Helical Fluctuations, Fractal Dimensions and Path Integral in the Theory of Turbulence

1986 ◽  
pp. 82-104 ◽  
Author(s):  
E. Levich
Keyword(s):  
Path Integral ◽  
Fractal Dimensions

Fractal dimensions of dynamically triangulated random surfaces

1992 ◽  
Vol 2 (12) ◽  
pp. 2181-2190 ◽  
Author(s):  
Christian Münkel ◽  
Dieter W. Heermann
Keyword(s):  
Fractal Dimensions ◽  
Random Surfaces

Structure characterization of ground calcium carbonate flocs by fractal analysis and their effects on handsheet properties

TAPPI Journal ◽  
2013 ◽  
Vol 12 (3) ◽  
pp. 17-23 ◽  
Author(s):  
WANHEE IM ◽  
HAK LAE LEE ◽  
HYE JUNG YOUN ◽  
DONGIL SEO
Keyword(s):  
Fractal Analysis ◽  
Structural Characteristics ◽  
Fractal Dimensions ◽  
Strength Loss ◽  
Structure Characterization ◽  
Uniform Size ◽  
Cross Sectional ◽  
Floc Size ◽  
Mass Fractal ◽  
Handsheet Properties

Preflocculation of filler particles before their addition to pulp stock provides the most viable and practical solution to increase filler content while minimizing strength loss. The characteristics of filler flocs, such as floc size and structure, have a strong influence on preflocculation efficiency. The influence of flocculant systems on the structural characteristics of filler flocs was examined using a mass fractal analysis method. Mass fractal dimensions of filler flocs under high shear conditions were obtained using light diffraction spectroscopy for three different flocculants. A single polymer (C-PAM), a dual cationic polymer (p-DADMAC/C-PAM) and a C-PAM/micropolymer system were used as flocculants, and their effects on handsheet properties were investigated. The C-PAM/micropolymer system gave the greatest improvement in tensile index. The mass fractal analysis showed that this can be attributed to the formation of highly dense and spherical flocs by this flocculant. A cross-sectional analysis of the handsheets showed that filler flocs with more uniform size were formed when a C-PAM/micropolymer was used. The results suggest that a better understanding of the characteristics of preflocculated fillers and their influence on the properties of paper can be gained based on a fractal analysis.

Vapour Pressure Isotope Effect on Evaporation from Pure Organic Phases - a PIMD Approach

2020 ◽  
Author(s):  
Luis Vasquez ◽  
Agnieszka Dybala-Defratyka
Keyword(s):  
Path Integral ◽  
Vapour Pressure ◽  
Density Functional ◽  
Isotope Effects ◽  
Tight Binding ◽  
Decomposition Analysis ◽  
Energy Decomposition Analysis ◽  
Special Importance ◽  
Non Covalent Interactions ◽  
Covalent Interactions

<p></p><p>Very often in order to understand physical and chemical processes taking place among several phases fractionation of naturally abundant isotopes is monitored. Its measurement can be accompanied by theoretical determination to provide a more insightful interpretation of observed phenomena. Predictions are challenging due to the complexity of the effects involved in fractionation such as solvent effects and non-covalent interactions governing the behavior of the system which results in the necessity of using large models of those systems. This is sometimes a bottleneck and limits the theoretical description to only a few methods.<br> In this work vapour pressure isotope effects on evaporation from various organic solvents (ethanol, bromobenzene, dibromomethane, and trichloromethane) in the pure phase are estimated by combining force field or self-consistent charge density-functional tight-binding (SCC-DFTB) atomistic simulations with path integral principle. Furthermore, the recently developed Suzuki-Chin path integral is tested. In general, isotope effects are predicted qualitatively for most of the cases, however, the distinction between position-specific isotope effects observed for ethanol was only reproduced by SCC-DFTB, which indicates the importance of using non-harmonic bond approximations.<br> Energy decomposition analysis performed using the symmetry-adapted perturbation theory (SAPT) revealed sometimes quite substantial differences in interaction energy depending on whether the studied system was treated classically or quantum mechanically. Those observed differences might be the source of different magnitudes of isotope effects predicted using these two different levels of theory which is of special importance for the systems governed by non-covalent interactions.</p><br><p></p>

