FRACTAL GEOMETRY AND ECOLOGY OF LICHENS

Fractals ◽  
1993 ◽  
Vol 01 (03) ◽  
pp. 346-353 ◽  
Author(s):  
ANGELO DE MARCHI ◽  
DAVIDE CASSI
Keyword(s):  
Mathematical Model ◽  
Direct Measurement ◽  
Fractal Geometry ◽  
Fractal Dimensions ◽  
Life Forms ◽  
Point Of View ◽  
Rhizocarpon Geographicum

From a morphological point of view lichens are usually classified in three life-forms: foliose, crustose and fruticose. In this paper we consider one lichen for each of them [a foliose (Parmelia tiliacea), a crustose (Rhizocarpon geographicum) and a fruticose (Cladonia mediterranea) lichen], and by direct measurement we show that these samples have fractal geometry and we detemine their fractal dimensions and fractality ranges. On the basis of these results, we then discuss the possible ecological causes that could have selected these geometries and that should be considered in a realistic mathematical model of growth.

On the displacements of the contours of the optic-electronic space images. Mathematical modeling of displacement

2017 ◽  
Vol 992 (4) ◽  
pp. 32-38 ◽  
Author(s):  
E.G. Voronin
Keyword(s):  
Mathematical Modeling ◽  
Remote Sensing ◽  
Mathematical Model ◽  
Point Of View ◽  
Design Features ◽  
Space Images ◽  
Electronic Imaging ◽  
Measuring Accuracy ◽  
Physical Laws

The article opens a cycle of three consecutive publications dedicated to the phenomenon of the displacement of the same points in overlapping scans obtained adjacent CCD matrices with opto-electronic imagery. This phenomenon was noticed by other authors, but the proposed explanation for the origin of displacements and the resulting estimates are insufficient, and developed their solutions seem controversial from the point of view of recovery of the measuring accuracy of opticalelectronic space images, determined by the physical laws of their formation. In the first article the mathematical modeling of the expected displacements based on the design features of a scanning opto-electronic imaging equipment. It is shown that actual bias cannot be forecast, because they include additional terms, which may be gross, systematic and random values. The proposed algorithm for computing the most probable values of the additional displacement and ways to address some of the systematic components of these displacements in a mathematical model of optical-electronic remote sensing.

Emulsion Stability Evaluation Using Fractal Dimensions Approach

2007 ◽  
Vol 555 ◽  
pp. 177-182 ◽  
Author(s):  
Snezana Pašalić ◽  
P.B. Jovanić ◽  
B. Bugarski
Keyword(s):  
Visual Information ◽  
Emulsion Stability ◽  
Fractal Dimensions ◽  
Ccd Camera ◽  
Point Of View ◽  
Stable Region ◽  
Stability Evaluation ◽  
Water Emulsion ◽  
The Moment ◽  
Oil In Water Emulsion

There are many developed strategies for evaluating emulsion stability, aimed at determining the life circle of emulsions. Most of them are based on rheological properties of emulsions. There are, however, very few based on direct emulsion observations. In this paper we present a developed method for the emulsion stability evaluation by direct observation of optical emulsion properties. We propose the fractal dimension approach as a stability quantification measure. The method is based on the measure of emulsion transmittance properties, which are directly dependent on the emulsion stability at the moment of measurement. The oil in water emulsion was used as a test emulsion. The system is classified as stable emulsion and our intention was to find the moment when it starts to break. Emulsion transmittance properties were measure applying a system for acquisition of visual information, which is based on a CCD camera and a fast PC configuration equipped with the capturing software. The acquired sets of visual information were analyzed by the OZARIA software package. The fractal dimensions were determined by the box counting method. For these experiments, 100 boxes of different sizes were used. Experimental emulsions were measured after 7, 14, 21 and 28 days from the moment of creation. A slight increase in fractal dimensions was observed, which indicates that the emulsions are still in the stable region, or from the fractal point of view emulsion are still regular and no significant irregularities were observed. From the first experiments the applied methodology proved to be sensitive enough to be used for emulsions stability evaluation.

