Capacity Dimension

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Federico Maggi - One of the best experts on this subject based on the ideXlab platform.

  • a mesocosm experiment of suspended particulate matter dynamics in nutrient and biomass affected waters
    Water Research, 2016
    Co-Authors: Fiona H.m. Tang, Federico Maggi
    Abstract:

    An experimental study was conducted to test the hypothesis that the biomass growing after an increase in available nutrient in an aquatic ecosystem affects the flocculation dynamics of suspended particulate matter (SPM). The experiment was carried out in a settling column equipped with a turbulence generating system, a water quality monitoring system, and an automated μPIV system to acquire micro photographs of SPM. Three SPM types were tested combinatorially at five turbulence shear rates, three nutrient concentrations, and three mineral concentrations. Analyses of experimental data showed that nutrient availability together with the presence of biomass increased the SPM size by about 60% at low shear as compared to nutrient- and biomass-free conditions; a lower increase was observed at higher shears. In contrast, only 2% lower fractal (Capacity) Dimension and nearly invariant settling velocity were observed than in nutrient- and biomass-free conditions. Likewise, SPM size and Capacity Dimension were found to be insensitive to the SPM concentration. Although limited to nearly homogeneous mineral mixes (kaolinite), these experimental findings not only reject the hypothesis that SPM in natural waters can be dealt with as purely mineral systems in all instances, but also anticipate that SPM dynamics in natural waters increasingly exposed to the threat of anthropogenic nutrient discharge would lead to an increased advective flow of adsorbed chemicals and organic carbon.

  • Reconstructing the fractal Dimension of granular aggregates from light intensity spectra
    Soft matter, 2015
    Co-Authors: Fiona H.m. Tang, Federico Maggi
    Abstract:

    There has been growing interest in using the fractal Dimension to study the hierarchical structures of soft materials after realising that fractality is an important property of natural and engineered materials. This work presents a method to quantify the internal architecture and the space-filling Capacity of granular fractal aggregates by reconstructing the three-Dimensional Capacity Dimension from their two-Dimensional optical projections. Use is made of the light intensity of the two-Dimensional aggregate images to describe the aggregate surface asperities (quantified by the perimeter-based fractal Dimension) and the internal architecture (quantified by the Capacity Dimension) within a mathematical framework. This method was tested on control aggregates of diffusion-limited (DLA), cluster-cluster (CCA) and self-correlated (SCA) types, stereolithographically-fabricated aggregates, and experimentally-acquired natural sedimentary aggregates. Statistics of the reconstructed Capacity Dimension featured correlation coefficients R ≥ 98%, residuals NRMSE ≤ 10% and percent errors PE ≤ 4% as compared to controls, and improved earlier approaches by up to 50%.

  • Effect of variable fractal Dimension on the floc size distribution of suspended cohesive sediment
    Journal of Hydrology, 2007
    Co-Authors: Federico Maggi, Francesca Mietta, Johan C. Winterwerp
    Abstract:

    Flocculation of suspended cohesive sediment, well-known to impact the floc size distribution and vertical fluxes, and cause morphodynamic changes of marine and riverine environments, is modelled by means of a population balance equation that implements a novel description of floc geometry: the Capacity Dimension of fractal flocs, normally assumed constant over the population, has recently been argued to change during flocculation. Our experiments have shown that a power-law function of the Dimensionless floc size can conveniently be used to describe these changes. This description of floc Capacity Dimension is used to explore in detail the extent to which the geometrical properties of flocs affect aggregation and breakup processes, and contribute to shaping their size distribution. A comparison of experimental floc size distributions from settling column test with computed distributions for two hypotheses of floc Capacity Dimension (i.e., constant and variable) and two hypotheses of flocculation reactions (i.e., semi-stochastic and deterministic) are shown. This suggests that the use of variable rather than constant floc Capacity Dimension, and the use of semi-stochastic and asymmetric reactions rather than deterministic and symmetric, result in better predictions of the floc size distribution in the environmental conditions herein analysed.

