Fractal dimensions of aggregates determined from steady-state size distributions

1991 ◽  
Vol 25 (12) ◽  
pp. 2031-2038 ◽  
Author(s):  
Qing Jiang ◽  
Bruce E. Logan
Keyword(s):  
Steady State ◽  
Fractal Dimensions ◽  
Size Distributions ◽  
State Size

scholarly journals Steady-State Size Distributions in Probabilistic Models of the Cell Division Cycle

1985 ◽  
Vol 45 (4) ◽  
pp. 523-540 ◽  
Author(s):  
Kenneth B. Hannsgen ◽  
John J. Tyson ◽  
Layne T. Watson
Keyword(s):  
Steady State ◽  
Cell Division ◽  
Probabilistic Models ◽  
Cell Division Cycle ◽  
Size Distributions ◽  
State Size

scholarly journals Steady-state size distributions for collisional populations:

Icarus ◽  
2003 ◽  
Vol 164 (2) ◽  
pp. 334-345 ◽  
Author(s):  
David P. O'Brien ◽  
Richard Greenberg
Keyword(s):  
Steady State ◽  
Size Distributions ◽  
State Size

Fundamentals of Particle Flocculation and Removal From Water

1994 ◽  
Vol 344 ◽  
Author(s):  
Patrick T. Spicer ◽  
Sotiris E. Pratsinis
Keyword(s):  
Growth Rate ◽  
Steady State ◽  
Shear Rate ◽  
Aluminum Sulfate ◽  
Stirred Tank ◽  
Turbulent Shear ◽  
Size Distributions ◽  
Floc Size ◽  
Shear Rates ◽  
State Size

AbstractThe flocculation of polystyrene particles with aluminum sulfate or alum (Al2 (SO4)3) by turbulent shear was studied as a function of the applied shear rates (63–129 s−1) and flocculant concentrations (11 and 32 mg/L) in a stirred tank. Increasing the shear rate increased the floc growth rate but decreased the maximum attainable floc size. Increasing the concentration of alum increased the floc growth rate and the maximum floc size. A steady state between floc growth and breakage was attained after which the floc size distribution no longer changed. The normalized steady state size distributions allowed evaluation of the relative contributions of shear rate and flocculant concentration to the performance of the process.

Inference of barchan interaction properties from a comparison of theoretical modelling and observation

2021 ◽  
Author(s):  
Dominic Robson ◽  
Andreas Baas ◽  
Alessia Annibale
Keyword(s):  
Size Distribution ◽  
Mean Field ◽  
Theoretical Modelling ◽  
Size Distributions ◽  
Mean Field Model ◽  
Theoretical Understanding ◽  
Object Based ◽  
Mean Width ◽  
Barchan Dunes ◽  
State Size

<p>It is well known that barchan dunes are not isolated bedforms but are able to interact with one another both directly, through collisions and the emission/absorption of flux, and indirectly, due to the effects of turbulence in the wake of a dune.  In recent years, wave-tank experiments, continuum simulations, and cellular automata models have enabled researchers to model barchan-barchan interactions.  The findings from these studies have been fed into object-based models of entire fields of barchans and used to predict the size distributions.  Although there has been some success with these techniques, each model has failed to reproduce certain known properties on the field-scale; for instance, that the mean width is constant with downwind distance.  Furthermore, previous attempts have not been based on a theoretical understanding of the role of interactions in determining the dune size distribution, thus limiting their potential as universal models of barchan swarms.</p><p>Mean-field models are relatively simple in terms of the mathematics, but have shown some degree of success in the modelling of barchan fields, although previous work has  focused only on specific cases of interaction rules.  We have developed a more general mean-field model which can include many different forms of interaction, making it applicable to a variety of problems, including socio-economic systems as well as fields of interacting barchans.  Despite the generality of our model, we have been able to derive expressions for the dependence of the steady-state size distribution, and its moments, on the choice of interaction rules.  This means that, by making a measurement of the size distribution of a barchan field, we are able to infer properties of the interactions at play. </p><p>To demonstrate the power of such a model we have measured size distributions of several barchan fields in the area of Tarfaya, Morocco.  Measurements were made by recording locations of seven distinct points on each barchan to yield morphometric parameters of each dune and compile the size-distribution.  By comparing the distribution and its moments to those predicted by the model, we can infer certain properties of the interaction rules, such as the relative probabilities of the different forms of collision.  The results show an example of how our model provides a more comprehensive understanding of the way in which dune-dune interactions determine properties on the scale of the field. </p>

scholarly journals Improved Dynamic Light Scattering using an adaptive and statistically driven time resolved treatment of correlation data

2019 ◽  
Vol 9 (1) ◽  
Author(s):  
Alexander V. Malm ◽  
Jason C. W. Corbett
Keyword(s):  
Steady State ◽  
Light Scattering ◽  
Dynamic Light Scattering ◽  
Size Fraction ◽  
Power Relationship ◽  
Time Resolved ◽  
Size Fractions ◽  
Use Of Data ◽  
Primary Advantage ◽  
State Size

Abstract Dynamic Light Scattering (DLS) is a ubiquitous and non-invasive measurement for the characterization of nano- and micro-scale particles in dispersion. The sixth power relationship between scattered intensity and particle radius is simultaneously a primary advantage whilst rendering the technique sensitive to unwanted size fractions from unclean lab-ware, dust and aggregated & dynamically aggregating sample, for example. This can make sample preparation iterative, challenging and time consuming and often requires the use of data filtering methods that leave an inaccurate estimate of the steady state size fraction and may provide no knowledge to the user of the presence of the transient fractions. A revolutionary new approach to DLS measurement and data analysis is presented whereby the statistical variance of a series of individually analysed, extremely short sub-measurements is used to classify data as steady-state or transient. Crucially, all sub-measurements are reported, and no data are rejected, providing a precise and accurate measurement of both the steady state and transient size fractions. We demonstrate that this approach deals intrinsically and seamlessly with the transition from a stable dispersion to the partially- and fully-aggregated cases and results in an attendant improvement in DLS precision due to the shorter sub measurement length and the classification process used.

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