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Academic literature on the topic 'Calcul fractal'

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Published: 8 June 2024

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  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers

Journal articles on the topic "Calcul fractal":

1

ANTAR, Monia. "Autosimilarité et mémoire longue : Les rendements des indices boursiers tunisiens sont-ils chaotiques ?" Journal of Academic Finance 7, no. 2 (November 17, 2016): 1–32. http://dx.doi.org/10.59051/joaf.v7i2.60.

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La Finance fractale est venue au secours des modèles classiques incapables d’expliquer les anomalies boursières et des modèles linéaires inadéquats pour caractériser les processus complexes. La caractérisation des séries financières est toujours d’actualité. Le calcul de l’exposant de Hurst, de la dimension fractale, de l’exposant de Lyapunov, de la fenêtre de Theiler et la réalisation du test de déterminisme, nous ont permis de mieux appréhender la dynamique des rentabilités des indices cotés sur la Bourse de Tunis. Les résultats montrent que les rentabilités ne sont pas linéaires, suivent des lois alpha stables, présentent une mémoire longue mais ne sont toutefois pas chaotiques. L’hypothèse d’un mouvement fractal brownien est privilégiée.
2

Badariotti, Dominique. "Des fractales pour l’urbanisme?" Cahiers de géographie du Québec 49, no. 137 (March 9, 2006): 133–56. http://dx.doi.org/10.7202/012297ar.

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Résumé À partir de l’analyse de la morphologie de l’agglomération transfrontalière Strasbourg-Kehl, cet article traite de l’apport des analyses fractales dans le domaine de l’urbanisme. Outre quelques résultats d’ensemble désormais classiques, comme le calcul de la dimension fractale ou l’édition de la courbe du comportement scalant, il aborde le sujet des dimensions particulières de certains tissus spécifiques comme le centre-ville, les ensembles pavillonnaires, les grands ensembles et les zones techniques périphériques. Il propose également deux nouveaux indicateurs élaborés à partir des mesures de fractalité et susceptibles d’intéresser l’urbanisme et les recherches urbaines.
3

Rodríguez-Velásquez, Javier, Signed Prieto-Bohórquez, Catalina Correa-Herrera, Yolanda Soracipa-Muñoz, Ninfa Chaves-Torres, Álvaro Javier Narváez-Mejía, José Mojica- Madera, Mónica Aguilera-Rodríguez, Diego Tapia-Herrera, and Jairo Jattin. "Comportamiento fractal de infecciones asociadas al cuidado de la salud en el Hospital de Meissen ESE II Nivel, para los años 2011, 2012 y 2013." Infectio 22, no. 2 (February 2, 2018): 70. http://dx.doi.org/10.22354/in.v22i2.711.

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Introducción: la dimensión fractal estadística ha sido de utilidad para la caracterización de diversos fenómenos, incluyendo la dinámica cardiaca fetal y del adulto, así como comportamientos asociados al sistema inmune. Las Infecciones Asociadas al Cuidado de la Salud son un problema de salud de alta importancia a nivel mundial.Objetivo: establecer el comportamiento fractal estadístico de la frecuencia de aparición de Infecciones Asociadas al Cuidado de la Salud.Material y métodos: Se aplicó la ley de Zipf-Mandelbrot a la distribución de frecuencias de aparición agrupadas por especialidad de Infecciones Asociadas al Cuidado de la Salud en el Hospital Meissen ESE II Nivel, para los años 2011, 2012 y 2013. Se calculó la dimensión fractal estadística para cada año, hallando los rangos en los que se desenvuelve la dinámica en estos años y posteriormente se realizaron simulaciones de estas dinámicas anuales.Resultados: Se observó un comportamiento a escala de la dinámica de aparición de Infecciones Asociadas al Cuidado de la Salud por especialidad, los valores de la dimensión fractal fue de 0,6104, 0,7560 y 0,4332 para los años 2011, 2012 y 2013 respectivamente.Conclusión: La ley de Zipf/Mandelbrot permite caracterizar de forma objetiva y reproducible el comportamiento de la frecuencia de aparición de las Infecciones Asociadas al Cuidado de la Salud en el tiempo; las dimensiones fractales acotadas consecutivas en el tiempo permitirían generar predicciones, constituyendo una herramienta de ayuda para la vigilancia epidemiológica y la clínica.
4

Rodríguez Velásquez, Javier, Signed Prieto, Ferando Polo, Catalina Correa, Yolanda Soracipa, Vanessa Blanco, and Andrés Camilo Rodríguez. "Diagnóstico fractal y euclidiano de células de cuello uterino." Revista Repertorio de Medicina y Cirugía 23, no. 1 (March 1, 2014): 47–55. http://dx.doi.org/10.31260/repertmedcir.v23.n1.2014.741.

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Basados en geometría fractal se hizo un diagnóstico objetivo y reproducible de células de cuello uterino, que diferencia las normales de aquellas con lesión de bajo grado (LEIBG) o cancerígenas, identificando en forma cuantitativa las células ASCUS. Objetivo: establecer una metodología diagnóstica de las células cervicales normales y preneoplásicas con aplicación simultánea de geometría fractal y euclidiana para definir parámetros matemáticos distintivos de cada uno de dichos estados. Métodos: fotografías digitales de doce células de citologías de mujeres entre 20 y 55 años (tres normales superficiales, tres normales intermedias, tres LEIBG y tres ASCUS). Mediante un programa se calculó la dimensión fractal de tres objetos matemáticos: núcleo, citoplasma y totalidad, a partir del método box-counting; de manera simultánea se determinó el número de pixeles ocupados por la superficie de cada uno y los espacios ocupados por el borde de estos objetos en cada una de las cinco rejillas, para comparar los valores obtenidos. Resultados: al superponer las rejillas de dos y cuatro pixeles los valores de los espacios de ocupación del núcleo permiten establecer diferencias matemáticas entre los grupos de células, presentando como valores en la rejilla dos: normales superficiales (53-56), normales intermedias (75), LEIBG (120-159) y ASCUS (104-121). Conclusiones: se estableció una metodología matemática diagnóstica que diferencia estados preneoplásicos con base en medidas fractales y euclidianas simultáneas del borde del núcleo celular. Abreviaturas: LEIBG, lesión escamosa intraepitelial de bajo grado; ASCUS atypical squamous cells of undetermined significance (células escamosas atípicas de significado indeterminado); GF, geometría fractal.
5

