Hamiltonian triangular refinements and space-filling curves

We have introduced here the concept of Hamiltonian triangular refinement. For any Hamiltonian triangulation it is shown that there is a refinement which is also a Hamiltonian triangulation and the corresponding Hamiltonian path preserves the nesting condition of the corresponding space-filling curve. We have proved that the number of such Hamiltonian triangular refinements is bounded from below and from above. The relation between Hamiltonian triangular refinements and space-filling curves is also explored and explained

Local refinement based on the 7-triangle longest-edge partition

The triangle longest-edge bisection constitutes an efficient scheme for refining a mesh by reducing the obtuse triangles, since the largest interior angles are subdivided. In this paper we specifically introduce a new local refinement for triangulations based on the longest-edge trisection, the 7-triangle longest-edge (7T-LE) local refinement algorithm. Each triangle to be refined is subdivided in seven sub-triangles by determining its longest edge. The conformity of the new mesh is assured by an automatic point insertion criterion using the oriented 1-skeleton graph of the triangulation and three partial division patterns

Growth and Guidance: A Study of Neuron Morphology and How it is Modified by Fractal and Euclidean Electrodes In Vitro.

For well over a century, neuroscientists have been studying the inherent ties between neuronal morphology and functionality. Santiago Ramón y Cajal, in his work that ultimately awarded him a Nobel Prize in 1906, established that neurons function as the fundamental unit of the nervous system. Ramón y Cajal himself recognized the relationship between neuronal form and function by proposing the wiring economy principle, which states that the nervous system’s complex network of neurons is efficiently wired in a way that minimizes wiring length. The research within this dissertation works towards the goal of optimizing the design of the electrode-neuron interface of medical implants by building upon Ramón y Cajal’s foundational ideas and integrating them with the techniques of fractal analysis.The dissertation begins by addressing the question of how electrode geometry impacts the morphology of the networks of neurons and glia interfacing with the electrode. This was done by interacting dissociated mouse retinal cell cultures in vitro with vertically aligned carbon nanotube (VACNT) electrodes grown on a silicon dioxide (SiO2) substrate and patterned into Euclidean and fractal geometries. The VACNT-SiO2 material system was shown to perform exceptionally well at guiding neurons onto the VACNTs and glia onto the surrounding SiO2. Furthermore, the electrode geometries that performed the best at supporting a healthy network of neurons and glia were those that balanced providing a large VACNT electrode area with maintaining connectedness in the surrounding SiO2 surface and allowing it to interpenetrate the VACNT electrode. Following these in vitro experiments, three-dimensional models of pyramidal neurons from the CA1 region of the rat hippocampus were reconstructed using confocal microscopy. The fractal properties of the neurons and how these relate to their functionality were then analyzed. It was then demonstrated that the natural, fractal behavior of the neurons, though limited in its scaling range, was sufficient to provide the neurons with an optimal balance between connectivity and building and operating costs. The dissertation concludes by reviewing the results of these studies, providing directions for future work, and discussing the implications regarding electrode design. This dissertation includes previously published co-authored material

