Symplectic integrators very nearly conserve the total energy and are particularly useful when treating long times. We demonstrate some of the properties of these integrators by exploring the structure of first-, second-, and fourth-order symplectic integrators and apply them to the simple harmonic oscillator. We consider numeric, geometric, and analytic aspects of the integrators with particular attention to the computed energies.
Results of the development of an advanced fabrication process for superconductor integrated circuits (ICs) with 20 kA cm 2 Nb AlO x Nb Josephson junctions is presented. The process has 4 niobium superconducting layers, one MoN x resistor layer with 4.0 Ohm per square sheet resistance for the junction shunting and circuit biasing, and employs circular Josephson junctions with the minimum diameter of 1 m; total 11 photolithography levels. The goal of this process development is the demonstration of the feasibility of 80 GHz clock speeds in superconducting ICs for digital signal processing (DSP) and high performance computing. Basic components of Rapid Single Flux Quantum (RSFQ) logic such as DC/SFQ, SFQ/DC converters, Josephson transmission lines (JTLs), and simple digital circuits such as T-flip-flops and 4-bit digital counters have been fabricated and tested. The T-flip-flops were shown to operate up to 400 GHz with the widest margin of operation of 13% at 325 GHz. Digital testing results on the 4-bit counters as well as the junctions, resistors, and other process parameters are also presented. Prospects for yet higher speeds and very large scale integration are discussed.
Abstract:The conversion of time domain data via the fast Fourier (FFT) and Hilbert-Huang (HHT) transforms is compared. The FFT treats amplitude vs. time information globally as it transforms the data to an amplitude vs. frequency description. The HHT is not constrained by the assumptions of stationarity and linearity, required for the FFT, and generates both amplitude and frequency information as a function of time. The behavior and flexibility of these two transforms are examined for a number of different time domain signal types.
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