Mathematical model of the eroding effect on the surface morphology of Compressed Earth Bricks

2021 ◽  
Vol 9 (3) ◽  
pp. 245-249
Keyword(s):  
Mathematical Model ◽  
Fractal Dimension ◽  
Surface Morphology ◽  
Stochastic Modeling ◽  
Solid Surface ◽  
Fractal Geometry ◽  
Building Materials ◽  
Euclidean Geometry ◽  
Modeling Techniques

A solid-surface morphology has a rough character that prevents it from being described by Euclidean geometry; fractal geometry is plausible. From considering that the deposition of particles and their detachment significantly influences roughness, an expression based on stochastic modeling techniques was obtained to predict the fractal dimension of a surface based on the dynamics of the processes that occur in it. The model obtained was used to characterize whether fiber in building materials made of poured earth influences the surface's morphology and the effects of erosion

Fractal geometry and its uses for characterizing microstructure

1993 ◽  
Vol 51 ◽  
pp. 488-489
Author(s):  
John C. Russ
Keyword(s):  
Fractal Dimension ◽  
Fractal Geometry ◽  
Euclidean Geometry ◽  
Boundary Line ◽  
Natural Objects ◽  
Classical Geometry ◽  
Self Similar ◽  
Fractional Dimensions

Observers of nature at scales from microscopic to global have long recognized that few structures are actually described by Euclidean geometry. Mountains are not cones, clouds are not ellipsoids, and surfaces are not planes. Classical geometry allows dimensions of 0 (point), 1 (line), 2 (surface), and 3 (volume). The advent of a new geometry that allows for fractional dimensions between these integer topological values has stirred much interest because it seems to provide a tool for describing many natural objects. As is the case for many new tools, this fractal geometry is subject to some overuse and abuse.A classic illustration of fractal dimension concerns the length of a boundary line, such as the coast of Britain. Measuring maps with different scales, or striding along the coastline with various measuring rods, produces a result that depends on the resolution. More than this is required for the coastline to be fractal, however: It must also be self-similar.

scholarly journals Surface Morphology: Theoretical Model and Correlation with Experimental Results

2019 ◽  
Vol 9 (1) ◽  
pp. 3308-3313
Keyword(s):  
Fractal Dimension ◽  
Surface Morphology ◽  
Fractal Geometry ◽  
Experimental Results ◽  
Dispersed Phase ◽  
Dynamic Parameters ◽  
Dispersed System ◽  
Roughness Exponent ◽  
Theoretical Results ◽  
Solid Type

In this work, we propose a model for the description of the surface morphogenesis of a dispersed system of the solid-solid type. To obtain the model, stochastic formalism based on the master equation and the principles of fractal geometry was applied, so that the surface morphology is characterized by the fractal dimension and the roughness exponent, which are expressed as a function of the composition of the dispersed system and the dynamic parameters associated with surface formation. Theoretical results obtained were compared with experimental results, finding that the variable that shows a significant effect on the morphology of the surface of the solid-solid dispersed system is the specific surface area of the particles of the dispersed phase found in the surface, as predict theoretically.

scholarly journals The Fractal Geometry of Growth: Fluctuation–Dissipation Theorem and Hidden Symmetry

2021 ◽  
Vol 9 ◽  
Author(s):  
Petrus H. R. dos Anjos ◽  
Márcio S. Gomes-Filho ◽  
Washington S. Alves ◽  
David L. Azevedo ◽  
Fernando A. Oliveira
Keyword(s):  
Fractal Dimension ◽  
Fractal Geometry ◽  
Euclidean Geometry ◽  
Fractal Structure ◽  
Growth Dynamics ◽  
Kpz Equation ◽  
Field Equations ◽  
Fluctuation Dissipation ◽  
Hidden Symmetry ◽  
Fluctuation Dissipation Theorem

Growth in crystals can be usually described by field equations such as the Kardar-Parisi-Zhang (KPZ) equation. While the crystalline structure can be characterized by Euclidean geometry with its peculiar symmetries, the growth dynamics creates a fractal structure at the interface of a crystal and its growth medium, which in turn determines the growth. Recent work by Gomes-Filho et al. (Results in Physics, 104,435 (2021)) associated the fractal dimension of the interface with the growth exponents for KPZ and provides explicit values for them. In this work, we discuss how the fluctuations and the responses to it are associated with this fractal geometry and the new hidden symmetry associated with the universality of the exponents.

Optimal Density Determination of Bouguer Anomaly Using Fractal Analysis (Case of study: Charak area,IRAN)

2005 ◽  
Vol 1 (1) ◽  
pp. 21-24
Author(s):  
Hamid Reza Samadi
Keyword(s):  
Surface Roughness ◽  
Fractal Dimension ◽  
Fractal Analysis ◽  
Fractal Geometry ◽  
Host Rock ◽  
Bouguer Anomaly ◽  
Research Area ◽  
Density Difference ◽  
Optimal Density

In exploration geophysics the main and initial aim is to determine density of under-research goals which have certain density difference with the host rock. Therefore, we state a method in this paper to determine the density of bouguer plate, the so-called variogram method based on fractal geometry. This method is based on minimizing surface roughness of bouguer anomaly. The fractal dimension of surface has been used as surface roughness of bouguer anomaly. Using this method, the optimal density of Charak area insouth of Hormozgan province can be determined which is 2/7 g/cfor the under-research area. This determined density has been used to correct and investigate its results about the isostasy of the studied area and results well-coincided with the geology of the area and dug exploratory holes in the text area