Rodríguez Velásquez, Javier, Signed Prieto Bohórquez, Fernando Polo Nieto, Catalina Correa Herrera, Yolanda Soracipa Muñoz, Vanessa Blanco, and Andrés Camilo Rodríguez. "Diferenciación geométrica fractal y euclidiana de arterias normales y reestenosadas. Armonía matemática arterial." Revista Repertorio de Medicina y Cirugía 23, no. 2 (June 1, 2014): 139–44. http://dx.doi.org/10.31260/repertmedcir.v23.n2.2014.729.

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Antecedentes: se desarrolló una metodología que diferencia normalidad de reestenosis coronaria en un modelo de experimentación con porcinos, basada en geometría fractal y el concepto de armonía matemática intrínseca (AMI). Objetivo: desarrollar una metodología que permita la diferenciación matemática de arterias normales y reestenosadas a través de la aplicación simultánea de geometría euclidiana y fractal. Materiales y métodos: se midieron imágenes de placas histológicas de tres arterias normales y tres reestenosadas, calculando la dimensión fractal mediante el método de box-counting de tres islas delimitadas por las capas arteriales y después se calculó la AMI; al mismo tiempo se calculó el número de cuadros que ocupa la superficie de las tres islas definidas y se establecieron diferencias entre grupos. Resultados: la dimensión fractal de las arterias normales estuvo entre 1.0184 y 1.2578 y en las reestenosadas entre 0.6881 y 1.1651; los valores del número de cuadros ocupados por la superficie de las arterias oscilaron entre 34 y 76 para las arterias normales y para las reestenosadas entre 91 y 162, así pues las islas de las arterias normales tuvieron siempre valores de ocupación menores a 100, mientras que las reestenosadas presentaron siempre un valor mayor o igual en al menos una de sus islas. Conclusiones: se reveló una autoorganización matemática fractal y euclidiana del proceso de reestenosis arterial que permite establecer diferencias entre dichos estados, cuantificando el avance de la oclusión arterial. Abreviaturas: AMI, armonía matemática intríseca; EAC, enfermedad arterial coronaria.
6

Proença, Claudia Belmiro, Aura Conci, and Solly A. Segenreich. "Investigação para detecção automática de falhas têxteis." Journal of the Brazilian Society of Mechanical Sciences 21, no. 3 (September 1999): 493–507. http://dx.doi.org/10.1590/s0100-73861999000300011.

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Este trabalho apresenta uma aplicação de Dimensão Fractal (DF) e técnicas de segmentação de imagens na inspeção industrial automática. Foi desenvolvido um sistema para a indústria têxtil objetivando a detecção de defeitos. A indústria têxtil se particulariza por ter um tipo de produção que torna inviável a utilização das técnicas de extração de características morfológiocas, usualmente empregadas em sistemas de controle de qualidade baseados na visão. Basicamente o sistema implementado compara dados obtidos de imagens digitalizadas, as características destes dados dependem do método selecionado. Dois tipos de métodos podem ser usados: métodos de segmentação e dimensão fractal. Para implementação no sistema, métodos de segmentação conhecidos foram adaptados e aperfeiçoados visando a determinação de variações em uma imagem do tecido (o que caracteriza a existência de uma falha). Na utilização da Dimensão Fractal como uma ferramenta para análise de imagens e controle de qualidade utiliza-se um algoritmo que calcula os valores de dimensão fractal de imagens em toda a região teoricamente admissível (2 <= DF <= 3). Os vários métodos foram comparados quanto a sua eficiência, precisão e aplicabilidade.
7

Miranda Hamburger, Fabio. "Diseño de una antena fractal de 2400 MHz." Revista Tecnología en Marcha 25, no. 4 (December 11, 2012): 71. http://dx.doi.org/10.18845/tm.v25i4.621.

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<p>El presente estudio describe el diseño de una antena fractal con una frecuencia de 2400 MHz de frecuencia. Se utilizó el fractal descrito por Waclaw Spierpi<em>ń</em>ski. La figura inicial, también conocida como semilla, se fraccionó utilizando triángulos equiláteros con la finalidad de generar un perímetro que se asemeje a una porción significativa de la longitud de la onda. El uso de <span>λ </span>(lambda) para determinar un perímetro idóneo reduce la resistencia a la radiación. Con base en <span>λ</span>, se calcula el número adecuado de iteraciones para diseñar la antena.</p>
8

Rodríguez, Javier, Signed Prieto, Héctor Posso, Ricardo Cifuentes, Catalina Correa, Yolanda Soracipa, Fredy López, Laura Méndez, Hebert Bernal, and Alejandro Salamanca. "Fractales: ayuda diagnóstica para células preneoplásicas y cancerígenas del epitelio escamoso cervical confirmación de aplicabilidad clínica." Revista Med 24, no. 1 (June 16, 2016): 79–88. http://dx.doi.org/10.18359/rmed.2334.