  • Extraction of the 3-D Capacity Dimension from 2-D projections of fractal flocs
    2003
    Co-Authors: Federico Maggi
    Abstract:

    The optical measurements of flocs foreseen in the settling column are 2-D projections of 3-D fractal structures formed in a turbulent environment by means of aggregation and break-up processes. Based on numerical analysis, the resulting structures appear non-homogenous fractals with a full spectrum of fractal Dimensionalities, MAGGI(2002). The Dimensionality that possesses a high value in our investigation is the Capacity Dimension. It relates to the floc mass and, therefore, it is directly usable in modelling the settling velocity, WINTERWERP (1999), and many other geometrical properties. On the other hand, we have noticed that the spectrum of fractal Dimensionalities can give indications on the rate of growth of the flocs and on the dynamics of the processes involved in flocculation, MAGGI (2002). Despite the easy computation of all Dimensionalities within the space of projection, the evaluation of the 3-D Capacity Dimension of the flocs from 2-D projections is still an open question. Complications arise because there is not yet a full theory which covers the problem of n-Dimensional projections of fractals embedded in an m-Dimensional domain. Little knowledge exists about how a project ion of a fractal affects the Capacity Dimension and, moreover, the full spectrum of fractal Dimensionalities. This investigation is focused on the numerical characterisation of the fractal structure of unknown objects from their projections. The main reason to approach this problem is the considerable consequence of a direct extraction of 3-D information from 2-D measurements in the modelling of cohesive aggregates. Even if the problem could be reducible to an empirical estimation of the relation (and correlation) between the Dimensions of two sets (the 3-D original set and the 2-D projected set), we still must explore theoretical research in literature. In the light of this, we discuss and investigate the problem of projections and cross-sections of 3-D fractals into a 2-D Euclidian space. In particular, we show the uncertainty when computing analytically the Capacity Dimension of 3-D fractals from 2-D projections. Subsequently, we perform two series of numerical experiments in order to show that the theory can be rigorously applied to a specific class of fractals (homogeneously distributed within the domain) and that, for fractal aggregates such as mud flocs (non-homogeneously distributed) the theory yields distorted results with respect to the numerical ones. We then establish whether we can apply it to our measurements or that we have to follow a different strategy. Next, we consider an empirical relation between a 2-D fractal (perimeter-based) Dimension of the projection and the 3-D Capacity Dimension of the aggregates, that are representative of mud flocs. We have learned that the theory is applicable to homogeneously distributed sets. For non-homogeneously distributed sets the numerical results diverge from the theory significantly. We have performed a numerical experiment to relate the 3-D Capacity Dimension and the perimeter-based Dimension of 2-D projections of artificially generated fractal flocs. We have observed that a hyperbolic-like correlation is well representative of the transformation of 3-D information into 2-D information. We have considered that this way to achieve information is independent from the length scales considered because the perimeter-based Dimension does not relate to any of the lengths, but rather to the resolution. The (theoretical and numerical) results herein discussed enable us to apply the knowledge here developed to the recordings of the flocs produced in the settling column.

Jiaying Zhai - One of the best experts on this subject based on the ideXlab platform.

  • change in soil particle size distribution and erodibility with latitude and vegetation restoration chronosequence on the loess plateau china
    International Journal of Environmental Research and Public Health, 2020
    Co-Authors: Jiaying Zhai, Wulan Entemake, Hongwei Xu, Yang Wu, Yahui Song, Qing Qu
    Abstract:

    Analyzing the dynamics of soil particle size distribution (PSD) and erodibility is important for understanding the changes of soil texture and quality after cropland abandonment. This study aimed to determine how restoration age and latitude affect soil erodibility and the multifractal Dimensions of PSD during natural recovery. We collected soil samples from grassland, shrubland, and forests with different restoration ages in the steppe zone (SZ), forest-steppe zone (FSZ), and forest zone (FZ). Various analyses were conducted on the samples, including multifractal analysis and erodibility analysis. Our results showed that restoration age had no significant effect on the multifractal Dimensions of PSD (Capacity Dimension (D0), information Dimension (D1), information Dimension/Capacity Dimension ratio (D1/D0), correlation Dimension (D2)), and soil erodibility. Multifractal Dimensions tended to increase, while soil erodibility tended to decrease, with restoration age. Latitude was negatively correlated with fractal Dimensions (D0, D2) and positively correlated with K and D1/D0. During vegetation restoration, restoration age, precipitation, and temperature affect the development of vegetation, resulting in differences in soil organic carbon, total nitrogen, soil texture, and soil enzyme activity, and by affecting soil structure to change the soil stability. This study revealed the impact of restoration age and latitude on soil erosion in the Loess Plateau.

Yafeng Wang - One of the best experts on this subject based on the ideXlab platform.

