Fatigue crack analysis of ferrite material by acoustic emission technique

Among various methods of Non-destructive techniques (NDT), analysis using released acoustic emission (AE) waves due to crack propagation is very effective due to its dynamic monitoring features. In fragmentation theory for AE there are some proportional relationships among the AE parameters i.e. AE event, AE energy, area and volume of cracks etc., which are calculated from the released AE waves from the dynamic crack inside any material. The necessity of calculating the fractal dimension has been found in such relationships and the value is emphasized for determining the geometry of the irregularity in crack surface and crack volume. In this paper a novel approach for evaluating that value based on image processing by MATLAB is proposed. The images of the cracks during propagation are preserved and utilized to find out the fractal dimension for analyzing the crack propagation characteristics. The AE energy is also estimated from the received AE waves. The positioning of the sensors plays a great impact on this calculation. Finally, the theoretical proportionality relations of AE parameters are interpreted experimentally during crack propagation behavior in ferrite cast iron under fatigue loading

Fluid Dynamics of Watercolor Painting : Experiments and Modelling

In his classic study in 1908, A.M. Worthington gave a thorough account of splashes and their formation through visualization experiments. In more recent times, there has been renewed interest in this subject, and much of the underlying physics behind Worthington\u27s experiments has now been clarified. One specific set of such recent studies, which motivates this thesis, concerns the fluid dynamics behind Jackson Pollock\u27s drip paintings. The physical processes and the mathematical structures hidden in his works have received serious attention and have made the scientific pursuit of art a compelling area of exploration. Our current work explores the interaction of watercolors with watercolor paper. Specifically, we conduct experiments to analyze the settling patterns of droplets of watercolor paint on wet and frozen paper. Variations in paint viscosity, paper roughness, paper temperature, and the height of a released droplet are examined from time of impact, through its transient stages, until its final, dry state. Observable phenomena such as paint splashing, spreading, fingering, branching, rheological deposition, and fractal patterns are studied in detail and classified in terms of the control parameters. Using the one-dimensional (1-D) Saint-Venant differential equations, which are a simplification of the three-dimensional (3-D) Navier-Stokes equations from fluid dynamics, we created a computer-simulated, mathematical model of a droplet splash of watercolor paint onto a flat surface. The mathematical model is analyzed using a MATLAB code which considered changes in droplet height, radius, and velocity of dispersal over time. We also implemented a stochastic version of the Saint-Venant equations which captured the random fingering patterns of a droplet splash. Initial conditions for height, radius, and velocity of a radially spreading droplet were given at the onset of the simulation. Dynamic viscosity and fluid density were parameters incorporated into this system of differential equations, which could be easily adjusted in the MATLAB code for the paint type to be simulated. The stochastic nature of our model was designed to recreate the complex behavior of water splashes, the non-homogeneity of the watercolor paper, and the resulting patterns. We then computed the fractal dimension of each computer-generated droplet image to compare theoretical and experimental values. Analysis of the set of data consisting of over 10,000 trials was conducted to determine any significant statistical correlations among the spreading pattern, the number of fingers, viscosity, density and fractal dimension. Finally, we extended the system of differential equations based on the Saint-Venant equations to include the effects of temperature upon the paint-spreading pattern. In a similar manner, we compared the theoretical values of fractal dimensions generated by our MATLAB model to the experimental results for paint droplets on a frozen substrate

