Restrictions and Stability of Time-Delayed Dynamical Networks

This paper deals with the global stability of time-delayed dynamical networks. We show that for a time-delayed dynamical network with non-distributed delays the network and the corresponding non-delayed network are both either globally stable or unstable. We demonstrate that this may not be the case if the network's delays are distributed. The main tool in our analysis is a new procedure of dynamical network restrictions. This procedure is useful in that it allows for improved estimates of a dynamical network's global stability. Moreover, it is a computationally simpler and much more effective means of analyzing the stability of dynamical networks than the procedure of isospectral network expansions introduced in [Isospectral graph transformations, spectral equivalence, and global stability of dynamical networks. Nonlinearity, 25 (2012) 211-254]. The effectiveness of our approach is illustrated by applications to various classes of Cohen-Grossberg neural networks.Comment: 32 pages, 9 figure

Spatial field correlation, the building block of mesoscopic fluctuations

The absence of self averaging in mesoscopic systems is a consequence of long-range intensity correlation. Microwave measurements suggest and diagrammatic calculations confirm that the correlation function of the normalized intensity with displacement of the source and detector, $\Delta R$ and $\Delta r$, respectively, can be expressed as the sum of three terms, with distinctive spatial dependences. Each term involves only the sum or the product of the square of the field correlation function, $F \equiv F_{E}^2$. The leading-order term is the product, the next term is proportional to the sum. The third term is proportional to $[F(\Delta R)F(\Delta r) + [F(\Delta R)+F(\Delta r)] + 1]$.Comment: Submitted to PR

Optical Monitoring of PKS 1510-089: A Binary Black Hole System?

Three deep flux minima were observed with nearly the same time-scales and intervals for the blazar PKS 1510-089 in the past few years. A binary black hole system was proposed to be at the nucleus of this object, and a new minimum was predicted to occur in 2002 March. We monitored this source with a 60/90 cm Schmidt telescope from 2002 February to April. In combination with the data obtained by Xie et al. (2004) in the same period, we presented for the 2002 minimum a nearly symmetric light curve, which would be required by an eclipsing model of a binary black hole system. We also constrained the time-scale of the minimum to be 35 min, which is more consistent with the time-scales ~42 min of the three previous minima than the 89 min time-scale given by the same authors. The wiggling miniarcsecond radio jet observed in this object is taken as a further evidence for the binary black hole system. The `coupling' of the periodicity in light curve and the helicity in radio jet is discussed in the framework of a binary black hole system.Comment: 5 pages, 4 figures, accepted by MNRA

Field and intensity correlations in random media

Measurements of the microwave field transmitted through a random medium allows direct access to the field correlation function, whose complex square is the short range or C1 contribution to the intensity correlation function C. The frequency and spatial correlation function are compared to their Fourier pairs, the time of flight distribution and the specific intensity, respectively. The longer range contribution to intensity correlation is obtained directly by subtracting C1 from C and is in good agreement with theory.Comment: 9 pages, 5 figures, submitted to Phys.Rev.

Non-Fermi liquid behavior of SrRuO_3 -- evidence from infrared conductivity

The reflectivity of the itinerant ferromagnet SrRuO_3 has been measured between 50 and 25,000 cm-1 at temperatures ranging from 40 to 300 K, and used to obtain conductivity, scattering rate, and effective mass as a function of frequency and temperature. We find that at low temperatures the conductivity falls unusually slowly as a function of frequency (proportional to \omega^{-1/2}), and at high temperatures it even appears to increase as a function of frequency in the far-infrared limit. The data suggest that the charge dynamics of SrRuO_3 are substantially different from those of Fermi-liquid metals.Comment: 4 pages, 3 postscript figure

Time-Dependent Current Partition in Mesoscopic Conductors

The currents at the terminals of a mesoscopic conductor are evaluated in the presence of slowly oscillating potentials applied to the contacts of the sample. The need to find a charge and current conserving solution to this dynamic current partition problem is emphasized. We present results for the electro-chemical admittance describing the long range Coulomb interaction in a Hartree approach. For multiply connected samples we discuss the symmetry of the admittance under reversal of an Aharonov-Bohm flux.Comment: 22 pages, 3 figures upon request, IBM RC 1971

Analytic solution for nonlinear shock acceleration in the Bohm limit

The selfconsistent steady state solution for a strong shock, significantly modified by accelerated particles is obtained on the level of a kinetic description, assuming Bohm-type diffusion. The original problem that is commonly formulated in terms of the diffusion-convection equation for the distribution function of energetic particles, coupled with the thermal plasma through the momentum flux continuity equation, is reduced to a nonlinear integral equation in one variable. Its solution provides selfconsistently both the particle spectrum and the structure of the hydrodynamic flow. A critical system parameter governing the acceleration process is found to be $\Lambda = M^{-3/4}\Lambda_1$, where $\Lambda_1 =\eta p_1/mc$, with a suitably normalized injection rate $\eta$, the Mach number M >> 1, and the cut-off momentum $p_1$. We particularly focus on an efficient solution, in which almost all the energy of the flow is converted into a few energetic particles. It was found that (i) for this efficient solution (or, equivalently, for multiple solutions) to exist, the parameter $\zeta =\eta\sqrt{p_0 p_1}/mc$ must exceed a critical value $\zeta_{cr} \sim 1$ ($p_0$ is the injection momentum), (ii) the total shock compression ratio r increases with M and saturates at a level that scales as $ r \propto \Lambda_1 (iii) the downstream power-law spectrum has the universal index q=3.5 over a broad momentum range. (iv) completely smooth shock transitions do not appear in the steady state kinetic description.Comment: 39 pages, 3 PostScript figures, uses aasms4.sty, to appear in Aug. 20, 1997 issue ApJ, vol. 48