Flammability, morphological and mechanical properties of sugar palm fiber/polyester yarn-reinforced epoxy hybrid biocomposites with magnesium hydroxide flame retardant filler

2021 ◽  
pp. 004051752110086
Author(s):  
MJ Suriani ◽  
SM Sapuan ◽  
CM Ruzaidi ◽  
DS Nair ◽  
RA Ilyas
Keyword(s):  
Tensile Strength ◽  
Surface Morphology ◽  
Flame Retardant ◽  
Tensile Properties ◽  
Magnesium Hydroxide ◽  
Building Materials ◽  
Epoxy Composite ◽  
Sem Analysis ◽  
Palm Fiber ◽  
Sugar Palm Fiber

This paper aims to study the surface morphology, flammability and tensile properties of sugar palm fiber (SPF) hybrid with polyester (PET) yarn-reinforced epoxy composite with the addition of magnesium hydroxide (Mg(OH)2) as a flame retardant. The composites were prepared by hybridized epoxy and Mg(OH)2/PET with different amounts of SPF contents (0%, 20%, 35% and 50%) using the cold press method. Then these composites were tested by horizontal burning analysis, tensile strength testing and scanning electron microscopy (SEM) analysis. The specimen with 35% SPF (Epoxy/PET/SPF-35) with the incorporation of Mg(OH)2 as a flame retardant showed the lowest burning rate of 13.25 mm/min. The flame took a longer time to propagate along with the Epoxy/PET/SPF-35 specimen and at the same time producing char. Epoxy/PET/SPF-35 also had the highest tensile strength of 9.69 MPa. Tensile properties of the SPF hybrid with PET yarn (SPF/PET)-reinforced epoxy composite was decreased at 50% SPF content due to the lack of interfacial bonding between the fibers and matrix. Surface morphology analysis through SEM showed uniform distribution of the SPF and matrix with less adhesion, which increased the flammability and reduced the tensile properties of the hybrid polymeric composites. These composites have potential to be utilized in various applications, such as automotive components, building materials and in the aerospace industry.

Pascal's Prism

2012 ◽  
Vol 96 (536) ◽  
pp. 213-220
Author(s):  
Harlan J. Brothers
Keyword(s):  
Probability Theory ◽  
Fractal Geometry ◽  
Euclidean Geometry ◽  
Fibonacci Series ◽  
Pascal’S Triangle ◽  
Number Sequences ◽  
Definition Of ◽  
Image Position ◽  
Pascal's Triangle

Pascal's triangle is well known for its numerous connections to probability theory [1], combinatorics, Euclidean geometry, fractal geometry, and many number sequences including the Fibonacci series [2,3,4]. It also has a deep connection to the base of natural logarithms, e [5]. This link to e can be used as a springboard for generating a family of related triangles that together create a rich combinatoric object.2. From Pascal to LeibnizIn Brothers [5], the author shows that the growth of Pascal's triangle is related to the limit definition of e.Specifically, we define the sequence sn; as follows [6]:

Mathematical model of static platelet adhesion on a solid surface

2003 ◽  
Vol 67A (2) ◽  
pp. 582-590 ◽  
Author(s):  
Sergei L. Vasin ◽  
Igor A. Titushkin ◽  
Viktor I. Sevastianov
Keyword(s):  
Mathematical Model ◽  
Solid Surface ◽  
Platelet Adhesion

Fractal geometry of ammonoid sutures

Paleobiology ◽  
1995 ◽  
Vol 21 (3) ◽  
pp. 329-342 ◽  
Author(s):  
Timothy M. Lutz ◽  
George E. Boyajian
Keyword(s):  
Fractal Dimension ◽  
Fractal Geometry ◽  
Two Dimensional ◽  
Evolutionary Time ◽  
Linear Features ◽  
Divider Method ◽  
Richardson Method ◽  
Components Analysis ◽  
Box Method ◽  
Range Of Variation

Interior chamber walls of ammonites range from smoothly undulating surfaces in some taxa to complex surfaces, corrugated on many scales, in others. The ammonite suture, which is the expression of the intersection of these walls on the exterior of the shell, has been used to assess anatomical complexity. We used the fractal dimension to measure sutural complexity and to investigate complexity over evolutionary time and showed that the range of variation in sutural complexity increased through time. In this paper we extend our analyses and consider two new parameters that measure the range of scales over which fractal geometry is a satisfactory metric of a suture. We use a principal components analysis of these parameters and the fractal dimension to establish a two-dimensional morphospace in which the shapes of sutures can be plotted and in which variations and evolution of suture morphology can be investigated. Our results show that morphospace coordinates of ammonitic sutures correspond to visually perceptible differences in suture shape. However, three main classes of sutures (goniatitic, ceratitic, and ammonitic) are not unambiguously discriminated in this morphospace. Interestingly, ammonitic sutures occupy a smaller morphospace than other suture types (roughly one-half of the morphospace of goniatitic and ceratitic sutures combined), and the space they occupied did not change dimensions from the Jurassic to the late Cretaceous.We also compare two methods commonly used to measure the fractal dimension of linear features: the Box method and the Richardson (or divider) method. Both methods yield comparable results for ammonitic sutures but the Richardson method yields more precise results for less complex sutures.

Sign in / Sign up

Export Citation Format

Share Document