  • multifractal characteristics of soil particle size distribution under different land use types on the loess plateau china
    Catena, 2008
    Co-Authors: De Wang, Bojie Fu, Wenwu Zhao, Huifeng Hu, Yafeng Wang
    Abstract:

    Soil particle-size distribution (PSD) is one of the most important physical attributes due to its great influence on soil properties related to water movement, productivity, and soil erosion. The multifractal measures were useful tools in characterization of PSD in soils with different taxonomies. Land-use type largely influences PSD in a soil, but information on how this occurs for different land-use types is very limited. In this paper, multifractal Renyi Dimension was applied to characterize PSD in soils with the same taxonomy and different land-use types. The effects of land use on the multifractal parameters were then analyzed. The study was conducted on the hilly-gullied regions of the Loess Plateau, China. A Calcic Cambisols soil was sampled from five land-use types: woodland, shrub land, grassland, terrace farmland and abandoned slope farmland with planted trees (ASFP). The result showed that: (1) entropy Dimension (D-1) and entropy Dimension/Capacity Dimension ratio (D-1/D-0) were significantly positively correlated with finer particle content and soil organic matter. (2) D-0, D-1 and D-1/D-0 were significantly influenced by land use. Land use could explain 24.6-58.5% of variability of D-0, D-1/D-0 and D-1, which may be potential parameters to reflect soil physical properties and soil quality influenced by land use. (c) 2007 Elsevier B.V All rights reserved.

Seungkyu Ryu - One of the best experts on this subject based on the ideXlab platform.

  • Transportation network redundancy: Complementary measures and computational methods
    Transportation Research Part B: Methodological, 2018
    Co-Authors: Anthony Chen, Sarawut Jansuwan, Chao Yang, Seungkyu Ryu
    Abstract:

    Redundancy is vital for transportation networks to provide utility to users during disastrous events. In this paper, we develop two network-based measures for systematically characterizing the redundancy of transportation networks: travel alternative diversity and network spare Capacity. Specifically, the travel alternative diversity Dimension is to evaluate the existence of multiple modes and effective routes available for travelers or the number of effective connections between a specific origin-destination pair. The network spare Capacity Dimension is to quantify the network-wide residual Capacity with an explicit consideration of travelers’ mode and route choice behaviors as well as congestion effect. They can address two fundamental questions in the pre-disaster transportation system evaluation and planning, i.e., "how many effective redundant alternatives are there for travelers in the normal or disruptive event?" and "how much redundant Capacity does the network have?" To implement the two measures in practice, computational methods are provided to evaluate the network redundancy. Numerical examples are also presented to demonstrate the features of the two redundancy measures as well as the applicability of the computational methods. The analysis results reveal that the two measures have different characterizations on network redundancy from different perspectives, and they can complement each other by providing meaningful information to both travelers and planners.

Qing Qu - One of the best experts on this subject based on the ideXlab platform.

  • change in soil particle size distribution and erodibility with latitude and vegetation restoration chronosequence on the loess plateau china
    International Journal of Environmental Research and Public Health, 2020
    Co-Authors: Jiaying Zhai, Wulan Entemake, Hongwei Xu, Yang Wu, Yahui Song, Qing Qu
    Abstract:

    Analyzing the dynamics of soil particle size distribution (PSD) and erodibility is important for understanding the changes of soil texture and quality after cropland abandonment. This study aimed to determine how restoration age and latitude affect soil erodibility and the multifractal Dimensions of PSD during natural recovery. We collected soil samples from grassland, shrubland, and forests with different restoration ages in the steppe zone (SZ), forest-steppe zone (FSZ), and forest zone (FZ). Various analyses were conducted on the samples, including multifractal analysis and erodibility analysis. Our results showed that restoration age had no significant effect on the multifractal Dimensions of PSD (Capacity Dimension (D0), information Dimension (D1), information Dimension/Capacity Dimension ratio (D1/D0), correlation Dimension (D2)), and soil erodibility. Multifractal Dimensions tended to increase, while soil erodibility tended to decrease, with restoration age. Latitude was negatively correlated with fractal Dimensions (D0, D2) and positively correlated with K and D1/D0. During vegetation restoration, restoration age, precipitation, and temperature affect the development of vegetation, resulting in differences in soil organic carbon, total nitrogen, soil texture, and soil enzyme activity, and by affecting soil structure to change the soil stability. This study revealed the impact of restoration age and latitude on soil erosion in the Loess Plateau.