A note on design-based versus model-based variance estimation in stereology

2002 ◽  
Vol 34 (03) ◽  
pp. 484-490 ◽  
Author(s):  
Asger Hobolth ◽  
Eva B. Vedel Jensen
Keyword(s):  
Mathematical Model ◽  
Original Problem ◽  
Variance Estimation ◽  
Point Of View ◽  
Systematic Sampling ◽  
Variance Estimator ◽  
Shape Model ◽  
Model Based ◽  
Versus Model ◽  
Special Case

Recently, systematic sampling on the circle and the sphere has been studied by Gual-Arnau and Cruz-Orive (2000) from a design-based point of view. In this note, it is shown that their mathematical model for the covariogram is, in a model-based statistical setting, a special case of the p-order shape model suggested by Hobolth, Pedersen and Jensen (2000) and Hobolth, Kent and Dryden (2002) for planar objects without landmarks. Benefits of this observation include an alternative variance estimator, applicable in the original problem of systematic sampling. In a wider perspective, the paper contributes to the discussion concerning design-based versus model-based stereology.

Effective Properties of Superconducting and Superfluid Composites

1998 ◽  
Vol 12 (29n31) ◽  
pp. 3063-3073 ◽  
Author(s):  
Leonid Berlyand
Keyword(s):  
Mathematical Model ◽  
Linear Problem ◽  
Effective Properties ◽  
Point Of View ◽  
Periodicity Cell ◽  
Unit Size ◽  
Composite Media ◽  
Homogenization Procedure

We consider a mathematical model which describes an ideal superfluid with a large number of thin insulating rods and an ideal superconductor reinforced by such rods. We suggest a homogenization procedure for calculating effective properties of both composite media. From the numerical point of view the procedure amounts to solving a linear problem in a periodicity cell of unit size.

A GALLERY OF CHUA ATTRACTORS PART VI

2007 ◽  
Vol 17 (06) ◽  
pp. 1801-1910 ◽  
Author(s):  
ELEONORA BILOTTA ◽  
GIANPIERO DI BLASI ◽  
FAUSTO STRANGES ◽  
PIETRO PANTANO
Keyword(s):  
Phase Space ◽  
Spatial Organization ◽  
Fractal Dimensions ◽  
Point Of View ◽  
Experimental Investigations ◽  
Technical Data ◽  
Future Studies ◽  
Small Set ◽  
Methodological Approaches

In this article, we conclude our series of papers on the analysis and visualization of Chua attractors and their generalizations. We present a gallery of 144 n-scroll, 15 hyperchaotic and 37 synchronized systems. Along with time series and FFT we provide 3D visualizations; for some attractors we also supply Lyapunov coefficients and fractal dimensions. The goal in constructing our Gallery has been to make the general public aware of the enormous variety of chaotic phenomena and to change the widespread impression that they are isolated rarities. The Gallery provides a valuable collection of images and technical data which can be used to analyze these phenomena and to reproduce them in future studies. From a scientific point of view, we have tried to identify new methodological approaches to the study of chaos, opening nontraditional perspectives on the complexity of this domain. In our papers, we have discussed a broad range of topics, ranging from techniques for visualizing Chua attractors to computational methods allowing us to make a statistical classification of attractors' positions in phase space and to describe the evolutionary processes through which their shapes change over time. We see these processes as analogous to population dynamics in artificial environments. Within these environments, we use experimental methods to identify the models which guide morphogenetic change and which organize genetic landscapes in parameter space. This paper is organized as follows. First, we provide formal descriptions of the attractors generated by n-scroll, hyperchaotic and synchronized systems. The next section describes a Gallery of Chua attractors, generated by gradually varying the parameters and analyzing the resulting bifurcation maps. We then describe software tools allowing us to perform statistical analyses on selected sets of attractors, to visualize them, to explore their organization in phase space, and to conduct experimental investigations of the morphogenetic processes through which a small set of base attractors can generate a broad range of different forms. In the last section, we describe the creation of a Virtual 3D Gallery displaying some of the attractors we have presented in our six papers. The attractors are organized by theme, as they might be in a museum. The environment allows users to explore the attractors, interact with shapes, listen to music and sounds generated by the attractors, change their spatial organization, and create new shapes. To complete the paper — and the series — we propose a number of general conclusions.

scholarly journals Web Application for Statistical Tracking and Predicting the Evolution of Active Cases with the Novel Coronavirus (SARS-CoV-2)

2021 ◽  
pp. 70-74
Author(s):  
Iulia Clitan ◽  
◽  
Adela Puscasiu ◽  
Vlad Muresan ◽  
Mihaela Ligia Unguresan ◽  
...  
Keyword(s):  
Neural Network ◽  
Mathematical Model ◽  
Web Application ◽  
Point Of View ◽  
The Novel ◽  
End User ◽  
First Case ◽  
Novel Coronavirus ◽  
Second Wave ◽  
Over Time

