Synchrotron X-ray microtomography and multifractal analysis for the characterization of pore structure and distribution in softwood pellet biochar

Biochar pores in the micrometer range (1–100 µm) derive from cellular structures of the plant biomass subjected to pyrolysis or can be the result of mechanical processing, such as pelleting. In this study, synchrotron X-ray microtomography was used to investigate the internal pore structure of softwood pellet biochar produced by slow pyrolysis at 550 and 700 °C. The microtomographic data sets consisted of 2025 images of 2560 × 2560 voxels with a voxel side length of 0.87 µm. The three-dimensional reconstructions revealed that pelleting and pyrolysis significantly altered the pore structures of the wood feedstock, creating a network of connected pores between fragments that resembled the wood morphology. While higher pyrolysis temperature increased the specific surface area (as determined by BET nitrogen adsorption), it did not affect the total observed porosity. Multifractal analysis was applied to assess the characteristics of the frequency distribution of pores along each of the three dimensions of reconstructed images of five softwood pellet biochar samples. The resulting singularity and Rényi spectra (generalized dimensions) indicated that the distribution of porosity had monofractal scaling behavior, was homogeneous within the analyzed volumes and consistent between replicate samples. Moreover, the pore distributions were isotropic (direction-independent), which is in strong contrast with the anisotropic pore structure of wood. As pores at the scale analyzed in this study are relevant, for example, for the supply of plant accessible water and habitable space for microorganisms, our findings combined with the ability to reproduce biochar with such pore distribution offer substantial advantages in various biochar applications.

Generalized fractal dimensions of invariant measures of full-shift systems over compact and perfect spaces: generic behavior

In this paper, we show that, for topological dynamical systems with a dense set (in the weak topology) of periodic measures, a typical (in Baire’s sense) invariant measure has, for each q > 0 {q>0} , zero lower q-generalized fractal dimension. This implies, in particular, that a typical invariant measure has zero upper Hausdorff dimension and zero lower rate of recurrence. Of special interest is the full-shift system ( X , T ) {(X,T)} (where X = M ℤ {X=M^{\mathbb{Z}}} is endowed with a sub-exponential metric and the alphabet M is a compact and perfect metric space), for which we show that a typical invariant measure has, for each q > 1 {q>1} , infinite upper q-correlation dimension. Under the same conditions, we show that a typical invariant measure has, for each s ∈ ( 0 , 1 ) {s\in(0,1)} and each q > 1 {q>1} , zero lower s-generalized and infinite upper q-generalized dimensions.

Multiscale measures of phase-space trajectories

<p>Several attempts have been made in characterizing the multiscale nature of fluctuations from nonlinear and nonstationary time series. Particularly, the study of their fractal structure has made use of different approaches like the structure function analysis, the evaluation of the generalized dimensions, and so on. Here we report on a different approach for characterizing phase-space trajectories by using the empirical modes derived via the Empirical Mode Decomposition (EMD) method. We show how the derived Intrinsic Mode Functions (IMFs) can be used as source of local (in terms of scales) information allowing us in deriving multiscale measures when looking at the behavior of the generalized fractal dimensions at different scales. This formalism is applied to three pedagogical examples like the Lorenz system, the Henon map, and the standard map. We also show that this formalism is readily applicable to characterize both the behavior of the Earth’s climate during the past 5 Ma and the dynamical properties of the near-Earth electromagnetic environment as monitored by the SYM-H index.</p>

Entropy and Multifractality in Relativistic Ion-Ion Collisions

Entropy production in multiparticle systems is investigated by analyzing the experimental data on ion-ion collisions at AGS and SPS energies and comparing the findings with those reported earlier for hadron-hadron, hadron-nucleus, and nucleus-nucleus collisions. It is observed that the entropy produced in limited and full phase space, when normalized to maximum rapidity, exhibits a kind of scaling which is nicely supported by Monte Carlo model HIJING. Using Rényi’s order q information entropy, multifractal characteristics of particle production are examined in terms of generalized dimensions, Dq. Nearly the same values of multifractal specific heat, c, observed in hadronic and ion-ion collisions over a wide range of incident energies suggest that the quantity c might be used as a universal characteristic of multiparticle production in hadron-hadron, hadron-nucleus, and nucleus-nucleus collisions. The analysis is extended to the study of spectrum of scaling indices. The findings reveal that Rényi’s order q information entropy could be another way to investigate the fluctuations in multiplicity distributions in terms of spectral function f(α), which has been argued to be a convenient function for comparison sake not only among different experiments but also between the data and theoretical models.