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Antecedentes: Se desarrolló un método diagnóstico fractal para evaluar células del cuello uterino utilizando el concepto de Armonía Matemática Intrínseca (AMI) y variabilidad celular, el cual diferencia matemáticamente células normales de células L-SIL y H-SIL, haciendo innecesario el diagnóstico de células ASCUS.Objetivo: confirmar la capacidad diagnóstica de la metodología desarrollada mediante un estudio ciego de comparación con el Gold StandardMétodos: se tomaron fotografías digitales de 50 preparaciones citológicas de mujeres entre 20 y 55 años: 5 con diagnóstico de citología normal y 45 con diferentes grados de lesión hasta carcinoma, incluyendo 5 ASCUS. Se calculó la dimensión fractal de tres objetos matemáticos: núcleo, citoplasma y totalidad, a partir de la superposición de cinco rejillas. Además se evaluó su dimensión fractal mediante el concepto de AMI y variabilidad celular. Los resultados obtenidos se compararon con el diagnóstico citopatológico convencional determinando su sensibilidad, especificidad y coeficiente kappa.Resultados: La sensibilidad y especificidad fue del 100%, y el coeficiente Kappa de 1.Conclusiones: Los resultados en una población diferente a la inicial son una evidencia de la capacidad de esta metodología para diagnosticar objetiva y cuantitativamente células normales, L-SIL y H-SIL, así como aclarar el diagnóstico de las células ASCUS con base en la dimensión fractal y el concepto de AMI y variabilidad.
9

Rodríguez Velásquez, Javier Oswado, Signed Prieto Bohórquez, Catalina Correa Herrera, Marcela Mejia, Benjamín Ospino, Ángela Munevar, Beatriz Amaya, Yurany Duarte, Sandra Medina, and Carolina Felipe. "Simulación de estructuras eritrocitarias con base en la geometria fractal y euclidiana." Archivos de Medicina (Manizales) 14, no. 2 (November 20, 2014): 276–84. http://dx.doi.org/10.30554/archmed.14.2.316.2014.

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Antecedentes: La aplicación simultánea de la geometría fractal y euclidiana fundamentó el desarrollo de una metodología diagnóstica de la morfofisiología eritocitaria, con la cual se obtiene un método diagnóstico objetivo y reproducible para la detección de anormalidades patológicas en extendidos de muestras de sangre, útil para determinar la viabilidad de bolsas para trasfusión.Objetivo: determinar posibles trayectorias de evolución entre estructuras eritrocitarias desde normalidad a equinocitos aplicando el diagnóstico previamente desarrollado a partir de la geometría fractal y la euclidiana.Materiales y métodos: con base en la metodología diagnóstica previamente desarrollada, se tomaron 8 eritrocitos normales, con los cuales se desarrollaron simulaciones de tres posibles trayectorias de evolución. Para ello inicialmente se calculó la dimensión fractal, el número de pixeles ocupados por la superficie eritrocitaria y el número de espacios tocados por el borde al superponer una rejilla de 5x5 píxeles en el espacio generalizado fractal de Box counting. Posteriormente se realizaron variaciones geométricas del borde de cada eritrocito, de tal forma que al evaluar simultáneamente el borde y la superficie se mantuvieran proporciones superficie/borde características del estado requerido para cada simulación, de acuerdo con los resultados previos. Resultados: Se obtuvieron simulaciones de posibles trayectorias de normalidad a equinocitos, con medidas cuantitativas, objetivas y reproducibles. Conclusiones: la organización fractal/euclidiana en la arquitectura de los glóbulos rojos, permite el desarrollo de trayectorias acausales de alteración celular hacia equinocitos, de utilidad en el diagnóstico del eritrocito en la práctica clínica diaria.
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Forero, Germán, Javier Oswado Rodríguez Velásquez, Signed Prieto Bohórquez, Frank Pernett, Catalina Correa, Esmeralda Guzmán, Camila Sarmiento, and Sergio Diaz. "Sistemas dinámicos aplicados a la dinámica cardiaca en 18 horas mediante una ley matemática exponencial." Archivos de Medicina (Manizales) 16, no. 2 (December 31, 2016): 335–44. http://dx.doi.org/10.30554/archmed.16.2.1775.2016.

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Objetivo: Confirmar la capacidad diagnostica de una ley exponencial de ayuda diagnostica, desarrollada para 21 horas con base en la teoría de sistemas dinámicos junto con la geometría fractal, en evaluaciones realizadas en 18 horas, mediante un estudio de concordancia diagnóstica con respecto al Gold estándar. Materiales y métodos: Se realizó un estudio de 60 dinámicas cardiacas evaluadas en holter y registros electrocardiográficos continuos, de los cuales 15 provienen de sujetos normales y 45 de pacientes con diferentes tipos de patologías cardiacas. Se desarrollaron simulaciones teóricas de la secuencia de las frecuencias cardiacas durante 18 horas, y se construyeron atractores. Se calculó la dimensión fractal de cada atractor y su ocupación espacial en el espacio generalizado de Box-Counting. Se determinó el diagnóstico matemático a partir de la ley y se calculó sensibilidad, especificidad y coeficiente Kappa. Resultados: se encontraron valores para normalidad entre 219 y 373 en la rejilla Kp y entre 49 y 70 para enfermedad aguda, evidenciando que el método permite diferenciar normalidad de enfermedad aguda mediante la ocupación espacial de los atractores valorados desde la ley matemática en 18 horas. Se encontraron valores de sensibilidad y especificidad del 100% y un coeficiente Kappa de 1 al comparar el diagnóstico físico-matemático con el Gold estándar. Conclusión: la ley exponencial de los sistemas dinámicos cardiacos aplicada en 18 horas es útil como herramienta de ayuda diagnóstica, permitiendo cuantificar casos normales, en evolución hacia la enfermedad y en estados agudos.
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Journal articles Dissertations / Theses Books

Dissertations / Theses on the topic "Calcul fractal":

1

Lamorlette, Aymeric. "Caractérisation macroscopique du milieu végétal pour les modèles physiques de feux de forêts." Thesis, Vandoeuvre-les-Nancy, INPL, 2008. http://www.theses.fr/2008INPL044N/document.