Multi-scale active shape description in medical imaging

Shape description in medical imaging has become an increasingly important research field in recent years. Fast and high-resolution image acquisition methods like Magnetic Resonance (MR) imaging produce very detailed cross-sectional images of the human body - shape description is then a post-processing operation which abstracts quantitative descriptions of anatomically relevant object shapes. This task is usually performed by clinicians and other experts by first segmenting the shapes of interest, and then making volumetric and other quantitative measurements. High demand on expert time and inter- and intra-observer variability impose a clinical need of automating this process. Furthermore, recent studies in clinical neurology on the correspondence between disease status and degree of shape deformations necessitate the use of more sophisticated, higher-level shape description techniques. In this work a new hierarchical tool for shape description has been developed, combining two recently developed and powerful techniques in image processing: differential invariants in scale-space, and active contour models. This tool enables quantitative and qualitative shape studies at multiple levels of image detail, exploring the extra image scale degree of freedom. Using scale-space continuity, the global object shape can be detected at a coarse level of image detail, and finer shape characteristics can be found at higher levels of detail or scales. New methods for active shape evolution and focusing have been developed for the extraction of shapes at a large set of scales using an active contour model whose energy function is regularized with respect to scale and geometric differential image invariants. The resulting set of shapes is formulated as a multiscale shape stack which is analysed and described for each scale level with a large set of shape descriptors to obtain and analyse shape changes across scales. This shape stack leads naturally to several questions in regard to variable sampling and appropriate levels of detail to investigate an image. The relationship between active contour sampling precision and scale-space is addressed. After a thorough review of modem shape description, multi-scale image processing and active contour model techniques, the novel framework for multi-scale active shape description is presented and tested on synthetic images and medical images. An interesting result is the recovery of the fractal dimension of a known fractal boundary using this framework. Medical applications addressed are grey-matter deformations occurring for patients with epilepsy, spinal cord atrophy for patients with Multiple Sclerosis, and cortical impairment for neonates. Extensions to non-linear scale-spaces, comparisons to binary curve and curvature evolution schemes as well as other hierarchical shape descriptors are discussed

Fractal analyses of some natural systems

Fractal dimensions are estimated by the box-counting method for real world data sets and for mathematical models of three natural systems. 1 he natural systems are nearshore sea wave profiles, the topography of Shei-pa National Park in Taiwan, and the normalised difference vegetation index (NDV1) image of a fresh fern. I he mathematical models which represent the natural systems utilise multi-frequency sinusoids for the sea waves, a synthetic digital elevation model constructed by the mid-point displacement method for the topography and the Iterated Function System (IFS) codes for the fern leaf. The results show that similar fractal dimensions are obtained for discrete sub-sections of the real and synthetic one-dimensional wave data, whilst different fractal dimensions are obtained for discrete sections of the real and synthetic topographical and fern data. The similarities and differences are interpreted in the context of system evolution which was introduced by Mandelbrot (1977). Finally, the results for the fern images show that use of fractal dimensions can successfully separate void and filled elements of the two-dimensional series

Non-Linear Lattice

The development of mathematical techniques, combined with new possibilities of computational simulation, have greatly broadened the study of non-linear lattices, a theme among the most refined and interdisciplinary-oriented in the field of mathematical physics. This Special Issue mainly focuses on state-of-the-art advancements concerning the many facets of non-linear lattices, from the theoretical ones to more applied ones. The non-linear and discrete systems play a key role in all ranges of physical experience, from macrophenomena to condensed matter, up to some models of space discrete space-time

Two Phase Flow, Phase Change and Numerical Modeling

The heat transfer and analysis on laser beam, evaporator coils, shell-and-tube condenser, two phase flow, nanofluids, complex fluids, and on phase change are significant issues in a design of wide range of industrial processes and devices. This book includes 25 advanced and revised contributions, and it covers mainly (1) numerical modeling of heat transfer, (2) two phase flow, (3) nanofluids, and (4) phase change. The first section introduces numerical modeling of heat transfer on particles in binary gas-solid fluidization bed, solidification phenomena, thermal approaches to laser damage, and temperature and velocity distribution. The second section covers density wave instability phenomena, gas and spray-water quenching, spray cooling, wettability effect, liquid film thickness, and thermosyphon loop. The third section includes nanofluids for heat transfer, nanofluids in minichannels, potential and engineering strategies on nanofluids, and heat transfer at nanoscale. The forth section presents time-dependent melting and deformation processes of phase change material (PCM), thermal energy storage tanks using PCM, phase change in deep CO2 injector, and thermal storage device of solar hot water system. The advanced idea and information described here will be fruitful for the readers to find a sustainable solution in an industrialized society

Synthesis, Characterisation and Device Application of Silicon Nanoparticles produced by Mechanical Attrition

