Fractal Analysis of Microstructural and Fractograpghic Images for Evaluation of Materials

Materials have hierarchically organized complex structures at different length scales. Quantitative description of material behaviour is dependent on four fundamental length scales [1], which are of concern to materials scientists. These are (1) nano scale, 1-103 nm, (2)micro scale, 1-10 3 μm, (3) macro scale, 1-103mm, and (4) global size scale, 1-106 m. While the nano scale corresponds to, often, highly ordered atomic structures, the global size scale relates geophysical phenomena and large man made engineering structures. Micro scale and macro scale correspond to size of material samples used in laboratories, for designing and for fabrication of miniature to small machineries

Characterizing the diffusional behavior and trafficking pathways of Kv2.1 using single particle tracking in live cells

2013 Spring.Includes bibliographical references.Studying the diffusion pattern of membrane components yields valuable information regarding membrane structure, organization, and dynamics. Single particle tracking serves as an excellent tool to probe these events. We are investigating of the dynamics of the voltage gated potassium channel, Kv2.1. Kv2.1 uniquely localizes to stable, micro-domains on the cell surface where it plays a non-conducting role. The work reported here examines the diffusion pattern of Kv2.1 and determines alternate functional roles of surface clusters by investigating recycling pathways using single particle tracking in live cells. The movement of Kv2.1 on the cell surface is found to be best modeled by the combination of a stationary and non-stationary process, namely a continuous time random walk in a fractal geometry. Kv2.1 surface structures are shown to be specialized platforms involved in trafficking of Kv channels to and from the cell surface in hippocampal neurons and transfected HEK cells. Both Kv2.1 and Kv1.4, a non-clustering membrane protein, are inserted and retrieved from the plasma membrane at the perimeter of Kv2.1 clusters. From the distribution of cluster sizes, using a Fokker-Planck formalism, we find there is no evidence of a feedback mechanism controlling Kv2.1 domain size on the cell surface. Interestingly, the sizes of Kv2.1 clusters are rather governed by fluctuations in the endocytic and exocytic machinery. Lastly, we pinpoint the mechanism responsible for inducing Kv2.1 non-ergodic dynamics: the capture of Kv2.1 into growing clathrin-coated pits via transient binding to pit proteins

Data-Centric Energy Efficient Adaptive Sampling Techniques for Wireless Pollution Sensor Networks

PhDAir pollution is one of the gravest problems being faced by modern world, and urban traffic emissions are the single major source of air pollution. This work is founded on collaboration with environmental scientists who need fine grained data to enable better understanding of pollutant distribution in urban street canyons. “Wireless sensor networks” can be used to deploy a significant number of sensors within a space as small as a single street canyon and capture simultaneous readings both in the time and space domain. Sensor energy management becomes the most critical constraints of such a solution, because of the energy hungry gas sensors. Hence, the main research objective addressed in this thesis is to propose novel temporal and spatial adaptive sampling techniques for wireless pollution sensor nodes that take into account the pollution data characteristics, and enable the sensor nodes to sample, only when, an important event happens to collect accurate statistics in as efficient a manner as possible. The major contributions of this thesis can be summarised as: 1) Better understanding of underlying pollution data characteristics (based on real datasets collected during pollution trials in Cyprus and India) using techniques from time series analysis and more advanced methods from multi-fractal analysis and nonlinear dynamical systems. 2)Proposal of novel adaptive temporal sampling algorithm called Exponential Double Smoothing based Adaptive Sampling (EDSAS) that exploits the presence of slowly decaying autocorrelations and local linear trends. The algorithm uses a time series prediction method based upon exponential double smoothing for irregularly sampled data. This algorithm has been compared against a random walk based stochastic scheduler called e-Sense and found to give better sampling performance. EDSAS has been extended to the spatial domain by incorporating distributed hierarchical agglomerative clustering mechanism. 3)Proposal of a novel spatial sampling algorithm called Nearest Neighbour based Adaptive Spatial Sampling (NNASS) that exploits the non-linear dynamics existing in pollution data to compute predictability measures to adapt the sampling intervals for the sensor nodes. NNASS has been compared against another spatial sampling algorithm called ASAP and found to give comparable or better sampling performance

