Fractal Geometry and Properties of Doped BaTiO3 Ceramics

2010 ◽  
Vol 67 ◽  
pp. 42-48 ◽  
Author(s):  
V.V. Mitic ◽  
V.B. Pavlovic ◽  
L. Kocic ◽  
V. Paunovic ◽  
L. Zivkovic
Keyword(s):  
Fractal Dimension ◽  
Solid State ◽  
Fractal Geometry ◽  
Grain Shape ◽  
Grain Structure ◽  
Fractal Method ◽  
Ceramic Structure ◽  
New Approach ◽  
Fractal Modeling ◽  
Dielectrical Properties

Taking into account that the complex grain structure is difficult to describe by using traditional analytical methods, in this study, in order to establish ceramic grain shapes of sintered BaTiO3, new approach on correlation between microstructure and properties of doped BaTiO3 ceramics based on fractal geometry has been developed. BaTiO3 ceramics doped with various dopants (MnCO3, Er2O3, Yb2O3) were prepared using conventional solid state procedure, and were sintered at 1350oC for four hours. The microstructure of sintered specimens was investigated by SEM-5300. Using method of fractal modeling a reconstruction of microstructure configurations, like grains shapes, or intergranular contacts has been successfully done. Furthermore, the area of grains surface was calculated using fractal correction that expresses the irregularity of grains surface through fractal dimension. The presented results, indicate that fractal method for ceramics structure analysis provides a new approach for describing, predicting and modeling the grain shape and relations between the BaTiO3-ceramic structure and dielectrical properties.

scholarly journals Comparison and Review of the Advantages of the Fractal Method (Variogram) With Respect to the Nettelton in Determining the Density of the Bouguer Plane in the Southern Hormozgan: Iran

2013 ◽  
Vol 3 (1) ◽  
pp. 1-8
Author(s):  
Samadi Hamid Reza ◽  
Teymoorian Asghar
Keyword(s):  
Surface Roughness ◽  
Fractal Dimension ◽  
Fractal Geometry ◽  
Bouguer Anomaly ◽  
Research Area ◽  
Common Method ◽  
Fractal Method ◽  
Optimal Density ◽  
Regional Geology

In this paper we describe a comparison between the methods of Variogram and Nettelton to establish the density of the Bouguer plane. The Nettelton’s method is a common method for determining the density along a profile which is based on the least chosen profile’s topographic resemblance with the chosen density of related to that profile of the region. The 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 in south of Hormozgan province can be determined which is 2/7 g/cm3forthe under-research area. The density of the Bouguer plane in the region by the Nettelton’s method has been calculated 2/3g/cm3. This determined optimal density has been used in correcting and reviewing its result in the case of Isostazy state and some very good results have been achieved which has an amazing coincidence with the regional geology and the drilled exploration wells in the area.

TEM studies of solid-state reactions in sputter-deposited Nb/Al multilayer thin films

1996 ◽  
Vol 54 ◽  
pp. 1020-1021
Author(s):  
F. Ma ◽  
S. Vivekanand ◽  
K. Barmak ◽  
C. Michaelsen
Keyword(s):  
Thin Films ◽  
Solid State ◽  
Stoichiometric Composition ◽  
Analytical Electron Microscopy ◽  
Grain Structure ◽  
Solid State Reactions ◽  
Multilayer Thin Films ◽  
X Ray Diffraction ◽  
X Ray ◽  
Sputter Deposited

Solid state reactions in sputter-deposited Nb/Al multilayer thin films have been studied by transmission and analytical electron microscopy (TEM/AEM), differential scanning calorimetry (DSC) and X-ray diffraction (XRD). The Nb/Al multilayer thin films for TEM studies were sputter-deposited on (1102)sapphire substrates. The periodicity of the films is in the range 10-500 nm. The overall composition of the films are 1/3, 2/1, and 3/1 Nb/Al, corresponding to the stoichiometric composition of the three intermetallic phases in this system.Figure 1 is a TEM micrograph of an as-deposited film with periodicity A = dA1 + dNb = 72 nm, where d's are layer thicknesses. The polycrystalline nature of the Al and Nb layers with their columnar grain structure is evident in the figure. Both Nb and Al layers exhibit crystallographic texture, with the electron diffraction pattern for this film showing stronger diffraction spots in the direction normal to the multilayer. The X-ray diffraction patterns of all films are dominated by the Al(l 11) and Nb(l 10) peaks and show a merging of these two peaks with decreasing periodicity.

