Influence of Aperture Distribution on Flow in Fractal-Fracture Networks

<p>While fractal models are often employed for describing the geometry of fracture networks, a constant aperture is mostly assigned to all the fractures when such models are flow simulated. While network geometry controls connectivity, it is fracture aperture that controls the conductivity of individual fractures as described by the well-known cubic-law. It would therefore be of practical interest to investigate flow patterns in a fractal-fracture network where the apertures also scale as a power-law in accordance to their position in the hierarchy of the fractal. A set of synthetic fractal-fracture networks and two well-connected natural fracture maps that belong to the same fractal system are used for this purpose. The former, with connectivity above the percolation threshold, are generated by spatially locating the fractured and un-fractured blocks in a deterministic and random manner. A set of sub-networks are generated from a given fractal-fracture map by systematically removing the smaller fracture segments. A streamline simulator based on Darcy's law is used for flow simulating the fracture networks, which are conceptualized as two-dimensional fracture continuum models. Porosity and permeability are assigned to a fracture within the continuum model based on its aperture value and there is nearly no matrix porosity or permeability. The recovery profiles and time-of-flight values for each network and its dominant sub-networks at different time steps are compared.</p><p>The results from both the synthetic networks and the natural maps show that there is no significant decrease in recovery in the dominant sub-networks of a given fractal-fracture network. It may therefore be concluded that in the case of such hierarchical fractal-fracture systems with scaled aperture, the smaller fractures do not significantly contribute to the fluid flow.</p><p><strong>Key-words: </strong>Fractal-fracture; Connectivity; Aperture; Dominant Sub-networks; Streamline Simulator; Recovery</p>

A New Image Encryption Algorithm with Cantor Diagonal Scrambling Based on the PUMCML System

In this paper, a new spatiotemporal chaotic Parameter Uncertainty Mixed Coupled Map Lattice (PUMCML) is proposed. The Cantor diagonal matrix is generated from the Cantor set, and the ordered rotation scrambling strategy for this matrix is used to generate the scrambled image. Cantor set is a fractal system, so the Cantor set has a good effect on chaotic image encryption. The dynamic behavior of the PUMCML system is analyzed. The system has good chaotic property, so it is very suitable for chaotic image encryption. Using the PUMCML system, a diffusion strategy based on the mixture of Arnold and Logistic is proposed. Compared with other algorithms, the encryption effect of the proposed method is better and more secure.

PROPERTIES OF A COMPLEX DYNAMIC SYSTEM IN THE STRUCTURE OF WORDPLAY AND ITS TRANSLATION

The article studies structural characteristics of wordplay and ways of its translation from English into Russian. The research is a case study of wordplay translation in the lyrics of еру American rap artist Eminem. We argue that the theory of complex dynamic systems helps reveal the many aspects of wordplay. The vertical and horizontal axes of wordplay, the peculiarities of their use in the artist’s verses, as well as the difficulties of translating wordplay were considered. Any difficulties and differences that result from the translation process may be overcome if the language is viewed as a complex fractal system. It is concluded that the modern system approach provides a completely different conceptual framework for the linguist. The properties of a language as a dynamic system should be taken into account in wordplay investigation and wordplay translation to ensure adequate interpretation of the ideas meant by the author.

Linking temporal scales of suspended sediment transport in rivers: towards improving transferability of prediction

Purpose Suspended sediment (SS) transport in rivers is highly variable, making it challenging to develop predictive models that are applicable across timescales and rivers. Previous studies have identified catchment and hydro-meteorological variables controlling SS concentrations. However, due to the lack of long-term, high-frequency SS monitoring, it remains difficult to link SS transport dynamics during high-flow events with annual or decadal trends in SS transport. This study investigated how processes driving SS transport during high-flow events impact SS transport dynamics and trends observed over longer timescales. Methods Suspended sediment samples from the River Aire (UK) (1989–2017) were used to (i) statistically identify factors driving SS transport over multiple timescales (high-flow events, intra- and inter-annual) and (ii) conceptualize SS transport as a fractal system to help link and interpret the effect of short-term events on long-term SS transport dynamics. Results and discussion Antecedent moisture conditions were a dominant factor controlling event-based SS transport, confirming results from previous studies. Findings also showed that extreme high-flow events (in SS concentration or discharge) mask factors controlling long-term trends. This cross-timescale effect was conceptualized as high fractal power, indicating that quantifying SS transport in the River Aire requires a multi-timescale approach. Conclusion Characterizing the fractal power of a SS transport system presents a starting point in developing transferrable process-based approaches to quantify and predict SS transport, and develop management strategies. A classification system for SS transport dynamics in river systems in terms of fractal power could be developed which expresses the dominant processes underlying SS transport.

