Stochastic analysis of a three‐phase fluidized bed: Fractal approach

Fan, Liang‐Shih; Neogi, D.; Yashima, M.; Nassar, Raja

doi:10.1002/aic.690361008

Cited by 111 publications

(51 citation statements)

References 19 publications

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“…., s, and y is a time value from 1 to u. The sample range of X(t) for lag s is: (3) and the sample variance of X(t) is: (4) giving the scaling relationship (Fan et al 1990):…”

Section: (T) = [B(t) -B(t -Dt)]mentioning

confidence: 99%

“…Fractal analysis was used to quantify the random nature of the time record of excurrent velocity as first proposed by Hurst et al (1947), quantified by Mandelbrot & Van Ness (1968), and simplified by Fan et al (1990). In the case of time record analysis, a fractal analysis yields a fractal dimension for the record between 1 and 2, with increasing values corresponding to a more space-filling record.…”

Section: Fractal Analysismentioning

confidence: 99%

“…., s, and y is a time value from 1 to u. The sample range of X(t) for lag s is: (3) and the sample variance of X(t) is: (4) giving the scaling relationship (Fan et al 1990):In practice, H was calculated via Eq. (5) using the slope of a least squares regression of a plot of versus the time lag, s (on log-log axes).…”

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confidence: 99%

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Unsteadiness of bivalve clam jet flow according to environmental conditions

Delavan¹,

Webster²

2011

Aquat. Biol.

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To determine whether hard clams Mercenaria mercenaria alter excurrent jet velocity as a function of environmental factors, this laboratory study quantified the excurrent jet velocity as a function of bulk mean crossflow velocity, density of clam patch, and clam size. The excurrent velocity was measured via the non-intrusive particle image velocimetry technique. The flow and unsteady patterns in the time records of vertical velocity near the tip of the excurrent siphon were analyzed by calculating the mean, variance, power spectral density, fractal dimension, lacunarity, and mean jet-to-crossflow ratio. The results revealed that clams vary their excurrent flow characteristics according to bulk mean crossflow velocity; in particular, the texture of the time record of velocity varied. Further, the jet-to-crossflow velocity ratio was larger for smaller clams, and the response of clams to the density of the clam patch was dependent on the size of the animal. These observed behaviors may impact the predation success of blue crabs Callinectes sapidus and knobbed whelks Busycon carica under various environmental conditions. In this context, the results indicated that blue crabs dominate the predator-prey system because of the dependence on clam size and bulk mean crossflow velocity. Alternatively, the varying clam excurrent siphon velocity behavior may provide hydrodynamic signaling of the clam patch recruitment status to settling larvae.KEY WORDS: Predator-prey · Olfactory predation · Jets-in-crossflow · Bivalve · Non-consumptive predator effects · Lacunarity Resale or republication not permitted without written consent of the publisherAquat Biol 13: [175][176][177][178][179][180][181][182][183][184][185][186][187][188][189][190][191] 2011 acteristics of the excurrent flow as a function of bulk mean crossflow velocity and clam size are of interest because the predators of this system, blue crabs and knobbed whelks, both consume clams and use olfactory navigation as a means of locating prey, but the turbulence regimes in which they are successful are highly disparate. Blue crabs are less successful predators during highly turbulent hydrodynamic conditions (Jackson et al. 2007). In contrast, knobbed whelks are successful in highly turbulent regimes (Ferner & Weissburg 2005). Also, blue crabs prefer clams of a small size range despite the fact that they can consume prey over a wide size range (Micheli 1995). Therefore, as clams increase in size, they become less susceptible to predation by blue crabs while maintaining their susceptibility to whelk predation. Thus, there may be alternate strategies for predator avoidance depending on the size of the clams and the turbulence regime of the environment in which they live.The influence of the density of the clam patch was also of interest because there may be predator avoidance strategies depending on the proximity of conspecifics. High-density patches may appear as one large, hard to eat prey to blue crabs, and small clams may have higher survival rates in these ...

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“…., s, and y is a time value from 1 to u. The sample range of X(t) for lag s is: (3) and the sample variance of X(t) is: (4) giving the scaling relationship (Fan et al 1990):…”

Section: (T) = [B(t) -B(t -Dt)]mentioning

confidence: 99%

Section: Fractal Analysismentioning

confidence: 99%

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Unsteadiness of bivalve clam jet flow according to environmental conditions

Delavan¹,

Webster²

2011

Aquat. Biol.

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“…Examples of different signal processing techniques are (i) analyses of variance and Fourier spectra (Fan etal., 1986), (ii) Hurst analysis or R/S analysis (Drahog et al, 1992;Fan et al, 1990), (iii) wavelet transformation and similar techniques, determining the instantaneous frequency. This technique was used by Bakshi et al (1995), based on a gas holdup signal, and by Hervieu and Seleghim (1995), based on a pressure signal.…”

Section: Introductionmentioning

confidence: 99%

Characterization of regimes and regime transitions in bubble columns by chaos analysis of pressure signals

Letzel

Schouten

Krishna

et al. 1997

Chemical Engineering Science

197

125

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“…Hence, it is highly desirable that we also understand the three-phase fluidized bed's microscopic or mesoscopic dynamic characteristics, such as pressure and bulk-density fluctuations, if robust operation and effective control are to be achieved (see, for example, Fan et al, 1990). Nevertheless, the majority of publications on three-phase fluidized beds are concerned with the deterministic, global or static properties of such beds (Ostergaard, 1971;Epstein, 1981Epstein, , 1983Muroyama and Fan, 1985).…”

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confidence: 98%