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

scholarly journals Towards Manufacturing of Ultrafine-Laminated Structures in Metallic Tubes by Accumulative Extrusion Bonding

Metals ◽  
2021 ◽  
Vol 11 (3) ◽  
pp. 389
Author(s):  
Matthew R. Standley ◽  
Marko Knezevic
Keyword(s):  
Solid State ◽  
Wall Thickness ◽  
Complex Geometry ◽  
Tube Wall ◽  
Film Theory ◽  
Radial Strain ◽  
Surface Preparation ◽  
Grain Structure ◽  
Outer Diameter ◽  
Laminated Structures

A severe plastic deformation process, termed accumulative extrusion bonding (AEB), is conceived to steady-state bond metals in the form of multilayered tubes. It is shown that AEB can facilitate bonding of metals in their solid-state, like the process of accumulative roll bonding (ARB). The AEB steps involve iterative extrusion, cutting, expanding, restacking, and annealing. As the process is iterated, the laminated structure layer thicknesses decrease within the tube wall, while the tube wall thickness and outer diameter remain constant. Multilayered bimetallic tubes with approximately 2 mm wall thickness and 25.25 mm outer diameter of copper-aluminum are produced at 52% radial strain per extrusion pass to contain eight layers. Furthermore, tubes of copper-copper are produced at 52% and 68% strain to contain two layers. The amount of bonding at the metal-to-metal interfaces and grain structure are measured using optical microscopy. After detailed examination, only the copper-copper bimetal deformed to 68% strain is found bonded. The yield strength of the copper-copper tube extruded at 68% improves from 83 MPa to 481 MPa; a 480% increase. Surface preparation, as described by the thin film theory, and the amount of deformation imposed per extrusion pass are identified and discussed as key contributors to enact successful metal-to-metal bonding at the interface. Unlike in ARB, bonding in AEB does not occur at ~50% strain revealing the significant role of more complex geometry of tubes relative to sheets in solid-state bonding.

Statistical Assessment of the Effects of Grain-Structure Representation and Micro-Properties on the Behavior of Bonded Block Models for Brittle Rock Damage Prediction

2021 ◽  
Vol 13 (14) ◽  
pp. 7889
Author(s):  
Carlos Efrain Contreras Inga ◽  
Gabriel Walton ◽  
Elizabeth Holley
Keyword(s):  
Grain Size ◽  
Grain Shape ◽  
Grain Structure ◽  
Minor Effect ◽  
Unique Contribution ◽  
Structure Generation ◽  
Structure Representation ◽  
The Real ◽  
Study Results ◽  
Block Models

The ability to predict the mechanical behavior of brittle rocks using bonded block models (BBM) depends on the accuracy of the geometrical representation of the grain-structure and the applied micro-properties. This paper evaluates the capabilities of BBMs for predictive purposes using an approach that employs published micro-properties in combination with a Voronoi BBM that properly approximates the real rock grain-structure. The Wausau granite, with Unconfined Compressive Strength (UCS) of 226 MPa and average grain diameter of 2 mm, is used to evaluate the effectiveness of the predictive approach. Four published sets of micro-properties calibrated for granites with similar mineralogy to the Wausau granite are used for the assessment. The effect of grain-structure representation in Voronoi BBMs is analyzed, considering grain shape, grain size and mineral arrangement. A unique contribution of this work is the explicit consideration of the effect of stochastic grain-structure generation on the obtained results. The study results show that the macro-properties of a rock can be closely replicated using the proposed approach. When using this approach, the micro-properties have a greater impact on the realism of the predictions than the specific grain-structure representation. The grain shape and grain size representations have a minor effect on the predictions for cases that do not deviate substantially from the real average grain geometry. However, the stochastic effect introduced by the use of randomly-generated Voronoi grain-structures can be significant, and this effect should be considered in future studies.