Rapid determination of fractal structure of bacterial assemblages in wastewater treatment: implications to process optimisation

1998 ◽  
Vol 38 (2) ◽  
pp. 9-15 ◽  
Author(s):  
J. Guan ◽  
T. D. Waite ◽  
R. Amal ◽  
H. Bustamante ◽  
R. Wukasch
Keyword(s):  
Wastewater Treatment ◽  
Fractal Structure ◽  
Structural Information ◽  
Rapid Determination ◽  
Fractal Dimensions ◽  
Structure Information ◽  
Treatment Processes ◽  
On Line ◽  
Bacterial Aggregates

A rapid method of determining the structure of aggregated particles using small angle laser light scattering is applied here to assemblages of bacteria from wastewater treatment systems. The structure information so obtained is suggestive of fractal behaviour as found by other methods. Strong dependencies are shown to exist between the fractal structure of the bacterial aggregates and the behaviour of the biosolids in zone settling and dewatering by both pressure filtration and centrifugation methods. More rapid settling and significantly higher solids contents are achievable for “looser” flocs characterised by lower fractal dimensions. The rapidity of determination of structural information and the strong dependencies of the effectiveness of a number of wastewater treatment processes on aggregate structure suggests that this method may be particularly useful as an on-line control tool.

scholarly journals Impact of Coseismic Frictional Melting on Particle Size, Shape Distribution and Chemistry of Experimentally-Generated Pseudotachylite

2020 ◽  
Vol 8 ◽  
Author(s):  
Leny Montheil ◽  
Virginia G. Toy ◽  
James M. Scott ◽  
Thomas M. Mitchell ◽  
David P. Dobson
Keyword(s):  
Particle Size ◽  
Host Rock ◽  
Fractal Dimensions ◽  
Rock Composition ◽  
Slip Rates ◽  
Shape Distribution ◽  
Frictional Behavior ◽  
Particle Size And Shape ◽  
Frictional Melting ◽  
Glass Compositions

In natural friction melts, or pseudotachylites, clast textures and glass compositions can influence the frictional behavior of faults hosting pseudotachylites, and are, in turn, sensitive to the processes involved in pseudotachylite formation. Quantification of these parameters in situations where the host rock composition and formation conditions are well-constrained, such as analogue experiments, may yield calibrations that can be employed in analysis of natural pseudotachylites. In this paper, we experimentally-generated pseudotachylites in granitoid rocks (tonalite and Westerly granite) at Pconf = 40 MPa and slip rates of ∼0.1 m s−1, comparable to the conditions under which natural pseudotachylite is known to form in Earth’s upper crust. We find variations in both clast textures and glass compositions that reflect formation processes, and probably influence the frictional behavior of similar natural faults hosting pseudotachylite. Quantification of particle size and shape distribution with a semi-automatic image analysis method, combined with analysis of glass and host-rock composition of these experimentally generated pseudotachylites, reveals that the textures of pseudotachylite material evolved by combinations of 1) comminution, 2) heterogeneous frictional flash melting, and 3) homogeneous (diffusive) clast melting and/or marginal decrepitation. Fractal dimensions of pseudotachylite-hosted clasts (D ∼ 3) that are greater than those of marginal fragmented host rock particles (gouge, D ∼ 2.4), reflect an increase of the intensity of comminution by slip localisation during a pre-melting phase. Chemical analyses demonstrate that these pseudotachylite glasses were generated by frictional flash melting, where host rock phases melt individually. Biotite is the least resistant to melting, feldspar intermediate, and quartz is the most resistant. The peudotachylite glass generated in these experiments has an alkaline composition, is depleted in SiO2 compared to the bulk host-rock, and shows heterogeneous compositions in a single sample related to proximity to host-rock minerals. The percentage contributions of host rock phases to the melt, calculated by a mixing model, shows that glass compositions are dominated by plagioclase and biotite. Within the melt, margins of clasts were dissolved uniformly by diffusion and/or affected by marginal decrepitation, resulting in convex and round shapes with convexities averaging ∼0.8 and circularities averaging ∼0.65.

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