Nonlinear resonant tunneling diode (RTD) circuits for microwave A/D conversion

Short-duration electrical pulses play important roles in ultrafast time-domain metrology: they are used to sample rapidly varying signals or as probe signals in ranging radars, time-domain reflectometry and in communication. In this work, we design a nonlinear transmission, which is loaded with resonant tunneling diode to be suitable for microwave A/D conversion. A resonant tunneling diode (RTD) has a negative differential resistance that means when the voltage increases the current decreases. The equivalent circuit of monostable line is given. The simulation is performed by using OrCad program. Results show that a spike is produced and after a charging time constant, another switching occurs. Hence – similar to a relaxation oscillator – the spiking period is determined by the amplitude and frequency of the input current. The transmission line itself ensures the generation and propagation of identical spikes, such as solitons formed after few diodes.     

Master Equation and Fokker–Planck Equation: Comparison of Entropy and of Rate Constants

A usual approximation of the master equation is provided by the Fokker–Planck equation. For chemical systems with one species, we prove generally that the prediction of the rate constant of the metastable state given by the Master equation and the Fokker–Planck approximation differ exponentially with respect to the size of the system. We show that this is related to the fact that the entropy of the metastable state is not described correctly by the Fokker–Planck equation. We prove that the rate given by the Fokker–Planck equation overestimates that rate given by the Master equation.     

Numerical predictions and experiments on the free-plate edge mode

In this paper, te edge mode variation is studied with three different methods: the reciprocal work method, already used by Torvik [J. Acoust. Soc. Am. 41 (1967) 346] to model this phenomenon, the S-parameter method and a finite element model that are applied for the first time to the study of the edge resonance. Moreover, laser probe measurements of the edge mode have also been performed and compared to the numerical predictions. The good agreement between the numerical predictions and the experimental data allows full understanding of the resonant phenomenon. The edge resonance is linked to the strong increase in amplitude of two complex Lamb waves, and the edge mode is proved to radiate into the plate as the first symmetrical Lamb mode S(0). Displacements at the edge and away from the edge have been computed and measured to evaluate the spatial and temporal behaviour of the edge mode. The dependence of the edge resonance frequency and amplitude on the Poisson coefficient has also been studied.     

Operators that are points of spectral continuity,II

This paper continues an earlier study of those bounded operators on a Hilbert space at which the spectrum is continuous, where the spectrum is considered as a function whose domain is the set of all bounded operators furnished with the norm topology and whose range is the collection of compact subsets of the complex plane furnished with the Hausdorff metric. In this paper the points of continuity of the essential spectrum, the approximate point spectrum, and certain related subsets of the spectrum are characterized.The first author was supported by National Science Foundation Grant MCS 77-28396.     

The median procedure in cluster analysis and social choice theory

Classical approachs for fitting and aggregation problems, specially in cluster analysis, social choice theory and paired comparisons methods, consist in the minimization of a remoteness function between relational data and a relational model. The notion of median, with its algebraic, metric, geometrical and statistical aspects, allow a unified treatment of many of base problems. Properties of median procedures are organized according to four directions: stabilities and axiomatic characterizations; Arrow-like properties; combinatorial properties; effective computational possibilities. Finally, interesting mathematical problems, related to the notion of median are surveyed.     

Zeno and anti-Zeno effects for quantum Brownian motion

In this Letter, we investigate the occurrence of the Zeno and anti-Zeno effects for quantum Brownian motion. We single out the parameters of both the system and the reservoir governing the crossover between Zeno and anti-Zeno dynamics. We demonstrate that, for high reservoir temperatures, the short time behavior of environment induced decoherence is ultimately responsible for the occurrence of either the Zeno or the anti-Zeno effect. Finally, we suggest a way to manipulate the decay rate of the system and to observe a controlled continuous passage from decay suppression to decay acceleration using engineered reservoirs in the trapped ion context.     

Two-step melting in two dimensions: first-order liquid-hexatic transition

Melting in two spatial dimensions, as realized in thin films or at interfaces, represents one of the most fascinating phase transitions in nature, but it remains poorly understood. Even for the fundamental hard-disk model, the melting mechanism has not been agreed upon after 50 years of studies. A recent Monte?Carlo algorithm allows us to thermalize systems large enough to access the thermodynamic regime. We show that melting in hard disks proceeds in two steps with a liquid phase, a hexatic phase, and a solid. The hexatic-solid transition is continuous while, surprisingly, the liquid-hexatic transition is of first order. This melting scenario solves one of the fundamental statistical-physics models, which is at the root of a large body of theoretical, computational, and experimental research.