaries are constructed using (projective) representations of finite groups. Among the tools employed are: a diagrammatic approach for representing entangled states, a theorem on the necessary absence of information at certain times and locations, and a representation of bipartite unitaries based on a group Fourier transform.
[en] This paper extends the fast Fourier transform (FFT) network to interest derivative valuation under the Hull–White model driven by a Lévy process. The classical trinomial tree for the Hull–White model is a widely adopted approach in practice, but fails to accommodate the change in the driving stochastic process. Recent finance research supports the use of a Lévy process to replace Brownian motion in stochastic modeling. The FFT network overcomes the drawback of the trinomial approach but maintains its advantages in super-calibration to the term structure of interest rate and efficient computation to various kinds of interest rate derivatives under Lévy processes. The FFT network only requires knowledge of the characteristic function of the Lévy process driving the interest rate process, but not of the interest rate process itself. The numerical comparison between the closed-form solutions of interest rate caps and swaptions and those from FFT network confirms that the proposed network is accurate and efficient. We also demonstrate its use in pricing Bermudan swaptions and other American-style options. Finally, the FFT network is expanded to accommodate path-dependent variables, and is applied to interest rate target redemption notes and a range of accrual notes.
[en] The phase peculiarities of spectron in view of the dispersive Fourier transformation are studied. The numerical study for different initial pulses with various initial spectral phases has shown that along with the shaping of the spectron, not only the amplitude information can be transferred from the frequency domain to the time domain, but also the phase information