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La description aux échelles macroscopiques et gigascopiques des feux de forêts permet l'établissement de modèles physiques aptes à représenter l'évolution d'un feu avec une meilleure précision que les modèles empiriques de type Rothermel développés jusqu'alors. Cependant ces modèles nécessitent l'ajustement de paramètres dont la mesure directe est impossible, car les équations associées à ces modèles ne sont pas relatives à l'air et à la matière végétale mais aux milieux équivalents à la végétation pour l'échelle considérée. Les propriétés des milieux équivalents sont alors liées aux propriétés des milieux les constituant, mais la connaissance des propriétés des milieux constitutifs ne permet pas de connaître directement les propriétés du milieu équivalent. Ce travail consistera tout d'abord en la reconstruction du milieu végétal à l'aide d'outils issus de la géométrie fractale. Des méthodes de mesures de paramètres géométriques venant de la foresterie ont ensuite été utilisées pour valider nos modèles de végétation. Enfin, des expériences numériques ont été menées sur nos structures reconstruites afin d'identifier les paramètres macroscopiques qui nous intéressent. Ces expériences permettent également de valider ou non les hypothèses effectuées lors de l'établissement des équations du milieu équivalent. Les paramètres ajustés sont la viscosité du milieu équivalent, le coefficient d'échange convectif et le coefficient d'extinction
The macroscopic and gigascopic scale description of forest fires allows physical modelings of the propagation which can predict the fire evolution with a better accuracy than usually developed empirical Rothermel-like models. However, those models need fitting for their parameters which cannot be measured directly as the models equations are related to the equivalent media at the considered scale and not related to the air and the vegetal material. The equivalent media properties are related to the inner media properties, but the inner media properties knowledge does not allow directly the equivalent media properties knowledge. This work is then aiming on the vegetal medium reconstruction using fractal geometry. Geometrical parameters measurement methods used in forestry sciences are applied for the vegetal modeling validation. Numerical studies are finally done on the reconstructed structures to fit the relevant macroscopic scale parameters. Those studies also allow us to validate or invalidate the assumptions which have been done for the equivalent medium equation development. Those parameters are: the equivalent medium viscosity, the convective heat transfer coefficient and the extinction coefficient
2

Emmanuel, Aurélien. "Courbes d'accumulations des machines à signaux." Electronic Thesis or Diss., Orléans, 2023. http://www.theses.fr/2023ORLE1079.

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Cette thèse s'inscrit dans l'étude d'un modèle de calcul géométrique : les machines à signaux. Nous y montrons comment tracer des graphes de fonctions à l'aide d'arbres unaire-binaires. Dans le monde des automates cellulaires, il est souvent question de particules ou signaux : des structures périodiques dans le temps et l'espace, autrement dit des structures qui se déplacent à vitesse constante. Lorsque plusieurs signaux se rencontrent, une collision a lieu, et les signaux entrant peuvent continuer, disparaître ou laisser place à d'autres signaux, en fonctions des règles de l'automate cellulaire. Les machines à signaux sont un modèle de calcul qui reprend ces signaux comme briques de base. Visualisées dans un diagramme espace-temps, l'espace en axe horizontal et le temps vertical s'écoulant vers le haut, ce modèle revient à calculer par le dessin de segments et demi-droites colorés. On trace, de bas en haut, des segments jusqu'à ce que deux ou plus s'intersectent, et l'on démarre alors de nouveau segments, en fonctions de règles prédéfinies. Par rapport aux automates cellulaires, les machines à signaux permettent l'émergence d'un nouveau phénomène : la densité des signaux peut être arbitrairement grande et même infinie, y compris en partant d'une configuration initiale de densité finie. De tels points du diagramme espace-temps, des points au voisinage desquels se trouvent une infinité de signaux, sont appelés points d'accumulation. Ce nouveau phénomène permet de définir de nouveau problèmes, géométriquement. Par exemple : quels sont les points d'accumulations isolés possibles en utilisant des positions initiales et des vitesses rationnelles ? Peut-on faire en sorte que l'ensemble des points d'accumulation forment un segment ? un ensemble de Cantor ? Dans cette thèse, nous nous attelons à caractériser des graphes de fonctions qu'il est possible de dessiner par un ensemble d'accumulation. Elle s'inscrit dans l'exploration de la puissance de calcul des machines à signaux, qui s'inscrit plus généralement dans l'étude de la puissance de calcul de modèles non standards. Nous y montrons que les fonctions d'un segment compact de la droite réelle dont le graphe coïncide avec l'ensemble d'accumulation d'une machine à signaux sont exactement les fonctions continues. Nous montrons plus généralement comment les machines à signaux peuvent dessiner n'importe quel fonction semi-continue inférieurement. Nous étudions aussi la question sous des contraintes de calculabilité, avec le résultat suivant : si un diagramme de machine à signaux calculable coïncide avec le graphe d'un fonction suffisamment lipschitzienne, cette fonction est limite calculable d'une suite croissante de fonctions en escalier rationnelles
This thesis studies a geometric computational model: signal machines. We show how to draw function graphs using-binary trees. In the world of cellular automata, we often consider particles or signals: structures that are periodic in time and space, that is, structures that move at constant speed. When several signals meet, a collision occurs, and the incoming signals can continue, disappear, or give rise to new signals, depending on the rules of the cellular automaton. Signal-machines are a computational model that takes these signals as basic building blocks. Visualized in a space-time diagram, with space on the horizontal axis and time running upwards, this model consists of calculating by drawing segments and half-lines. We draw segments upwards until two or more intersect, and then start new segments, according to predefined rules. Compared to cellular automata, signal-machines allow for the emergence of a new phenomenon: the density of signals can be arbitrarily large, even infinite, even when starting from a finite initial configuration. Such points in the space-time diagram, whose neighborhoods contain an infinity of signals, are called accumulation points.This new phenomenon allows us to define new problems geometrically. For example, what are the isolated accumulation points that can be achieved using rational initial positions and rational velocities? Can we make so the set of accumulation points is a segment? A Cantor set? In this thesis, we tackle the problem of characterizing the function graphs that can be drawn using an accumulation set. This work fits into the exploration of the computational power of signal-machines, which in turn fits into the study of the computational power of non-standard models. We show that the functions from a compact segment of the line of Real numbers whose graph coincides with the accumulation set of a signal machine are exactly the continuous functions. More generally, we show how signal machines can draw any lower semicontinuous function. We also study the question under computational constraints, with the following result: if a computable signal-machine diagram coincides with the graph of a Lipschitz-function of sufficiently small Lipschitz coefficient, then that function is the limit of a growing and computable sequence of rational step functions
3

Lausberg, Conrad. "Calcul numérique de la dimension fractale d'un attracteur étrange." Phd thesis, Grenoble INPG, 1987. http://tel.archives-ouvertes.fr/tel-00325041.