Towards the Glass Transition in Vibrated Granular Matter

Granular materials are large sets of macroscopic particles that interact solely via contact forces. The static behavior depends on the contact network and on the surface friction forces between grains; when they are set in motion (typically by vibrations) their dynamics is dominated by inelastic collisions. For these reasons granular media show an extremely rich phenomenology, ranging from fluid-like properties (if strongly vibrated), to "jamming", glassy, behavior (if weakly vibrated), to aging and hysteretical phenomena observed when they become trapped in frozen, amorphous states. The objective of this work is to study these states and transitions, and to characterize the analogies found between the dynamic behavior of vibrated granular media and the glass transition observed in thermal glass-formers. These analogies justify the interest in granular materials, because granular media can be seen as simplified model systems useful in the study of out of equilibrium thermodynamics, and, in general, to the larger framework known as "complexity". The granular materials considered here are composed of spheric, polished glass spheres. Since the surface state plays an important role in the grain-grain interaction, some measurements were also performed with acid etched beads, having different surface roughness. The samples are vertically vibrated to achieve vibrofluidization. Different kinds of vibration are used, to highlight different properties of the system. We first consider the transition between the fluid and the subcooled glassy phase, using different experimental techniques. The most important one is a torsion oscillator, that interacts with the granular media via immersed probes. The torsion oscillator can be used in forced mode. A torque is applied on the probe, and we measure the mechanical response function (complex susceptibility). In general, a relaxation is found and it is interpreted as the signature of the irreversible energy loss (damping) in granular collisions. This relaxation has an intrinsic time scale, and systematic analysis of it shows that a clear parallel can be traced to the behavior of "strong" glasses. In particular, it is found that (i) the relaxation time is a function of a unified control parameter, proportional to the square root of the average vibration, and phenomenologically equivalent to an effective temperature; (ii) the functional form with which the relaxation times approach the final "frozen" state has an Arrhenius, or Vögel-Fulcher-Tamman (VFT) behavior. The same torsion oscillator is employed in free mode. In this case, no external torque is applied, and the probe moves adapting its position under the effect of the continuous rearrangements in the sample. The system is studied by computing the power spectral density of the (angular position) time series. The resulting spectra represent a "configurational noise" as the system randomly hops from one configuration to the following. This allows to define, using a completely different approach, the same intrinsic time scale observed in forced mode measurements. The comparison of the two techniques allows to obtain a more complete and detailed picture of the dynamics in the jamming region. From this comparison, it was inferred that the system is also influenced by an effective vibration frequency, and that the relaxation time has indeed a non-Arrhenius behavior as a function of a control parameter defined as as = √ Γ/ωs. A model was developed combining rheological observations to a statistic approach describing extremal phenomena. This model justifies the appearance of both the control parameter and the VFT evolution of the relaxation. Furthermore, the model is predictive and exposes the effect of a few other rheologic properties of granular system. The effect of surface roughness are considered, showing that the static and dynamic surface friction coefficients are well described by the model. A second relevant part of this work is devoted to an explicit verification that macroscopic probes act as Brownian objects. This fact is often used to interpret experimental data (also in the present work) and to propose theoretical model. However, no explicit evidence has ever been discussed. This is hard to do, using a constrained system such as the torsion oscillator, because the restoring coefficient influences the dynamics of diffusion. To overcome the problem we built a different apparatus, called "Brownian motor", where the probes are mounted on ball bearings, so that they are free to turn without constraint. The properties of the time series of the position of the free turning probe and of the torsionally constrained oscillator can finally be analyzed and compared with simple simulations. The data show an overall diffusion-like behavior, that is influenced by the presence of constraints. Using fractal analysis we estimate the diffusion, or Hurst exponent. This allows to verify that a "macroscopic" object (the probe) immersed in the "microscopic" granular medium indeed behaves as a Brownian object, and that its dynamics can be studied in detail, showing that it undergoes anomalous diffusion. This work is concluded with a discussion on a few possible developments. The most promising idea is a novel approach to the study of the geometrical properties of the contact network of granular assemblies, that is responsible for many of the properties of the granular sample. By using Magnetic Resonance Imaging, the static 3-D structure of granular media can be reconstructed with unprecedented accuracy, resolution and ease of reproducibility. From the spatial information we can extract all the properties of static granular media: the compaction factor, the grain-grain correlation function, the free volume and other observables. Systematic studies could allow experimental confirmations of the many theoretical models that have been proposed in the last years and that still lack a thorough comparison with experiments. This idea does not conclude the perspectives of this work, that are vast and intriguing. A few promising subjects are reviewed more into detail in the corresponding Perspective section. To name a few we cite: measurements of induced aging in non-vibrated samples, the Brownian motor, stick and slip phenomena and their comparison with earthquakes

