A pseudo-matched filter for chaos

A matched filter maximizes the signal-to-noise ratio of a signal. In the recent work of Corron et al. [Chaos 20, 023123 (2010)], a matched filter is derived for the chaotic waveforms produced by a piecewise-linear system. Motivated by these results, we describe a pseudo-matched filter, which removes noise from the same chaotic signal. It consists of a notch filter followed by a first-order, low-pass filter. We compare quantitatively the matched filter's performance to that of our pseudo-matched filter using correlation functions in a simulated radar application. On average, the pseudo-matched filter performs with a correlation signal-to-noise ratio that is 2.0 dB below that of the matched filter. Our pseudo-matched filter, though somewhat inferior in comparison to the matched filter, is easily realizable at high speed (> 1 GHz) for potential radar applications

Subwavelength position sensing using nonlinear feedback and wave chaos

We demonstrate a position-sensing technique that relies on the inherent sensitivity of chaos, where we illuminate a subwavelength object with a complex structured radio-frequency field generated using wave chaos and a nonlinear feedback loop. We operate the system in a quasi-periodic state and analyze changes in the frequency content of the scalar voltage signal in the feedback loop. This allows us to extract the object's position with a one-dimensional resolution of ~\lambda/10,000 and a two-dimensional resolution of ~\lambda/300, where \lambda\ is the shortest wavelength of the illuminating source.Comment: 4 pages, 4 figure

Ultra-high-frequency piecewise-linear chaos using delayed feedback loops

We report on an ultra-high-frequency (> 1 GHz), piecewise-linear chaotic system designed from low-cost, commercially available electronic components. The system is composed of two electronic time-delayed feedback loops: A primary analog loop with a variable gain that produces multi-mode oscillations centered around 2 GHz and a secondary loop that switches the variable gain between two different values by means of a digital-like signal. We demonstrate experimentally and numerically that such an approach allows for the simultaneous generation of analog and digital chaos, where the digital chaos can be used to partition the system's attractor, forming the foundation for a symbolic dynamics with potential applications in noise-resilient communications and radar

Baryons in QCD_{AS} at Large N_c: A Roundabout Approach

QCD_{AS}, a variant of large N_c QCD in which quarks transform under the color two-index antisymmetric representation, reduces to standard QCD at N_c = 3 and provides an alternative to the usual large N_c extrapolation that uses fundamental representation quarks. Previous strong plausibility arguments assert that the QCD_{AS} baryon mass scales as N_c^2; however, the complicated combinatoric problem associated with quarks carrying two color indices impeded a complete demonstration. We develop a diagrammatic technique to solve this problem. The key ingredient is the introduction of an effective multi-gluon vertex: a "traffic circle" or "roundabout" diagram. We show that arbitrarily complicated diagrams can be reduced to simple ones with the same leading N_c scaling using this device, and that the leading contribution to baryon mass does, in fact, scale as N_c^2.Comment: 9 pages, 9 pdf figures, ReVTeX with pdflate

LDC Borrowing with Default Risk

This paper presents a theoretical model to describe the effects of default risk on international lending to LDC sovereign borrowers. The threat of defaults in international lending is shown to give rise to many characteristics of the syndicated loan market: (1) quantity rationing of loans; (2) LDC policies designed to enhance creditworthiness; (3) prevalence of short maturities on international loans; and (4) a prevalence of bank lending relative to bond-market lending

Pion Photoproduction Amplitude Relations in the 1/N_c Expansion

We derive expressions for pion photoproduction amplitudes in the 1/N_c expansion of QCD, and obtain linear relations directly from this expansion that relate electromagnetic multipole amplitudes at all energies. The leading-order relations in 1/N_c compare favorably with available data, while the next-to-leading order relations seem to provide only a small improvement. However, when resonance parameters are compared directly, the agreement at O(1/N_c) or O(1/N_c^2) is impressive.Comment: 19 pages, ReVTeX, 50 eps files combine into 5 compound figure

Growth and External Debt Under Risk of Debt Repudiation

We analyze the pattern of growth of a nation which borrows abroad and which has the option of repudiating its foreign debt. We show that the equilibrium strategy of competitive lenders is to make the growth of the foreign debt contingent on the growth of the borrowing country. We give a closed-form solution to a linear version of our model. The economy, in that case, follows a two-stage pattern of growth. During the first stage, the debt grows more rapidly than the economy. During the second stage, both the debt and the economy grow at the same rate, and more slowly than in the first stage. During this second stage, the total interest falling due on the debt is never entirely repaid; only an amount proportional to the difference of the rate of interest and the rate of growth of the economy is repaid each period

How short is too short? Constraining zero-range interactions in nucleon-nucleon scattering

We discuss a number of constraints on the effects of zero-range potentials in quantum mechanics. We show that for such a potential $p \cot(\delta)$, where $p$ is the momentum of the nucleon in the center of mass frame and $\delta$ is the S-wave phase shift, must be a monotonically decreasing function of energy. This implies that the effective range of the potential is non-positive. We also examine scattering from the sum of two potentials, one of which is a short-range interaction. We find that if the short-range interaction is of zero-range then it must be attractive, and the logarithmic derivative of the radial wave function at the origin must be a monotonically decreasing function of energy. If the short-range interaction is not of zero range then a constraint which gives the minimum possible range for it to fit the phase shifts exists. The implications of these results for effective field theory treatments of nucleon-nucleon interactions are discussed.Comment: 5 pages, RevTeX. Version accepted for publication in Phys. Lett. B. Minor changes to the text have been made in order to clarify the scope of the pape