Cyclic behavior

Infinite Lattices Although cyclic behavior is certain to occur under even class c3 rules for finite systems, it is a rare occurrence for truly infinite systems cycles occur only with exceptional initial conditions. For a finite sized initial seed, fox example, the pattern either quickly dies or grows progressively larger with time. Most infinite seeds lead only to complex acyclic patterns. Under the special condition that the initial state is periodic with period m , however, the evolution of the infinite system will be the same as that of the finite CA of size N = m-, in this case, cycles of length << 2 can occur. 

Two of the study systems, Lake Michigan and Pond 3513, exhibit cyclic behavior in their concentrations of Pu(V) (Figure 2 and 3). The cycle in Lake Michigan seems to be closely coupled with the formation in the summer and dissolution in the winter of calcium carbonate and silica particles, which are related to primary production cycles in the lake(25). The experimental knowledge that both Pu(IV) and Pu(V) adsorb on calcium carbonate precipitates(20) confirms the importance of carbonate formation in the reduction of plutonium concentrations in late summer. Whether oxidation-reduction is important in this process has not been determined. 

A physical model of ONB for the explosive boiling and dryout, was suggested. In order to understand why dryout occurred even at a low value of vapor quality x, it is important to keep in mind that the liquid film does not cover the entire heated surface of the micro-channel, and two-phase flow is characterized by an unsteady cyclic behavior. The following assumptions are made in the development of the model ... 

There are three adjustable parameters in a Box-Jenkins analysis, one each for autoregression, differencing, and moving average terms. Corrections for cyclical behavior may be added as three optional terms. The approach is flexible, and provides much information. 

Wasserman, W. J., and Smith, L. D. (1978). The cyclic behavior of a cytoplasmic factor controlling nuclear membrane breakdown. J. Cell Biol. 78 R15-R22. 

First, the cyclical behavior is evident again. The integration process tends to smooth noise or variability in data and reveal more clearly the underlying trends in the data. The integral has the features of a sine wave with a period of slightly greater than 20 days. 

Apparent reversible and/or cyclical behavior Microbubble formation and coalescence versus microbubble fission and disappearance... 

The chemistry of arsenic in soil and aquatic ecosystems can bast be described as a complex array of homogeneous and hetergeneous chemical, biochemical, and geochemical reactions that together control the dissolved concentrations of arsenic in these systems. Although many of these reactions have been studied independently, the total description of the combined major reaction mechanisms that control the cyclic behavior of arsenic in environmental systems has largely been undeveloped. In the paper presented here, results obtained in laboratory and field studies are used to describe some of the major control mechanisms that affect the distribution as well as transformations of arsenic in an aquatic environment. 

Arsenic can exist in several oxidation states, as both inorganic and organometallic species, and in dissolved and gaseous phases (Table I). Dissolved arsenic species can adsorb to suspended solids and be carried down to the sediments in an aquatic system. Since gaseous arsenic compounds can form, arsenic can be removed from the sediments as dissolved gas or in gas bubbles (e.g. CH ). Thus, arsenic can cycle within aquatic ecosystems and this cyclic behavior has been reviewed by Ferguson and Gavis (1 ) and Woolson 2). In any given system, it is necessary to understand the behavior of a variety of different arsenic compounds as well as a variety of environmental compartments in order to totally characterize the cyclic behavior of this element. 

The particle formation rate depends on the rale of production of free radicals and on the relative rates of the various mechanisms in which these free radicals participate. A high rate of particle formation in the presence of small amounts of free emulsifier will contribute to unstable cyclic behavior. 

However, as lithium metal shows only poor cyclic behavior, LiCs has become a very interesting candidate for the negative electrode in rechargeable batteries. This point is stressed in two review articles, by Scrosati [173] and Fauteux and Koksbang [174]. 

The quinone accumulator is commonly defined in the special composition shown as No. 1 in Table 12 [71-78]. The cyclic behavior is good thick quinone/c.b. layers, up to 7 mm, were cycled at 10 mA/cm for up to 300 cycles [76,77]. However, The specific energy is rather low due to the low voltage. Moreover, stability of AQ/ AQH2 in the acid is problematic (cf. Section 2). p-Benzoquinone caimot be used because of its anodic instability, and employment of the heavier chloranil is raises... 

Many commodity prices exhibit cyclic behavior due to the investment cycle, so in some cases nonlinear models can be used, as in Figure 6.4c. Unfortunately, both the amplitude and the frequency of the price peaks usually vary somewhat erratically, making it difficult to fit the cyclic price behavior with simple wave models or even advanced Fourier transform methods. 

However, RF sequences exist that exhibit non-cyclic behavior. In the following we will refer to cyclic cases only. 

Pendulums were more accurate, followed by quartz oscillators. In 1880, Pierre and Jacques Curie discovered that sending a current through a quartz crystal could result in a resonance situation with cyclic behavior, making a quartz oscillator that could be used to mark time. Because crystals grow in miniature, quartz crystal watches became the standard in the 1960s. But the periodic nature of resonant quartz excitations depends on the shape of each crystal as well as the ambient temperature and humidity. Every crystal behaves differently, and none can constitute a reputable standard for the accuracy needed by global positioning systems, for example. 

In addition to bistability, the situation in which any of three stable states can be reached depending on the initial conditions -tristability- has also been reported in chemical systems (Orban et al., 1982). One can also have multistability among different types of cyclic behavior (Goldbeter, 1995) and other types of dynamics. 

This bi-modal nature of Mahogany Zone shale is consistent with the observations of Bradley (6). In this classic work Bradley noted the distinct cyclic behavior of accumulations of a lean marlstone and a rich oil shale. As previously noted, the cyclic accumulations were correlated with the earth s orbit and subsequent weather cycles. Since the cycles were detected at... 

Atmospheric Gases Cumulative versus Cyclic Behavior... 

The planktonic foraminiferal response during the late Pliocene event shows the cyclic behavior, but not the overall increase recorded by the benthic foraminifera. As with the middle Miocene shift, the late Pliocene increase represents the cyclic buildup of ice sheets accompanied by deep water cooling. The tropical surface water temperatures, however, varied between 26 and 28°C. 

The change in combustion activity, from the high rate in the absence of NO, to the low rate in the presence of NO, was monitored in several consecutive cycles. The methane conversion was measured as a function of time over a 0.3 wt% Pd/ H-ZSM-5 sample while the NO flow was switched on and off. The CH4 and O2 concentrations were kept constant at 7440 ppm and 1.87%, respectively, while the NO concentration was switched from 3560 ppm to zero in several cycles. As shown in Figure 14, at 6900 GHSV, the catalyst had a high combustion activity in the absence of NO, but when the NO flow was turned on, the combustion activity drastically dropped to about 20%, as the NO conversion increased to 60% in 20 min. The catalyst regained its combustion activity as the NO flow was interrupted again, and it dropped once more when NO was reintroduced. This cyclic behavior indicates that the transformation associated with the presence of NO is reversible. 

The authors acknowledge the provision of friction stir processed materials and data on monotonic and cyclic behavior of the NiAl bronze by M.W. Mahoney and C.B. Fuller, Rockwell Scientific Corporation. The Naval Surface Warfare Center (Carderock, MD) supplied the NiAl bronze materials, and the Defense Advanced Research Projects Agency (DARPA), with Dr. L. Christodolou as program sponsor, provided the funding for this work. 

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