Excess thermal noise generated during Poiseuille flow of certain polymer solutions

The previously reported results concerning the generation of excess thermal noise induced by capillary flow of aqueous solutions of poly(ethylene oxide) (PEO) are supplemented by measurements on the following solutions: PEO/DMF, PEO/i-PrOH, PS/THF, PVAC/cyclohexanone, and poly(acrylamide)/water. Similarly to the previous findings, a noise level increasing with the flow rate is recorded, the noise exhibiting a l/f -frequency spectrum. Within a certain flow range, distinct peaks are recorded in the spectrum (harmonics of a fundamental frequency,f ₀). Thef ₀-values of the various solutions under varying flow conditions arrange themselves along a commonf ₀-shear rate curve. They appear to be associated with transversal oscillations of the solution upstream the capillary entrance.     

Holes in the probability density of strongly colored noise driven systems

A qualitative change in the topology of the joint probability densityP(,x), which occurs for strongly colored noise in multistable systems, has recently been observed first by analog simulation (F. Moss and F. Marchesoni,Phys. Lett. A 131:322 (1988)) and confirmed by matrix continued fraction methods (Th. Leiber and H. Riskin, unpublished), and by analytic theory (P. Hänggi, P. Jung, and F. Marchesoni,J. Stat. Phys., this issue). Systems studied were of the classx=–U(x)/x+(t,), whereU(x) is a multistable potential and (t, ) is a colored, Gaussian noise of intensityD, for which =0, and (t) (s)=(D/)exp(–t–s/). When the noise correlation time is smaller than some critical value ₀, which depends onD, the two-dimensional densityP(,x) has the usual topology [P. Jung and H. Risken,Z. Phys. B 61:367 (1985); F. Moss and P. V. E. McClintock,Z. Phys. B 61:381 (1985)]: a pair of local maxima ofP(,x), which correspond to a pair of adjacent local minima ofU(x), are connected by a single saddle point which lies on thex axis. When >₀, however,the single saddle disappears and is replaced by a pair of off-axis saddles. A depression, or hole, which is bounded by the saddles and the local maxima thus appears. The most probable trajectory connecting the two potential wells therefore does not pass through the origin for >₀, but instead must detour around the local barrier. This observation implies that successful mean-first-passage-time theories of strongly colored noise driven systems must necessarily be two dimensional (Hänggiet al.). We have observed these holes for several potentialsU(x): (1)a soft, bistable potential by analog simulation (Moss and Marchesoni); (2) a periodic potential [Th. Leiber, F. Marchesoni, and H. Risken,Phys. Rev. Lett. 59:1381 (1987)] by matrix continued fractions; (3) the usual hard, bistable potential,U(x)=–ax ²/2+bx ⁴/4, by analog simulations only; and (4) a random potential for which the forcingf(x)=–U(x)/x is an approximate Gaussian with nonzero correlation length, i.e., colored spatiotemporal noise, by analog simulation. There is a critical curve ₀(D) in the versusD plane which divides the two topological behaviors. For a fixed value ofD, this curve is shifted toward larger values of ₀ for progressively weaker barriers between the wells. Therefore, strong barriers favor the observation of this topological transformation at smaller values of . Recently, an analytic expression for the critical curve, valid asymptotically in the small-D limit, has been obtained (Hänggiet al.).This paper will appear in a forthcoming issue of theJournal of Statistical Physics.     

Ensemble and trajectory statistics in a nonlinear partial differential equation

We have examined the influence of parametric noise on the solution behavioru(t, x) of a nonlinear initial value() problem arising in cell kinetics. In terms of ensemble statistics, the eventual limiting solution mean and variance are well-characterized functions of the noise statistics, and and depend on . When noise is continuously present along the trajectory, and are independent of the noise statistics and . However, in their evolution toward and , both _u (t, x) and _u ² (t, x) depend on the noise and.     

Can colored noise improve stochastic resonance?

The phenomenon of stochastic resonance is studied in the presence of colored noise. Several sources of colored noise are introduced and the consequences for the asymptotic time-periodic probability and the (phase-averaged) power spectrum are discussed. Based on space-time symmetry considerations, selection rules for the occurrence of-spikes in the power spectrum are derived. The effect of colored noise on the amplification of small periodic signals is studied in terms of effective, time-periodic Fokker-Planck equations: In overdamped systems driven by colored noise, we find that SR is suppressed with increasing noise color. In contrast, for colored noise induced by inertia (as well as for asymmetric dichotomic noise), one obtains an enhancement of SR. This latter result is obtained by studying the Kramers equation perturbed by a small periodic force.     

Electrochemical noise generated during the stress corrosion cracking of sensitized alloy 690

Electrochemical noise in current has been used to monitor the stress corrosion cracking (SCC) susceptibility of alloy 690 sensitized at 700 °C during 48 h in sodium thiosulfate at 90 °C. At 48 h of aging, the specimen failed by SCC and the corrosion current pulses had high intensity and low frequency, and were associated with the nucleation and propagation of stress corrosion cracks during slow strain rate tests. When the alloy was immune to SCC, the observed corrosion current pulses had a much higher frequency and lower intensity, indicating either uniform corrosion or passivation. The type of transients observed do not indicate the mechanism responsible for the observed embrittlement, but only the cracking initiation or propagation process.     

Stochastic resonance in surface catalytic oxidation of carbon monoxide induced by colored noise

Noise is generally considered as a disadvanta-geous factor, which would smear weak signals, there-fore, people always try to reduce its influence. How-ever, recent studies show that, for a nonlinear system, under certain circumstances, noise can enhance sys-tem抯 response to a signal. At specific noise intensity, the response of a system to a weak signal may reach its maximum, which is called 搒tochastic resonance?(SR). The concept of SR was originally put forward by Benzi and his collaborat…     

Stability of a budworm growth model with random perturbations

A budworm growth model perturbed by both white noises and regime switchings is proposed and analyzed. It is proven that there is a threshold. If this threshold is positive, then the model has a unique ergodic stationary distribution; if this threshold is negative, then the zero solution of the model is stable. The results show that both white noises and regime switchings can change the stability of the model greatly. Several numerical simulations based on realistic data are also introduced to illustrate the main results.     

Absolute continuity of the law for the two dimensional stochastic Navier–Stokes equations

We consider the two dimensional Navier–Stokes equations in vorticity form with a stochastic forcing term given by a gaussian noise, white in time and colored in space. First, we prove existence and uniqueness of a weak (in the Walsh sense) solution process $\xi$ and we show that, if the initial vorticity ${\xi }_0$ is continuous in space, then there exists a space–time continuous version of the solution. In addition we show that the solution $\xi (t,x)$ (evaluated at fixed points in time and space) is locally differentiable in the Malliavin calculus sense and that its image law is absolutely continuous with respect to the Lebesgue measure on $\mathbb{R}$.     

Photochemistry in rare gas clusters

We introduce a novel control method for a delayed dynamical system exhibiting high-dimensional chaos. The control is based on a negative feedback loop with an adaptive filtering, consisting of a selective filter, centered at the frequency of the orbit to be stabilized, with the addition of a time derivative correction. The validity of the method is also discussed in the framework of a space-like representation adopted to study the analogies between delayed dynamical systems and spatially extended systems. Received: 12 April 1999