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Cette thèse se veut d'abord une étude mathématique qui donne des bases théoriques au calcul numérique des dimensions fractales d'un attracteur. Des nombreuses expériences numériques relient la théorie aux exigences qui apparaissent dans les applications. L'algorithme de calcul des dimensions fractales propose par Paladin et Vulpiani, que nous appelons algorithme des points centraux, nous semble être le plus puissant parmi les algorithmes proposés. Nous donnons la description détaillée de cet algorithme, et espérons qu'elle est aussi compréhensible pour un non-spécialiste. Une méthode d'estimation d'erreur pour cet algorithme est proposée et justifiée par des résultats des expériences numériques. Le cout de l'algorithme est calcule. La thèse est complétée par l'étude d'un système dynamique, qui modélise une réaction biochimique chaotique, qui intervient dans le cycle de vie d'un genre d'amibes
4

Lausberg, Conrad. "Calcul numérique de la dimension fractale d'un attracteur étrange." Grenoble 2 : ANRT, 1987. http://catalogue.bnf.fr/ark:/12148/cb376070916.

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5

Lausberg, Conrad Cosnard Michel Laurent Pierre Jean. "Calcul numérique de la dimension fractale d'un attracteur étrange." S.l. : Université Grenoble 1, 2008. http://tel.archives-ouvertes.fr/tel-00325041.

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Bologna, Mauro. "The Dynamic Foundation of Fractal Operators." Thesis, University of North Texas, 2003. https://digital.library.unt.edu/ark:/67531/metadc4235/.

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The fractal operators discussed in this dissertation are introduced in the form originally proposed in an earlier book of the candidate, which proves to be very convenient for physicists, due to its heuristic and intuitive nature. This dissertation proves that these fractal operators are the most convenient tools to address a number of problems in condensed matter, in accordance with the point of view of many other authors, and with the earlier book of the candidate. The microscopic foundation of the fractal calculus on the basis of either classical or quantum mechanics is still unknown, and the second part of this dissertation aims at this important task. This dissertation proves that the adoption of a master equation approach, and so of probabilistic as well as dynamical argument yields a satisfactory solution of the problem, as shown in a work by the candidate already published. At the same time, this dissertation shows that the foundation of Levy statistics is compatible with ordinary statistical mechanics and thermodynamics. The problem of the connection with the Kolmogorov-Sinai entropy is a delicate problem that, however, can be successfully solved. The derivation from a microscopic Liouville-like approach based on densities, however, is shown to be impossible. This dissertation, in fact, establishes the existence of a striking conflict between densities and trajectories. The third part of this dissertation is devoted to establishing the consequences of the conflict between trajectories and densities in quantum mechanics, and triggers a search for the experimental assessment of spontaneous wave-function collapses. The research work of this dissertation has been the object of several papers and two books.
7

Pegon, Paul. "Transport branché et structures fractales." Thesis, Université Paris-Saclay (ComUE), 2017. http://www.theses.fr/2017SACLS444/document.

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Cette thèse est consacrée à l’étude du transport branché, de problèmes variationnels qui y sont liés et de structures fractales qui peuvent y apparaître. Le problème du transport branché consiste à connecter deux mesures de même masse par le biais d’un réseau en minimisant un certain coût, qui sera pour notre étude proportionnel à mLα afin de déplacer une masse m sur une distance L. Plusieurs modèles continus ont été proposés pour formuler le problème, et on s’intéresse plus particulièrement aux deux grands types de modèles statiques : le modèle Lagrangien et le modèle Eulérien, avec une emphase sur le premier. Après avoir posé proprement les bases de ces modèles, on établit rigoureusement leur équivalence en utilisant une décomposition de Smirnov des mesures vectorielles à divergence mesure. On s’intéresse par la suite à un problème d’optimisation de forme lié au transport branché qui consiste à déterminer les ensembles de volume 1 les plus proches de l’origine au sens du transport branché. On démontre l’existence d’une solution, décrite comme un ensemble de sous-niveau de la fonction paysage, désormais standard en transport branché. La régularité Hölder de la fonction paysage, obtenue ici sans hypothèse de régularité a priori sur la solution considérée, permet d’obtenir une borne supérieure sur la dimension de Minkowski de son bord, qui est non-entière et dont on conjecture qu’elle en est la dimension exacte. Des simulations numériques, basées sur une approximation variationnelle à la Modica-Mortola de la fonctionnelle du transport branché, ont été effectuées dans le but d’étayer cette conjecture. Une dernière partie de la thèse se concentre sur la fonction paysage, essentielle à l’étude de problèmes variationnels faisant intervenir le transport branché en ce sens qu’elle apparaît comme une variation première du coût d’irrigation. Le but est d’étendre sa définition et ses propriétés fondamentales au cas d’une source étendue, ce à quoi l’on parvient dans le cas d’un réseau possédant un système fini de racines, par exemple pour des mesures à supports disjoints. On donne une définition satisfaisante de la fonction paysage dans ce cas, qui vérifie en particulier la propriété de variation première et on démontre sa régularité Hölder sous des hypothèses raisonnables sur les mesures à connecter
This thesis is devoted to the study of branched transport, related variational problems and fractal structures that are likely to arise. The branched transport problem consists in connecting two measures of same mass through a network minimizing a certain cost, which in our study will be proportional to mLα in order to move a mass m over a distance L. Several continuous models have been proposed to formulate this problem, and we focus on the two main static models : the Lagrangian and the Eulerian ones, with an emphasis on the first one. After setting properly the bases for these models, we establish rigorously their equivalence using a Smirnov decomposition of vector measures whose divergence is a measure. Secondly, we study a shape optimization problem related to branched transport which consists in finding the sets of unit volume which are closest to the origin in the sense of branched transport. We prove existence of a solution, described as a sublevel set of the landscape function, now standard in branched transport. The Hölder regularity of the landscape function, obtained here without a priori hypotheses on the considered solution, allows us to obtain an upper bound on the Minkowski dimension of its boundary, which is non-integer and which we conjecture to be its exact dimension. Numerical simulations, based on a variational approximation a la Modica-Mortola of the branched transport functional, have been made to support this conjecture. The last part of the thesis focuses on the landscape function, which is essential to the study of variational problems involving branched transport as it appears as a first variation of the irrigation cost. The goal is to extend its definition and fundamental properties to the case of an extended source, which we achieve in the case of networks with finite root systems, for instance if the measures have disjoint supports. We give a satisfying definition of the landscape function in that case, which satisfies the first variation property and we prove its Hölder regularity under reasonable assumptions on the measures we want to connect
8

