Modulational instability in nonlocal Kerr-type media with random parameters

Modulational instability of continuous waves in nonlocal focusing and defocusing Kerr media with stochastically varying diffraction (dispersion) and nonlinearity coefficients is studied both analytically and numerically. It is shown that nonlocality with the sign-definite Fourier images of the medium response functions suppresses considerably the growth rate peak and bandwidth of instability caused by stochasticity. Contrary, nonlocality can enhance modulational instability growth for a response function with negative-sign bands.Comment: 6 pages, 12 figures, revTeX, to appear in Phys. Rev.

Aperiodicity in one-way Markov cycles and repeat times of large earthquakes in faults

A common use of Markov Chains is the simulation of the seismic cycle in a fault, i.e. as a renewal model for the repetition of its characteristic earthquakes. This representation is consistent with Reid's elastic rebound theory. Here it is proved that in {\it any} one-way Markov cycle, the aperiodicity of the corresponding distribution of cycle lengths is always lower than one. This fact concurs with observations of large earthquakes in faults all over the world

The effects of thyrotropin-releasing hormone and scopolamine in Alzheimer's disease and normal volunteers

Thyrotropin-releasing hormone (TRH), a neuromodulator and possibly a neurotransmitter in the central nervous system, was shown in a prior study of young normal volunteers to attenuate the memory impairment induced by the anticholinergic drug scopolamine. In the present study, the cognitive, behavioral and physiologic effects of high dose TRH (0.5 mg/kg), both alone and following administration of scopolamine, were examined in 10 Alzheimer's disease (AD) patients (mean age±SD=63.5 years) and 12 older normal volunteers (mean age=64.9±8.8 years). On the day AD subjects received TRH alone, modest but statistically significant improvement from baseline performance was documented on some tests of learning and memory, especially in those with mild dementia severity. In comparing cognitive test performance between the scopolamine alone and scopolamine+TRH conditions, only two test scores were significantly higher in the latter condition. In the group of older volunteers, TRH did not attenuate scopolamine-induced cognitive impairment, contrary to prior findings in a group of younger controls. In fact, older subjects performed worse after receiving scopolamine followed by TRH than after receiving scopolamine alone. In addition, no change from baseline cognitive performance was detected after subjects received TRH alone. These findings raise several questions and speculations on possible age-related changes in the cholinergic system, as well as on the mechanism of the interaction of TRH with the cholinergic system.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/68371/2/10.1177_026988119200600404.pd

Scale free networks of earthquakes and aftershocks

We propose a new metric to quantify the correlation between any two earthquakes. The metric consists of a product involving the time interval and spatial distance between two events, as well as the magnitude of the first one. According to this metric, events typically are strongly correlated to only one or a few preceding ones. Thus a classification of events as foreshocks, main shocks or aftershocks emerges automatically without imposing predefined space-time windows. To construct a network, each earthquake receives an incoming link from its most correlated predecessor. The number of aftershocks for any event, identified by its outgoing links, is found to be scale free with exponent $\gamma = 2.0(1)$. The original Omori law with $p=1$ emerges as a robust feature of seismicity, holding up to years even for aftershock sequences initiated by intermediate magnitude events. The measured fat-tailed distribution of distances between earthquakes and their aftershocks suggests that aftershock collection with fixed space windows is not appropriate.Comment: 7 pages and 7 figures. Submitte

The global picture of self-similar and not self-similar decay in Burgers Turbulence

This paper continue earlier investigations on the decay of Burgers turbulence in one dimension from Gaussian random initial conditions of the power-law spectral type $E_0(k)\sim|k|^n$. Depending on the power $n$, different characteristic regions are distinguished. The main focus of this paper is to delineate the regions in wave-number $k$ and time $t$ in which self-similarity can (and cannot) be observed, taking into account small-$k$ and large-$k$ cutoffs. The evolution of the spectrum can be inferred using physical arguments describing the competition between the initial spectrum and the new frequencies generated by the dynamics. For large wavenumbers, we always have $k^{-2}$ region, associated to the shocks. When $n$ is less than one, the large-scale part of the spectrum is preserved in time and the global evolution is self-similar, so that scaling arguments perfectly predict the behavior in time of the energy and of the integral scale. If $n$ is larger than two, the spectrum tends for long times to a universal scaling form independent of the initial conditions, with universal behavior $k^2$ at small wavenumbers. In the interval $2<n$ the leading behaviour is self-similar, independent of $n$ and with universal behavior $k^2$ at small wavenumber. When $1<n<2$, the spectrum has three scaling regions : first, a $|k|^n$ region at very small $k$\ms1 with a time-independent constant, second, a $k^2$ region at intermediate wavenumbers, finally, the usual $k^{-2}$ region. In the remaining interval, $n<-3$ the small-$k$ cutoff dominates, and $n$ also plays no role. We find also (numerically) the subleading term $\sim k^2$ in the evolution of the spectrum in the interval $-3<n<1$. High-resolution numerical simulations have been performed confirming both scaling predictions and analytical asymptotic theory.Comment: 14 pages, 19 figure

Modulational instability and nonlocality management in coupled NLS system

The modulational instability of two interacting waves in a nonlocal Kerr-type medium is considered analytically and numerically. For a generic choice of wave amplitudes, we give a complete description of stable/unstable regimes for zero group-velocity mismatch. It is shown that nonlocality suppresses considerably the growth rate and bandwidth of instability. For nonzero group-velocity mismatch we perform a geometrical analysis of a nonlocality management which can provide stability of waves otherwise unstable in a local medium.Comment: 15 pages, 12 figures, to be published in Physica Script

Point-occurrence self-similarity in crackling-noise systems and in other complex systems

It has been recently found that a number of systems displaying crackling noise also show a remarkable behavior regarding the temporal occurrence of successive events versus their size: a scaling law for the probability distributions of waiting times as a function of a minimum size is fulfilled, signaling the existence on those systems of self-similarity in time-size. This property is also present in some non-crackling systems. Here, the uncommon character of the scaling law is illustrated with simple marked renewal processes, built by definition with no correlations. Whereas processes with a finite mean waiting time do not fulfill a scaling law in general and tend towards a Poisson process in the limit of very high sizes, processes without a finite mean tend to another class of distributions, characterized by double power-law waiting-time densities. This is somehow reminiscent of the generalized central limit theorem. A model with short-range correlations is not able to escape from the attraction of those limit distributions. A discussion on open problems in the modeling of these properties is provided.Comment: Submitted to J. Stat. Mech. for the proceedings of UPON 2008 (Lyon), topic: crackling nois

A pilot placebo-controlled study of chronic m-CPP administration in Alzheimer's disease

Meta000000-Chlorophenylpiperazine (m-CPP), a serotonin agonist and metabolite of the anti-depressant trazodone, was administered chronically to eight moderate to severely affected Alzheimer patients to determine whether it would produce improvement in behavioral symptoms complicating this illness. In doses up to 80 mg/day for 16 days, m-CPP was well tolerated and resulted in small but significant increases in anergy and depression-related symptoms compared with placebo. The effects of chronic m-CPP in this study contrast with the reported beneficial effects of the parent compound trazodone and selective 5-HT reuptake inhibitors in treating behavioral symptoms in Alzheimer patients.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/29223/1/0000278.pd