Fractal analysis of large-scale structures

Con el avance de los tiempos se han ido definiendo estructuras o formas que ayudaran al ser humano a comprender mejor su entorno, a aproximarlo de alguna manera a su entendimiento. Es durante los siglos XIX-XX que aparece una nueva forma, lo que se pasar´ıa a llamar un fractal, un objeto matem´atico cuya aparente irregularidad se repite a diferentes escalas. Un objeto que no sigue la geometr´ıa de Euclides. Un objeto que, a pesar de estas curiosas caracter´ısticas, se puede vislumbrar en las costas, en las hojas de helecho o en la espuma cu´antica. Hausdorff plante´o una de las primeras definiciones de dimensi´on que se podr´ıa aplicar a un fractal, abriendo la puerta al c´alculo de la dimensi´on fractal, que ser´a la piedra angular de este trabajo. Se puede entender de muchas formas, pero la que mejor se adapta al inter´es de este trabajo es que la dimensi´on fractal proporciona una idea de lo irregular que es una distribuci´on. De c´omo se distribuyen los puntos que componen una estructura. Esto indica que puede dar informaci´on sobre el agrupamiento de una distribuci´on. En este trabajo se medir´a la dimensi´on fractal de las estructuras a gran escala del universo, a fin de comprobar si siguen una distribuci´on homog´enea. Para ello se emplear´an datos provistos por el conjunto de datos de grupos de galaxias BOSS (Baryon Oscillation Spectroscopic Survey) que forma parte del SDSS (Sloan Digital Sky Survey). En concreto, se trabajar´a con los datos conjuntos de los dos algoritmos de selecci´on de BOSS, para el casquete gal´actico norte: LOWZ, que selecciona objetos hasta un redshift tal que z ≈ 0.4 y CMASS, que selecciona objetos en un rango de 0.4 < z < 0.7. Este conjunto de ambos se denomina CMASSLOWZTOT North, y proporciona datos de unos 953255 objetos. El objetivo principal ser´a estudiar c´omo var´ıa la dimensi´on fractal de estas estructuras a gran escala con la distancia com´ovil, y analizar si los resultados coinciden con aquellos indicados en la literatura. Para lograr este objetivo se medir´a la dimensi´on fractal a trav´es de varios m´etodos: algoritmos de box-counting, la funci´on de correlaci´on de dos puntos y la transformada de Hankel del espectro de potencias. En primer lugar, para realizar los an´alisis con los programas de box-counting, ser´a necesario tener un mapa de la distribuci´on de los objetos en el cielo. Para ello se emplear´a la muestra proporcionada por SDSS y, con el lenguaje de programaci´on Python, se dibujar´a este mapa de distribuci´on. Los primeros m´etodos de box-counting que se emplear´an dividir´an este mapa en peque˜nas cajas bidimensionales, donde solo se tendr´an en cuenta para el tratamiento aquellas que tengan,al menos, un objeto en su interior. En uno de los m´etodos, las cajas no se superpondr´an, sino que ser´an adyacentes unas con otras (m´etodo est´andar), y en el otro, las muestras se superpondr´an entre s´ı (m´etodo gliding ; deslizante). Por otra parte, para el tercer m´etodo de box-counting, se tendr´a en cuenta una tercera componente, ya que dividir´a el set de datos en cubos. La tercera componente se dar´a poniendo el mapa de distribuci´on en escala de grises, donde la escala de grises corresponder´a a la distancia com´ovil. De esta manera se tendr´a una medici´on de la dimensi´on fractal a trav´es de tres m´etodos de box-counting. Continuando con los algoritmos de box-counting, se realizar´a una medici´on del m´etodo est´andar y del m´etodo de escala de grises formando el mapa del cielo con Healpix, que reproducir´a el cielo en una superficie esf´erica dividida en p´ıxeles de ´areas iguales, permitiendo asi una representaci´on m´as realista del cielo al seguir su geometr´ıa. El siguiente paso corresponder´a a emplear la funci´on de correlaci´on de dos puntos para realizar el c´alculo de la dimensi´on fractal. Se utilizar´a para calcular la funci´on de estructura, g(r) = 1 + ξ(r), su gradiente log-log (la funci´on de gradiente), γ(r) = dlog g(r)/dlog r, y la funci´on de dimensi´on fractal, D(r) = 3 + γ(r). En este caso, la funci´on de correlaci´on de dos puntos se obtendr´a midi´endola directamente, utilizando conteo de pares. Se emplear´a para este fin el estimador de Landy & Szalay. Una vez hecho esto, se proceder´a al c´alculo de la funci´on de correlaci´on de dos puntos v´ıa transformada de Hankel del espectro de potencias, y se seguir´a el mismo procedimiento anterior, es decir, calcular la funci´on de estructura, su gradiente log-log, etc. Una vez realizadas todas las mediciones para cada uno de los m´etodos, se encontrar´an los resultados mostrados en la Tabla 0. M´etodos SBC GBC GSBC HSBC HGSBC CF PS Dimensi´on Fractal Media 1.01 ± 0.08 1.12 ±0.08 2.42 ± 0.11 1.78 ± 0.04 1.40 ± 0.11 2.25± 0.03 2.22 ± 0.05 Tabla 0: Resultados obtenidos para la dimensi´on fractal media en un intervalo de 300 a 2400 [M pc h−1 ], para cada uno de los m´etodos. El error se ha estimado como la desviaci´on est´andar de las medidas. Adem´as, las siglas se refieren a: SBC- box-counting est´andar, GBC- box-counting deslizante, GSBC-box-counting en escala de grises, HSBC- box-counting est´andar con Healpix, BGSBC- box-counting en escala de grises con Healpix, CF - funci´on de correlaci´on, PS- espectro de potencias Encontr´andose que, para todos los m´etodos, se obtiene un car´acter homog´eneo de la dimensi´on fractal, aunque no se puede asegurar un ´unico valor, ya que difieren para cada m´etodo. Adem´as, en la literatura se encuentra que en estas escalas D ≈ 3, luego el m´etodo que m´as se acerca ser´ıa el que emplea escala de grises, aunque a´un estar´ıa lejos de esa cifra. Se concluir´a que se prueba la homogeneidad de las estructruras a gran escala en los intervalos analizados, aunque no con el mismo valor de la dimensi´on fractal dado por la literatura. A su vez, se propondr´a un estudio m´as detallado para poder localizar la franja en la que se pasa de un universo no homog´eneo a uno homog´eneo y, tambi´en, se propondr´a ahondar m´as en las relaciones entre la geometr´ıa fractal y la cosmolog´ıa siguiendo los pasos de diversos estudios. As´ı como tambi´en se propondr´a aumentar la escala en la que se han analizado los datos con el fin de tratar de obtener un resultado m´as acorde con el mostrado en la literatura