Senot, Maxime. "Modèle géométrique de calcul : fractales et barrières de complexité." Phd thesis, Université d'Orléans, 2013. http://tel.archives-ouvertes.fr/tel-00870600.

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Les modèles géométriques de calcul permettent d'effectuer des calculs à l'aide de primitives géométriques. Parmi eux, le modèle des machines à signaux se distingue par sa simplicité, ainsi que par sa puissance à réaliser efficacement de nombreux calculs. Nous nous proposons ici d'illustrer et de démontrer cette aptitude, en particulier dans le cas de processus massivement parallèles. Nous montrons d'abord à travers l'étude de fractales que les machines à signaux sont capables d'une utilisation massive et parallèle de l'espace. Une méthode de programmation géométrique modulaire est ensuite proposée pour construire des machines à partir de composants géométriques de base -- les modules -- munis de certaines fonctionnalités. Cette méthode est particulièrement adaptée pour la conception de calculs géométriques parallèles. Enfin, l'application de cette méthode et l'utilisation de certaines des structures fractales résultent en une résolution géométrique de problèmes difficiles comme les problèmes de satisfaisabilité booléenne SAT et Q-SAT. Ceux-ci, ainsi que plusieurs de leurs variantes, sont résolus par machines à signaux avec une complexité en temps intrinsèque au modèle, appelée profondeur de collisions, qui est polynomiale, illustrant ainsi l'efficacité et le pouvoir de calcul parallèle des machines à signaux.
9

Khalil, Lionel. "Généralisation des réseaux d'interaction avec l'agent amb de Mc Carthy : propriétés et applications." Palaiseau, Ecole polytechnique, 2003. http://www.theses.fr/2003EPXX0015.

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Morgado, Laerte Ferreira. "Um metodo para granulometria de imagens topograficas baseado na teoria de calculo da dimensão fractal." [s.n.], 1996. http://repositorio.unicamp.br/jspui/handle/REPOSIP/259957.

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Orientador: Vitor Baranauskas
Dissertação (mestrado) - Universidade Estadual de Campinas, Faculdade de Engenharia Eletrica e de Computação
Made available in DSpace on 2018-07-22T14:40:25Z (GMT). No. of bitstreams: 1 Morgado_LaerteFerreira_M.pdf: 5915978 bytes, checksum: acea29bf8767947951774780e3dfe2b9 (MD5) Previous issue date: 1996
Resumo: Apresentamos um método baseado na Teoria dos Fractais que permite efetuar o cálculo do grau de irregularidade em cada ponto da superfície de uma imagem topográfica. O algoritmo proposto fornece valores que são função da escala de observação, de forma a ignorar irregularidades com tamanhos muito maiores ou muito menores que o valor da escala. Dessa forma, é possível implementar duas funcionalidades: calcular os graus de irregularidade para todos os pixels de uma imagem em uma determinada escala de observação e calcular os graus de irregularidade em diversas escalas para um determinado pixel da imagem. Com a primeira funcionalidade, podemos segmentar a imagem topográfica em regiões de maior ou menor irregularidade quando observada sob uma determinada escala. Com a segunda funcionalidade, podemos estudar a variação do grau de irregularidade de um ponto da imagem quando variamos a escala de observação. Mostramos que esse estudo permite identificar os tamanhos das irregularidades que ocorrem em superfícies topográficas como, por exemplo, os tamanhos médios dos grãos e as distâncias médias entre eles. Um ambiente gráfico foi desenvolvido com a concepção de Orientação a Objetos em C++ para estudo desse algoritmo e pode ser facilmente usado para análise de outros algoritmos similares
Abstract: We describe a method based on the Theory of Fractals to calculate a measure of the degree of irregularity in each surface point of any topographic image. The proposed algorithm gives values that are dependent on the scale of observation so as to ignore irregularities which sizes are much greater or lower than the scale value. Therefore, it is possible to implement two features: calculation of the degrees of irregularity for all the pixels of an image in a given scale of observation and calculation of the degrees of irregularity in many scales of observation for a given image pixel. With the first feature we can segment the topographic image in regions of different degrees of irregularity in a given scale of observation. With the second feature we can study the variation of the degree of irregularity measured for an image pixel while we change the scale of observation. We show that the proposed method allows the identification of the sizes of irregularities that occur in topographic surfaces, such as the mean sizes of the grains
Mestrado
Mestre em Engenharia Elétrica
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Books on the topic "Calcul fractal":

1

A, Carpinteri, and Mainardi F. 1942-, eds. Fractals and fractional calculus in continuum mechanics. Wien: Springer, 1997.

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Michael, Frame, Mandelbrot Benoit B, and Mathematical Association of America, eds. Fractals, graphics, and mathematics education. [Washington, DC]: Published and distributed by the Mathematical Association of America, 2002.

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Júnior, Jacob Palis. Hyperbolicity and sensitive chaotic dynamics at homoclinic bifurcations: Fractal dimensions and infinitely many attractors. Cambridge: Cambridge University Press, 1993.