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.

scholarly journals Multicrack Localization in Rotors Based on Proper Orthogonal Decomposition Using Fractal Dimension and Gapped Smoothing Method

2016 ◽  
Vol 2016 ◽  
pp. 1-17 ◽  
Author(s):  
Zhiwen Lu ◽  
Dawei Dong ◽  
Shancheng Cao ◽  
Huajiang Ouyang ◽  
Chunrong Hua
Keyword(s):  
Fractal Dimension ◽  
Proper Orthogonal Decomposition ◽  
Orthogonal Decomposition ◽  
Smoothing Method ◽  
The Finite Element Method ◽  
New Approach ◽  
Rotor Systems ◽  
Crack Configuration ◽  
Proper Orthogonal ◽  
Robust To Noise

Multicrack localization in operating rotor systems is still a challenge today. Focusing on this challenge, a new approach based on proper orthogonal decomposition (POD) is proposed for multicrack localization in rotors. A two-disc rotor-bearing system with breathing cracks is established by the finite element method and simulated sensors are distributed along the rotor to obtain the steady-state transverse responses required by POD. Based on the discontinuities introduced in the proper orthogonal modes (POMs) at the locations of cracks, the characteristic POM (CPOM), which is sensitive to crack locations and robust to noise, is selected for cracks localization. Instead of using the CPOM directly, due to its difficulty to localize incipient cracks, damage indexes using fractal dimension (FD) and gapped smoothing method (GSM) are adopted, in order to extract the locations more efficiently. The method proposed in this work is validated to be effective for multicrack localization in rotors by numerical experiments on rotors in different crack configuration cases considering the effects of noise. In addition, the feasibility of using fewer sensors is also investigated.

Research of Method to Diagnosing Complex Fault of Compressor in Pipeline Station

2006 ◽  
Author(s):  
Zhao-Hui Wang ◽  
Lai-Bin Zhang ◽  
Wei Liang ◽  
Lixiang Duan
Keyword(s):  
Fractal Dimension ◽  
Diagnostic System ◽  
Normal Fault ◽  
Vibration Signal ◽  
Good Tool ◽  
Fractal Method ◽  
Fault Features ◽  
Complex Fault ◽  
Integrity Management ◽  
Oil Gas

The compressor is dynamical equipment in pipeline station to deliver oil gas, it’s fault can result big accident such as stopping delivery and producing economic losing, and some fault of compressor are very complex due to the compressor’s complicated structure. Many compressor have carried simple diagnostic system, which can only diagnose normal fault, are not effective for diagnosing complex fault because these fault attributes are not obvious. This paper has researched the method to diagnose complex fault, by collecting the compressor’s vibration signals, using wavelet noise reduction technique and the fractal dimension method to process the vibration signal, which can abstract the non-obvious characteristics of complex fault effectively. The basic principle of fractal method applied in fault diagnosis is described. The result implies that the fractal dimension of good compressor is 4.4, and the fractal dimension of faulty compressor is 5.36, and fractal dimension of compressor with complex faults is 5.42. It is illustrated that this method is very effective for describing the fault features and diagnosing the complex fault of complex. This method can diagnose and predict the complex fault with a high correctness, and has been used in the Shanxi-Beijing pipeline station successfully, Which provide a good tool for pipeline’s Safety and Integrity Management.

scholarly journals The Solutions to the Uncertainty Problem of Urban Fractal Dimension Calculation

Entropy ◽  
2019 ◽  
Vol 21 (5) ◽  
pp. 453 ◽  
Author(s):  
Chen
Keyword(s):  
Fractal Dimension ◽  
Spatial Analysis ◽  
Fractal Geometry ◽  
Fractal Dimensions ◽  
Dimension Estimation ◽  
Scale Free ◽  
Factors Influencing ◽  
Calculation Results ◽  
Fractal Patterns ◽  
Main Factors

Fractal geometry provides a powerful tool for scale-free spatial analysis of cities, but the fractal dimension calculation results always depend on methods and scopes of the study area. This phenomenon has been puzzling many researchers. This paper is devoted to discussing the problem of uncertainty of fractal dimension estimation and the potential solutions to it. Using regular fractals as archetypes, we can reveal the causes and effects of the diversity of fractal dimension estimation results by analogy. The main factors influencing fractal dimension values of cities include prefractal structure, multi-scaling fractal patterns, and self-affine fractal growth. The solution to the problem is to substitute the real fractal dimension values with comparable fractal dimensions. The main measures are as follows. First, select a proper method for a special fractal study. Second, define a proper study area for a city according to a study aim, or define comparable study areas for different cities. These suggestions may be helpful for the students who take interest in or have already participated in the studies of fractal cities.

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