Fractional Calculus and the Future of Science

Newton foresaw the limitations of geometry’s description of planetary behavior and developed fluxions (differentials) as the new language for celestial mechanics and as the way to implement his laws of mechanics. Two hundred years later Mandelbrot introduced the notion of fractals into the scientific lexicon of geometry, dynamics, and statistics and in so doing suggested ways to see beyond the limitations of Newton’s laws. Mandelbrot’s mathematical essays suggest how fractals may lead to the understanding of turbulence, viscoelasticity, and ultimately to end of dominance of the Newton’s macroscopic world view.Fractional Calculus and the Future of Science examines the nexus of these two game-changing contributions to our scientific understanding of the world. It addresses how non-integer differential equations replace Newton’s laws to describe the many guises of complexity, most of which lay beyond Newton’s experience, and many had even eluded Mandelbrot’s powerful intuition. The book’s authors look behind the mathematics and examine what must be true about a phenomenon’s behavior to justify the replacement of an integer-order with a noninteger-order (fractional) derivative. This window into the future of specific science disciplines using the fractional calculus lens suggests how what is seen entails a difference in scientific thinking and understanding

Telecommunications Networks

This book guides readers through the basics of rapidly emerging networks to more advanced concepts and future expectations of Telecommunications Networks. It identifies and examines the most pressing research issues in Telecommunications and it contains chapters written by leading researchers, academics and industry professionals. Telecommunications Networks - Current Status and Future Trends covers surveys of recent publications that investigate key areas of interest such as: IMS, eTOM, 3G/4G, optimization problems, modeling, simulation, quality of service, etc. This book, that is suitable for both PhD and master students, is organized into six sections: New Generation Networks, Quality of Services, Sensor Networks, Telecommunications, Traffic Engineering and Routing

Modelling and analysis of amplitude, phase and synchrony in human brain activity patterns

The critical brain hypothesis provides a framework for viewing the human brain as a critical system, which may transmit information, reorganise itself and react to external stimuli efficiently. A critical system incorporates structures at a range of spatial and temporal scales, and may be associated with power law distributions of neuronal avalanches and power law scaling functions. In the temporal domain, the critical brain hypothesis is supported by a power law decay of the autocorrelation function of neurophysiological signals, which indicates the presence of long-range temporal correlations (LRTCs). LRTCs have been found to exist in the amplitude envelope of neurophysiological signals such as EEG, EMG and MEG, which reveal patterns of local synchronisation within neuronal pools. Synchronisation is an important tool for communication in the nervous system and can also exist between disparate regions of the nervous system. In this thesis, inter-regional synchronisation is characterised by the rate of change of phase difference between neurophysiological time series at different neuronal regions and investigated using the novel phase synchrony analysis method. The phase synchrony analysis method is shown to recover the DFA exponents in time series where these are known. The method indicates that LRTCs are present in the rate of change of phase difference between time series derived from classical models of criticality at critical parameters, and in particular the Ising model of ferromagnetism and the Kuramoto model of coupled oscillators. The method is also applied to the Cabral model, in which Kuramoto oscillators with natural frequencies close to those of cortical rhythms are embedded in a network based on brain connectivity. It is shown that LRTCs in the rate of change of phase difference are disrupted when the network properties of the system are reorganised. The presence of LRTCs is assessed using detrended fluctuation analysis (DFA), which assumes the linearity of a log-log plot of detrended fluctuation magnitude. In this thesis it is demonstrated that this assumption does not always hold, and a novel heuristic technique, ML-DFA, is introduced for validating DFA results. Finally, the phase synchrony analysis method is applied to EEG, EMG and MEG time series. The presence of LRTCs in the rate of change of phase difference between time series recorded from the left and right motor cortices are shown to exist during resting state, but to be disrupted by a finger tapping task. The findings of this thesis are interpreted in the light of the critical brain hypothesis, and shown to provide motivation for future research in this area

Statistical physics approaches to the complex Earth system

Global climate change, extreme climate events, earthquakes and their accompanying natural disasters pose significant risks to humanity. Yet due to the nonlinear feedbacks, strategic interactions and complex structure of the Earth system, the understanding and in particular the predicting of such disruptive events represent formidable challenges for both scientific and policy communities. During the past years, the emergence and evolution of Earth system science has attracted much attention and produced new concepts and frameworks. Especially, novel statistical physics and complex networks-based techniques have been developed and implemented to substantially advance our knowledge for a better understanding of the Earth system, including climate extreme events, earthquakes and Earth geometric relief features, leading to substantially improved predictive performances. We present here a comprehensive review on the recent scientific progress in the development and application of how combined statistical physics and complex systems science approaches such as, critical phenomena, network theory, percolation, tipping points analysis, as well as entropy can be applied to complex Earth systems (climate, earthquakes, etc.). Notably, these integrating tools and approaches provide new insights and perspectives for understanding the dynamics of the Earth systems. The overall aim of this review is to offer readers the knowledge on how statistical physics approaches can be useful in the field of Earth system science