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Kaye, Brian H. Chaos & complexity: Discovering the surprising patterns of science and technology. Weinheim: VCH, 1993.

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Kaye, Brian H. Chaos & complexity: Discovering the surprising patterns of science and technology. Weinheim: VCH Verlagsgesellschaft, 1993.

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Kaye, Brian H. Chaos & complexity: Discovering the surprising patterns of science and technology. New York: Weinheim, 1993.

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PISRS 2011 International Conference on Analysis, Fractal Geometry, Dynamical Systems and Economics (2011 Messina, Italy). Fractal geometry and dynamical systems in pure and applied mathematics. Edited by Carfi David 1971-, Lapidus, Michel L. (Michel Laurent), 1956-, Pearse, Erin P. J., 1975-, Van Frankenhuysen Machiel 1967-, and Mandelbrot Benoit B. Providence, Rhode Island: American Mathematical Society, 2013.

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Ecole d'été de probabilités de Saint-Flour (25th 1995). Lectures on probability theory and statistics: Ecole d'Eté de Probabilités de Saint-Flour XXV--1995. Edited by Barlow M. T, Nualart David 1951-, Bernard P. 1944-, Barlow M. T, and Nualart David 1951-. Berlin: Springer, 1998.

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Bologna, Mauro, Bruce West, and Paolo Grigolini. Physics of Fractal Operators. Springer, 2003.

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Bologna, Mauro, Bruce West, and Paolo Grigolini. Physics of Fractal Operators. Springer New York, 2012.

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Book chapters on the topic "Calcul fractal":

1

Kolwankar, Kiran M., and Anil D. Gangal. "Local Fractional Calculus: a Calculus for Fractal Space-Time." In Fractals, 171–81. London: Springer London, 1999. http://dx.doi.org/10.1007/978-1-4471-0873-3_12.

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Gil’mutdinov, Anis Kharisovich, Pyotr Arkhipovich Ushakov, and Reyad El-Khazali. "Fractal Calculus Fundamentals." In Analog Circuits and Signal Processing, 21–39. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-45249-4_2.

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West, Bruce J., Paolo Grigolini, and Mauro Bologna. "Fractal Calculus for CERTs." In SpringerBriefs in Bioengineering, 69–83. Cham: Springer International Publishing, 2023. http://dx.doi.org/10.1007/978-3-031-46277-1_5.

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Chen, Wen, HongGuang Sun, and Xicheng Li. "Fractal and Fractional Calculus." In Fractional Derivative Modeling in Mechanics and Engineering, 83–114. Singapore: Springer Singapore, 2022. http://dx.doi.org/10.1007/978-981-16-8802-7_3.

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West, Bruce J., and W. Alan C. Mutch. "Fractal Calculus for Medicine." In On the Fractal Language of Medicine, 114–32. Boca Raton: CRC Press, 2024. http://dx.doi.org/10.1201/9781003495796-6.

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Saichev, Alexander I., and Wojbor A. Woyczyński. "Singular Integrals and Fractal Calculus." In Distributions in the Physical and Engineering Sciences, 149–82. Boston, MA: Birkhäuser Boston, 1997. http://dx.doi.org/10.1007/978-1-4612-4158-4_6.

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Saichev, Alexander I., and Wojbor Woyczynski. "Singular Integrals and Fractal Calculus." In Applied and Numerical Harmonic Analysis, 149–82. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-97958-8_6.

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Banerjee, Santo, D. Easwaramoorthy, and A. Gowrisankar. "Fractional Calculus on Fractal Functions." In Understanding Complex Systems, 37–60. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-62672-3_3.

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Gorenflo, R., and F. Mainardi. "Fractional Calculus." In Fractals and Fractional Calculus in Continuum Mechanics, 223–76. Vienna: Springer Vienna, 1997. http://dx.doi.org/10.1007/978-3-7091-2664-6_5.

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Gorenflo, R. "Fractional Calculus." In Fractals and Fractional Calculus in Continuum Mechanics, 277–90. Vienna: Springer Vienna, 1997. http://dx.doi.org/10.1007/978-3-7091-2664-6_6.

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Conference papers on the topic "Calcul fractal":

1

Shockro, Jennifer, and Haris J. Catrakis. "Large Scale Geometrical Aspects of Turbulent Jet Scalar Regions and Interfaces: Measurement and Modeling." In ASME/JSME 2007 5th Joint Fluids Engineering Conference. ASMEDC, 2007. http://dx.doi.org/10.1115/fedsm2007-37091.

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This study focuses on the measurement and modeling of large scale geometrical aspects of turbulent jet scalar regions and interfaces. While several previous studies have focused on the small scale geometrical properties using fractal ideas, examination of the large scale geometrical aspects requires the development of what we call generalized fractals, i.e. the scale-dependent generalization of the original self-similar geometric framework. Our work involves the purely meshless approach to the determination of the generalized fractal properties, pioneered by Catrakis, that eliminates the need for grid-based box counting. We investigate the purely meshless generalized fractal approach using experimental databases generated in our laboratories on fully-developed turbulent jets with a Reynolds number of Re ∼ 20,000 and a Schmidt number of Sc ∼ 2,000. In our approach, we examine the dependence of the generalized fractal aspects of the turbulent interfaces at various spatial resolution scales. Our results indicate that the large scale geometrical aspects are strongly scale dependent and amenable to modeling using generalized fractal functions.
2

Jaggard, Dwight L., and Y. Kim. "Scattering and Inverse scattering from bandlimited fractal slabs." In OSA Annual Meeting. Washington, D.C.: Optica Publishing Group, 1987. http://dx.doi.org/10.1364/oam.1987.wx4.

