Wide power range microwave feedback controller

A substantially constant power level is derived over a predetermined frequency band, in each of a plurality of relatively widely spaced power ranges, from a microwave load having a predetermined amplitude versus frequency response, such as an antenna. A microwave source of substantially constant amplitude drives a forward path connected between the source and the load. A feedback path responsive to the microwave power level in the forward path derives a control voltage for the PIN attenuator. The equalizer attenuator drives a linear, crystal amplitude detector. Attenuating means included in the forward and feedback paths are selectively connected in circuit to maintain the power level of the microwave input to the amplitude detector substantially constant, even though different power ranges are supplied to the load by the forward path

Power of change-point tests for long-range dependent data

We investigate the power of the CUSUM test and the Wilcoxon change-point tests for a shift in the mean of a process with long-range dependent noise. We derive analytic formulas for the power of these tests under local alternatives. These results enable us to calculate the asymptotic relative efficiency (ARE) of the CUSUM test and the Wilcoxon change point test. We obtain the surprising result that for Gaussian data, the ARE of these two tests equals 1, in contrast to the case of i.i.d. noise when the ARE is known to be 3/π.Herold Dehling and Aeneas Rooch were supported in part by the German Research Foundation (DFG) through the Collaborative Research Center SFB 823 Statistical Modelling of Nonlinear Dynamic Processes. Murad S. Taqqu was supported in part by NSF grant DMS-1309009 at Boston University. (SFB 823 - German Research Foundation (DFG); DMS-1309009 - NSF at Boston University)Published versio

Increasing power-law range in avalanche amplitude and energy distributions

Power-law type probability density functions spanning several orders of magnitude are found for different avalanche properties. We propose a methodology to overcome empirical constrains that limit the power-law range for the distributions of different avalanche observables like amplitude, energy, duration or size. By considering catalogs of events that cover different observation windows, maximum likelihood estimation of a global power-law exponent is computed. This methodology is applied to amplitude and energy distributions of acoustic emission avalanches in failure-under- compression experiments of a nanoporous silica glass, finding in some cases global exponents in an unprecedented broad range: 4.5 decades for amplitudes and 9.5 decades for energies. In the later case, however, strict statistical analysis suggests experimental limitations might alter the power-law behavior.Comment: 23 pages, 7 figure

Power of Change-Point Tests for Long-Range Dependent Data

We investigate the power of the CUSUM test and the Wilcoxon change-point test for a shift in the mean of a process with long-range dependent noise. We derive analytiv formulas for the power of these tests under local alternatives. These results enable us to calculate the asymptotic relative efficiency (ARE) of the CUSUM test and the Wilcoxon change point test. We obtain the surprising result that for Gaussian data, the ARE of these two tests equals 1, in contrast to the case of i.i.d. noise when the ARE is known to be $3/\pi$

Power Counting of Contact-Range Currents in Effective Field Theory

We analyze the power counting of two-body currents in nuclear effective field theories (EFTs). We find that the existence of non-perturbative physics at low energies, which is manifest in the existence of the deuteron and the 1S0 NN virtual bound state, combined with the appearance of singular potentials in versions of nuclear EFT that incorporate chiral symmetry, modifies the renormalization-group flow of the couplings associated with contact operators that involve nucleon-nucleon pairs and external fields. The order of these couplings is thereby enhanced with respect to the naive-dimensional-analysis estimate. Consequently, short-range currents enter at a lower order in the chiral EFT than has been appreciated up until now, and their impact on low-energy observables is concomitantly larger. We illustrate the changes in the power counting with a few low-energy processes involving external probes and the few-nucleon systems, including electron-deuteron elastic scattering and radiative neutron capture by protons.Comment: 5 pages. Minor revisions. Conclusions unchanged. Version to appear in Physical Review Letter

Strong asymmetry for surface modes in nonlinear lattices with long-range coupling

We analyze the formation of localized surface modes on a nonlinear cubic waveguide array in the presence of exponentially-decreasing long-range interactions. We find that the long-range coupling induces a strong asymmetry between the focusing and defocusing cases for the topology of the surface modes and also for the minimum power needed to generate them. In particular, for the defocusing case, there is an upper power threshold for exciting staggered modes, which depends strongly on the long-range coupling strength. The power threshold for dynamical excitation of surface modes increase (decrease) with the strength of long-range coupling for the focusing (defocusing) cases. These effects seem to be generic for discrete lattices with long-range interactions.Comment: 4 pages, 5 figures, submitted for publicatio

Critical Index and Fixed Point in the Transfer of Power in Nonlinear Gravitational Clustering

We investigate the transfer of power between different scales and coupling of modes during non-linear evolution of gravitational clustering in an expanding universe. We start with a power spectrum of density fluctuations that is exponentially damped outside a narrow range of scales and use numerical simulations to study evolution of this power spectrum. Non-Linear effects generate power at other scales with most power flowing from larger to smaller scales. The ``cascade'' of power leads to equipartition of energy at smaller scales, implying a power spectrum with index $n\approx -1$. We find that such a spectrum is produced in the range $1 < \delta < 200$ for density contrast $\delta$. This result continues to hold even when small scale power is added to the initial power spectrum. Semi-analytic models for gravitational clustering suggest a tendency for the effective index to move towards a critical index $n_c\approx -1$ in this range. For n<n_c, power in this range grows faster than linear rate, while if n>n_c, it grows at a slower rate - thereby changing the index closer to n_c. At scales larger than the narrow range of scales with initial power, a k^4 tail is produced. We demonstrate that non-linear small scales do not effect the growth of perturbations at larger scales.Comment: Title changed. Added two figures and some discussion. Postscript file containing all the figures is available at http://www.ast.cam.ac.uk/~jasjeet/papers/powspec.ps.gz Accepted for publication in the MNRA