Clustering and Connectivity of Fractal-Fracture Networks: Are they related?

<p>It well known that fracture networks display self-similarity in many cases and the connectivity and flow behavior of such networks are influenced by their respective fractal dimensions. One of the authors have previously implemented the concept of lacunarity, a parameter that quantifies spatial clustering, to demonstrate that a set of 7 nested natural fracture maps belonging to a single fractal system, but different visual appearances have different clustering attributes. Any scale-dependency in the clustering of fractures will also likely have significant implications for flow processes that depend upon fracture connectivity. It is therefore important to address the question as to whether the fractal dimension serves as a reasonable proxy  for the connectivity of a fractal-fracture network or is it the lacunarity parameter that may be used instead. The present study attempts to address this issue by studying the clustering behavior (lacunarity) and connectivity of fractal-fracture patterns. We compare the set of 7 nested fracture maps mentioned earlier which belong to a single fractal system, in terms of their lacunarity and connectivity values. The results indicate that while the maps that have the same fractal dimension have almost similar connectivity values, there exist subtle differences such that both the connectivity and clustering change systematically with the scale at which the networks are mapped. It is further noted that there appears to be an exact correlation between clustering and connectivity values. Therefore, it may be concluded that rather than fractal dimension, it is the lacunarity or scale-dependent clustering attribute that control connectivity in fracture networks.</p>

Fractal-Like Flow-Fields with Minimum Entropy Production for Polymer Electrolyte Membrane Fuel Cells

The fractal-type flow-fields for fuel cell (FC) applications are promising, due to their ability to deliver uniformly, with a Peclet number Pe~1, the reactant gases to the catalytic layer. We review fractal designs that have been developed and studied in experimental prototypes and with CFD computations on 1D and 3D flow models for planar, circular, cylindrical and conical FCs. It is shown, that the FC efficiency could be increased by design optimization of the fractal system. The total entropy production (TEP) due to viscous flow was the objective function, and a constant total volume (TV) of the channels was used as constraint in the design optimization. Analytical solutions were used for the TEP, for rectangular channels and a simplified 1D circular tube. Case studies were done varying the equivalent hydraulic diameter (Dh), cross-sectional area (DΣ) and hydraulic resistance (DZ). The analytical expressions allowed us to obtain exact solutions to the optimization problem (TEP→min, TV=const). It was shown that the optimal design corresponds to a non-uniform width and length scaling of consecutive channels that classifies the flow field as a quasi-fractal. The depths of the channels were set equal for manufacturing reasons. Recursive formulae for optimal non-uniform width scaling were obtained for 1D circular Dh -, DΣ -, and DZ -based tubes (Cases 1-3). Appropriate scaling of the fractal system providing uniform entropy production along all the channels have also been computed for Dh -, DΣ -, and DZ -based 1D models (Cases 4-6). As a reference case, Murray’s law was used for circular (Case 7) and rectangular (Case 8) channels. It was shown, that Dh-based models always resulted in smaller cross-sectional areas and, thus, overestimated the hydraulic resistance and TEP. The DΣ -based models gave smaller resistances compared to the original rectangular channels and, therefore, underestimated the TEP. The DZ -based models fitted best to the 3D CFD data. All optimal geometries exhibited larger TEP, but smaller TV than those from Murray’s scaling (reference Cases 7,8). Higher TV with Murray’s scaling leads to lower contact area between the flow-field plate with other FC layers and, therefore, to larger electric resistivity or ohmic losses. We conclude that the most appropriate design can be found from multi-criteria optimization, resulting in a Pareto-frontier on the dependencies of TEP vs TV computed for all studied geometries. The proposed approach helps us to determine a restricted number of geometries for more detailed 3D computations and further experimental validations on prototypes.