Fractal Analysis

Fractal analysis is becoming more and more common in all walks of life. This includes biomedical engineering, steganography and art. Writing one book on all these topics is a very difficult task. For this reason, this book covers only selected topics. Interested readers will find in this book the topics of image compression, groundwater quality, establishing the downscaling and spatio-temporal scale conversion models of NDVI, modelling and optimization of 3T fractional nonlinear generalized magneto-thermoelastic multi-material, algebraic fractals in steganography, strain induced microstructures in metals and much more. The book will definitely be of interest to scientists dealing with fractal analysis, as well as biomedical engineers or IT engineers. I encourage you to view individual chapters

Numerical Simulation and Characterisation of the Packing of Granular Materials

The scientific problems related to granular matter are ubiquitous. It is currently an active area of research for physicists and earth scientists, with a wide range of applications within the industrial community. Simple analogue experiments exhibit behaviour that is neither predicted nor described by any current theory. The work presented here consists of modelling granular media using a two-dimensional combined Finite-Discrete Element Method (FEM-DEM). While computationally expensive, as well as modelling accurately the dynamic interactions between independent and arbitrarily shaped grains, this method allows for a complete description of the stress state within individual grains during their transient motion. After a detailed description of FEM-DEM principles, this computational approach is used to investigate the packing of elliptical particles. The work is aimed at understanding the influence of the particle shape (the ellipse aspect ratio) on the emergent properties of the granular matrix such as the particle coordination number and the packing density. The diff erences in microstructure of the resultant packing are analysed using pair correlation functions, particle orientations and pore size distributions. A comparison between frictional and frictionless systems is carried out. It shows great diff erences not only in the calculated porosity and coordination number, but also in terms of structural arrangement and stress distribution. The results suggest that the particle's shape a ffects the structural order of the particle assemblage, which itself controls the stress distribution between the pseudo-static grains. The study then focuses on describing the stress patterns or \force chains" naturally generated in a frictional system. An algorithm based on the analysis of the contact force network is proposed and applied to various packs in order to identify the force chains. A statistical analysis of the force chains looking at their orientation, length and proportion of the particles that support the loads is then performed. It is observed that force chains propagate less efficiently and more heterogeneously through granular systems made of elliptical particles than through systems of discs and it is proposed that structural diff erences due to the particle shape lead to a signifi cant reduction in the length of the stress path that propagates across connected particles. Finally, the e ffect of compression on the granular packing, the emergent properties and the contact force distribution is examined. Results show that the force network evolves towards a more randomly distributed system (from an exponential to a Gaussian distribution), and it confi rms the observations made from simulations using discs. To conclude, the combined finite-discrete element method applied to the study of granular systems provides an attractive modelling strategy to improve the knowledge of granular matter. This is due to the wide range of static and dynamic problems that can be treated with a rigorous physical basis. The applicability of the method was demonstrated through to a variety of problems that involve di fferent physical processes modelled with the FEM-DEM (internal deformations, fracture, and complex geometry). With the rapid extension of the practical limits of computational models, this work emphasizes the opportunity to move towards a modern generation of computer software to understand the complexity of the phenomena associated with discontinua

Light in correlated disordered media

The optics of correlated disordered media is a fascinating research topic emerging at the interface between the physics of waves in complex media and nanophotonics. Inspired by photonic structures in nature and enabled by advances in nanofabrication processes, recent investigations have unveiled how the design of structural correlations down to the subwavelength scale could be exploited to control the scattering, transport and localization of light in matter. From optical transparency to superdiffusive light transport to photonic gaps, the optics of correlated disordered media challenges our physical intuition and offers new perspectives for applications. This article reviews the theoretical foundations, state-of-the-art experimental techniques and major achievements in the study of light interaction with correlated disorder, covering a wide range of systems -- from short-range correlated photonic liquids, to L\'evy glasses containing fractal heterogeneities, to hyperuniform disordered photonic materials. The mechanisms underlying light scattering and transport phenomena are elucidated on the basis of rigorous theoretical arguments. We overview the exciting ongoing research on mesoscopic phenomena, such as transport phase transitions and speckle statistics, and the current development of disorder engineering for applications such as light-energy management and visual appearance design. Special efforts are finally made to identify the main theoretical and experimental challenges to address in the near future.Comment: Submitted to Reviews of Modern Physics. Feedbacks are welcom

Multiscale modeling of segregation in granular flows

Modeling and simulation of segregation phenomena in granular flows are investigated. Computational models at different scales ranging from particle level (microscale) to continuum level (macroscale) are employed in order to determine the important microscale physics relevant to macroscale modeling. The capability of a multi-fluid model to capture segregation caused by density difference is demonstrated by simulating grain-chaff biomass flows in a laboratory-scale air column and in a combine harvester. The multi-fluid model treats gas and solid phases as interpenetrating continua in an Eulerian frame. This model is further improved by incorporating particle rotation using kinetic theory for rapid granular flow of slightly frictional spheres. A simplified model is implemented without changing the current kinetic theory framework by introducing an effective coefficient of restitution to account for additional energy dissipation due to frictional collisions. The accuracy of predicting segregation rate in a gas-fluidized bed is improved by the implementation. This result indicates that particle rotation is important microscopic physics to be incorporated into the hydrodynamic model. Segregation of a large particle in a dense granular bed of small particles under vertical vibration is studied using molecular dynamics simulations. Wall friction is identified as a necessary condition for the segregation. Large-scale force networks bearing larger-than-average forces are found with the presence of wall friction. The role of force networks in assisting rising of the large particle is analyzed. Single-point force distribution and two-point spatial force correlation are computed. The results show the heterogeneity of forces and a short-range correlation. The short correlation length implies that even dense granular flows may admit local constitutive relations. A modified minimum spanning tree (MST) algorithm is developed to asymptotically recover the force statistics in the force networks. This algorithm provides a possible route to constructing a continuum model with microstructural information supplied from it. Microstructures in gas fluidized beds are also analyzed using a hybrid method, which couples the discrete element method (DEM) for particle dynamics with the averaged two-fluid (TF) equations for the gas phase. Multi-particle contacts are found in defluidized regions away from bubbles in fluidized beds. The multi-particle contacts invalidate the binary-collision assumption made in the kinetic theory of granular flows for the defluidized regions. Large ratios of contact forces to drag forces are found in the same regions, which confirms the relative importance of contact forces in determining particle dynamics in the defluidized regions