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The fractal concept is useful in describing structures displaying dilation symmetry. Such structures are said to be self-similar. Physical structures, whether naturally occurring or man-made, are at best self-similar over a regime of interest between an appropriate inner and outer scale. Here we model such structures by a bandlimited Weierstrass function which incorporates these scales and possesses an identifiable fractional dimension denoted the fractal dimension. We call such structures bandlimited fractals. Of interest here is the scattering and inverse scattering of waves from 1-D bandlimited fractal slabs. We demonstrate exact and approximate methods for calculating the reflection from such slabs and relate the scattering data to the fractal dimension of the slab. In certain conditions, the solution of this forward problem provides a means for attacking the inverse problem. In the case of the latter, the fractal dimension is desired based on scattering data. Here we find criteria for the approximate solution of this inverse problem and demonstrate the method on bandlimited fractal slabs of varying dimension. This method is useful in the remote probing of turbulent media or in the scattering of optical waves from imperfect optical structures.
3

Bhattacharyya, Arka, Amartya Banerjee, Sayan Chatterjee, and Bhaskar Gupta. "Dual-Band Minkowski Fractal Patch Antenna With Polarization Diversity." In 2020 IEEE Calcutta Conference (CALCON). IEEE, 2020. http://dx.doi.org/10.1109/calcon49167.2020.9106540.

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Si, Xiuhua, Jinxiang Xi, and Xihai Tao. "The Study of Calcium Carbonate Scaling on Low Energy Surfaces." In 2010 14th International Heat Transfer Conference. ASMEDC, 2010. http://dx.doi.org/10.1115/ihtc14-22058.

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Scale deposition on heat transfer surfaces from water containing dissolved salts reduces the efficiency and performance of heat transfer equipments considerably. Scale deposition could be reduced through physical or chemical methods. In some cases, chemical methods are unacceptable, due to cost, contamination issues, etc. In these cases, physical methods are the only acceptable choices. Surface energy of the heat exchanger has been thought to be one important factor affecting the growth of fouling. Applying low energy surfaces to reduce scaling deposition is one of the effective physical methods. The formation and the characteristics of the calcium carbonate scaling on low energy surfaces have been studied in this paper. Copper and stainless steel surfaces were modified by micro-scale (μm thickness) PTFE (Poly-Tetrofluorethylene) films and nano-scale (nm thickness) thiolate SAMs (Self-Assembly Monolayers). The resulting surface energy of PTFE films and SAMs layers based on copper and stainless steel were significantly reduced compared with the original metal surfaces. To study the formation of the calcium carbonate scale, a recirculation cooling water system was used. The formation of the calcium carbonate scale on PTFE surfaces, SAMs surfaces, polished copper surfaces, and polished stainless steel surfaces were investigated respectively. The rate of calcium carbonate scale formation was decreased and the induction period was prolonged with the decrease of the heat transfer surface energy. The characteristics of the calcium carbonate scale formed on heat transfer surfaces with different surface energies was analyzed with fractal theory after taking photos with SEM (Scanning Electron Microscope). The fractal dimension values of the calcium carbonate scale on different heat transfer surfaces with different surface energies were calculated. The results showed that the fractal dimension values of calcium carbonate scale formed on lower energy PTFE and Cu-SAMs surfaces were greater than those that formed on higher energy Cu and stainless steel surfaces. Results of this study clearly indicated that the formation of calcium carbonate scaling on lower energy heat transfer surfaces is reduced.
5

Seal, Sayan, Prasun Chail, Souvik Roy, and Abhik Mukherjee. "Exploring the fractal nature in dynamics of crimes during recent Lok Sabha elections in West Bengal." In 2020 IEEE Calcutta Conference (CALCON). IEEE, 2020. http://dx.doi.org/10.1109/calcon49167.2020.9106565.

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Mishra, Asha S. "Application of Fractional Calculus in Reservoir Characterization From Pressure Transient Data in Fractal Reservoir With Phase Redistribution." In ASME 2009 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2009. http://dx.doi.org/10.1115/detc2009-86204.

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The present paper describes the use of pressure derivative and second derivative of integral of pressure in a fractal reservoir with matrix participation with phase redistribution in a geological environment that are not possible by conventional techniques. The analysis of this type of data in reservoir characterization is known as “inverse problem” and one can obtain information about interwell and vertical permeability distribution in a reservoir. The fractal geometry in a dynamic pressure transient tests data plays a very vital role for heterogeneity characterization. The pressure transient response is analyzed for flow in a connected fracture network and fracture with matrix participation. The computer aided matching technique for both pressure and its derivative by nonlinear regression techniques are used in estimating the reservoir properties from measured drawdown/buildup and falloff pressure data of heterogeneous reservoir. In the present paper the fractional calculus approach has been utilized to solve the diffusivity equation with phase redistribution in fractal reservoir. The pressure solution of the diffusivity is in terms of Laplace space and its analytical inversion is not possible. We have obtained numerically inversion of the problem and the pressure, pressure derivative, integral of pressure and its first and second derivative has been calculated. The permeability estimated from pressure transient test data of a well are in good agreement with the identified the geological model.
7

Bogdan, Paul, and Radu Marculescu. "A fractional calculus approach to modeling fractal dynamic games." In 2011 50th IEEE Conference on Decision and Control and European Control Conference (CDC-ECC 2011). IEEE, 2011. http://dx.doi.org/10.1109/cdc.2011.6161323.

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8

Repperger, D. W., K. A. Farris, C. C. Barton, and S. Tebbens. "Time series data analysis using fractional calculus concepts and fractal analysis." In 2009 IEEE International Conference on Systems, Man and Cybernetics - SMC. IEEE, 2009. http://dx.doi.org/10.1109/icsmc.2009.5346218.

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9

Butera, Salvatore, and Mario Di Paola. "A physical approach to the connection between fractal geometry and fractional calculus." In 2014 International Conference on Fractional Differentiation and its Applications (ICFDA). IEEE, 2014. http://dx.doi.org/10.1109/icfda.2014.6967378.

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Ławrynowicz, Julian, Tatsuro Ogata, and Osamu Suzuki. "Differential and integral calculus for a Schauder basis on a fractal set (I) (Schauder basis 80 years after)." In Lvov Mathematical School in the Period 1915-45. Warsaw: Institute of Mathematics Polish Academy of Sciences, 2009. http://dx.doi.org/10.4064/bc87-0-11.

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