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

Visualization and modeling of evaporation from pore networks by representative 2D micromodels

Evaporation is a key process for the water exchange between soil and atmosphere, it is controlled by the internal water fluxes and surface vapor fluxes. The focus of this thesis is to visualize and quantify the multiphase flow processes during evaporation from porous media. The retained liquid films in surface roughness (thick-film flow) and angular corners (corner flow) have been found to facilitate and dominate evaporation. Using the representative 2D micromodels (artificial pore networks) with different surface roughness and pore structures, this thesis gives visualizations of the corner and thick-film flow during the evaporation process, presents the enhanced hydraulic continuity by corner and thick-film flow, and tests the validity of the SSC-model which assumes corner flow is dominant for the mass transport during evaporation. Surface roughness and wettability are proved both experimentally and theoretically to play a key role for the time and temperature behaviors of the evaporation process, besides, this thesis shows that for a consistent description of the time-dependent mass loss and the geometry of the corner/thick-film flow region, the fractality of the evaporation front must be taken into account

Novel methods in retinal vessel calibre feature extraction for systemic disease assessment

Retina and its vascular network have unique branching characteristics morphology of which will change as a result of some systemic diseases, including hypertension, stroke and diabetes. Therefore, retinal image has been used as non-invasive screening window for risk assessment and prediction of such disease condition especially at the baseline. The assessment is based on a number of features among which vessel diameter (both individual and summary) and fractal dimension (FD) are the ones mostly associated with risk of diabetes and stroke. The association is linked to the higher risk of diabetes and stroke in people with narrower retinal arteriole diameter or change in overall fractal dimension independent of any risk factor (i.e. blood pressure, cardiovascular risk factors). Diameter measurement requires vessel edges to be located and tracked however; accurate edge perception is subject to image contrast, shadows, lighting condition and even presence of retinopathy legions close to vessel boundaries. This will lead to imprecision and inconsistencies between different automatic measurement techniques and may affect the significance of its association with disease condition in risk-assessment studies. As accuracy and success of diameter measurement is subject to large variations due to image artifacts it may not be suitable for fully automatic applications. In order to compensate for such error, at first two novel automatic vessel diameter measurement techniques were proposed and validated which were more robust in the presence of such image artifacts compared to similar methods. However, sometimes the exact edge location and actual diameter value is not of interest. In most case-control studies, it is of importance to comparatively evaluate the variations in retinal vessel diameter as a sign of retinopathy such as arteriolar nicking as an example of hypertensive retinopathy. Vessel diameter is often required to be compared with a reference value in many analytical assessments for diagnostic purpose. This includes monitoring the diameter variations of a specific vessel segment within single subject overtime or across multiple subjects. This helps ophthalmologists to understand whether it has undergone any significant change and perhaps associate it with a disease abnormality. A technique that can effectively quantify that change without being impaired by image artifacts is of more importance and one of the rationales of this study. This research hypothesized an edge independent solution for quantifying diameter variations when the actual diameter value is not required and proposed a new feature based on fractal analysis of vessel cross-section profile as a time series signal. This feature provides a link between FD as a global measure of the complexity and diameter variation as local property of a specific vessel segment. The clinical application of this feature has been validated on two population studies which showed promising result for assessment of mild non-proliferative diabetic retinopathy and 10-year stroke. This research work has also investigated whether the FD of retinal microvasculature would be affected by cyclic pulsations of retinal vessels and whether ECG synchronization is required prior to taking fundus images to compensate for this potential source of variations

Simulation of turbulence mixing in the atmosphere boundary layer and analysis of fractal dimension

In the first part of this paper, a flow model for numerical simulation of turbulent parameters in atmospheric boundary layer (ABL), based on finite volume method and large-eddy simulation is introduced. This model consists of balance equations for mass, momentum and energy (for potential temperature) equations. The Lagrangian dynamic model of Smagorinsky with restriction of size for the coefficient Cs was used for sub grid turbulent viscosity. The second part of this paper is devoted to the numerical aspects of flow model using proper orthogonal decomposition (POD) method. In the final part of this paper, results from numerical studies on flow in ABL for the neutral and stable case and analysis of fractal dimensions are presented. These results constitute important tests for the assessment of the predictive capacity for the stratified flow model in hand. ImaCalc program was used to study the fractal parameter and structure functions. We calculated the maximum value of fractal dimension D selected among all of the velocity intensity and vorticity modules which was a good indicator of flow's complexity. The data of evolution of D(t) in the middle section of the domain of the multifractal spectra along the main downstream axis were also calculated. The reduction in the maximum value of the fractal dimension for intermediate velocity and vorticity values is consistent with laboratory experiments and with wind wane measurements.Authors wishing to acknowledge financial support from RFBR (Grant No. 17-07-01391). Additional support for travel by European Research Community on Flow, Turbulence and Combustion (ERCOFTAC) and the Pan European Laboratory on Non-Homogeneous Turbulence (PELNoT).Peer ReviewedPostprint (author's final draft