Nanostructured silicon is a promising materials for research because it serves as building blocks for nanotechnological applications, such as nano and quantum electronics, sensors and energy applications. However, many of the synthesis methods come with an increased level of sophistication, and thus the unit cost of material produced is high. The study shows that cheap and mass production of silicon nanoparticles can be achieved e ciently with a topdown process of mechanical attrition, particularly using an orbital pulveriser. The inclusion of the powder in a polymeric binder resulted in a new class of nanocomposite whose electrical properties are promising for devise applications using simple printing processes. Scanning and transmission electron microscopy studies reveal that the powders consist of a wide range of size and shape distribution, with large faceted particles with sizes between 1 ô 3 m and relatively small particles of sizes 40ô100nm. The variation of the average particle size with milling time ts well with a rst order exponential decay model which was used to evaluate the limiting particle size as about 120nm. The structural properties of the nanocomposites was investigated using small angle X-ray scattering, while the electrical properties were investigated by conducting I ô V measurements on a metal-nanocomposite-metal structure. Further tests for electronic properties like eld e ect mobilities were achieved by using the nanocomposite as the active layer in an insulated gate eld e ect transistor structure. Electrical characterisation reveals that the carrier injection and transport is determined by two main factors: the concentration of particles constituting the composite, and the level of external bias voltage on the structure. The nanocomposite systems show a clear percolation threshold for charge conduction. Below the percolation threshold, transport is mainly limited by the matrix or insulating binding medium. Direct tunneling and eld emission (FE) are the major transport mechanism for all concentrations at low voltages, while thermally activated processes, such as hopping and thermionic emission are major contributors at low concentrations. At higher concentrations and eld, Poole-Frenkel and Richardson-Schottky conduction mechanisms, resulting from barrier limiting process in the interface, of the metal contact to an interfacial insulator is dominant. Similar pronounced contribution from space charge limited current process resulting from accumulation of charges at the interface, and traps in the bulk, is pronounced at concentrations above the percolation threshold. The transistors function as ambipolar devices, where the dominance of either carrier is deteri mined by the sign and swing direction of the gate potential. The best transistors fabricated have a hole mobility of 2:63 10ô5cm2=V s and electron mobility 7:81 10ô7cm2=V s

Geomorphometry 2020. Conference Proceedings

Geomorphometry is the science of quantitative land surface analysis. It gathers various mathematical, statistical and image processing techniques to quantify morphological, hydrological, ecological and other aspects of a land surface. Common synonyms for geomorphometry are geomorphological analysis, terrain morphometry or terrain analysis and land surface analysis. The typical input to geomorphometric analysis is a square-grid representation of the land surface: a digital elevation (or land surface) model. The first Geomorphometry conference dates back to 2009 and it took place in Zürich, Switzerland. Subsequent events were in Redlands (California), Nánjīng (China), Poznan (Poland) and Boulder (Colorado), at about two years intervals. The International Society for Geomorphometry (ISG) and the Organizing Committee scheduled the sixth Geomorphometry conference in Perugia, Italy, June 2020. Worldwide safety measures dictated the event could not be held in presence, and we excluded the possibility to hold the conference remotely. Thus, we postponed the event by one year - it will be organized in June 2021, in Perugia, hosted by the Research Institute for Geo-Hydrological Protection of the Italian National Research Council (CNR IRPI) and the Department of Physics and Geology of the University of Perugia. One of the reasons why we postponed the conference, instead of canceling, was the encouraging number of submitted abstracts. Abstracts are actually short papers consisting of four pages, including figures and references, and they were peer-reviewed by the Scientific Committee of the conference. This book is a collection of the contributions revised by the authors after peer review. We grouped them in seven classes, as follows: • Data and methods (13 abstracts) • Geoheritage (6 abstracts) • Glacial processes (4 abstracts) • LIDAR and high resolution data (8 abstracts) • Morphotectonics (8 abstracts) • Natural hazards (12 abstracts) • Soil erosion and fluvial processes (16 abstracts) The 67 abstracts represent 80% of the initial contributions. The remaining ones were either not accepted after peer review or withdrawn by their Authors. Most of the contributions contain original material, and an extended version of a subset of them will be included in a special issue of a regular journal publication