Since February 2020, when the first case of infection with SARS COV-2 virus appeared in Romania, the evolution of COVID-19 pandemic continues to have an ascending allure, reaching in September 2020 a second wave of infections as expected. In order to understand the evolution and spread of this disease over time and space, more and more research is focused on obtaining mathematical models that are able to predict the evolution of active cases based on different scenarios and taking into account the numerous inputs that influence the spread of this infection. This paper presents a web responsive application that allows the end user to analyze the evolution of the pandemic in Romania, graphically, and that incorporates, unlike other COVID-19 statistical applications, a prediction of active cases evolution. The prediction is based on a neural network mathematical model, described from the architectural point of view.

scholarly journals MATHEMATICAL MODELLING OF THE UNMANNED AERIAL VEHICLE DYNAMICS

2018 ◽  
pp. 37-44
Author(s):  
V. Y. Stepanov
Keyword(s):  
Mathematical Model ◽  
Mathematical Modelling ◽  
Unmanned Aerial Vehicle ◽  
Vehicle Dynamics ◽  
Point Of View ◽  
Dynamics Analysis ◽  
Aerial Vehicle ◽  
Main Components ◽  
Controlled Object

The article gives a classification of the main components of unmanned aerial vehicle (UAV) systems, gives the areas in which the application of UAVs is actual in practice today. Further, the UAV is considered in more detail from the point of view of its flight dynamics analysis, the equation necessary for creating a mathematical model, as well as the model of an ordinary dynamic system as a non-stationary nonlinear controlled object, is given. Next, a description of the developed software for modeling and a description of program algorithm are given. Finally, a conclusion describes the necessary directions for further scientific researches.

scholarly journals FRACTALS, NATURAL DISASTERS AND ECOLOGICAL PROBLEMS OF MALDIVES

2018 ◽  
pp. 18-25
Author(s):  
Boyko Ranguelov ◽  
Fathimath Shadiya
Keyword(s):  
Local Population ◽  
Fractal Dimensions ◽  
Point Of View ◽  
Negative Consequences ◽  
Fractal Nature ◽  
Fractal Properties ◽  
Level Increase ◽  
Ocean Level ◽  
Ecological Problems ◽  
Negative Phenomena

A new idea about the fractal nature of Maldives archipelago is under investigation. The origin of this famous Maldivian islands’ country is still questionable from geodynamic point of view. The present study is focused to the assessment of the fractal properties and the coefficients of the nonlinearity (fractal dimensions) of the areal spatial distribution of the major atolls of the Maldives. This is the most vulnerable area in the world from point of view of the global warming and the possible negative consequences to the country and population from the ocean level increase. From another side the natural hazards (tsunamis, storms, etc.) are common negative phenomena attacking the country. The strongly developed tourism – more than 30% of the GDP and the increased urbanization is another factor creating ecological problems to the local population. The relationships between the fractal nature and the possible ways to avoid the pollution are also in the focus of this research.

scholarly journals A mathematical model for production routing of mechanical engineering products

2021 ◽  
Vol 25 (3) ◽  
pp. 332-341
Author(s):  
I. V. Fokin ◽  
A. N. Smirnov
Keyword(s):  
Mathematical Model ◽  
Mechanical Engineering ◽  
Complex Geometry ◽  
3D Models ◽  
Point Of View ◽  
Structural Elements ◽  
Production Environment ◽  
Automatic Mode ◽  
The Cost ◽  
Production Routing

The aim was to create a mathematical model describing the development of a production (shop-to-shop) routing of mechanical engineering products based on a 3D model and allowing the cost of the final product to be reduced. The developed mathematical model was simulated based on 3D models designed in the Siemens NX system, which were subsequently imported into the *stp format and recognized by a designed module written in the Phyton programming language. The factors of the production environment affecting the formation of the production routing of mechanical engineering products were determined. A diagram of the algorithm for the “constructive element - technological operation - means of technological equipment (equipment-tool)” relationship was developed. Based on the results of testing the developed mathematical model, the use of neural networks as a tool for the implementation and automation of the work was found advantageous as compared to the standard scheme of work of a process engineer when developing a production routing of mechanical engineering products. These advantages include a decrease in the time for the development of a routing and the cost of the final product. The developed model has a practical limitation consisting in a rather complex geometry of some structural elements of a unit, which impedes the development of an algorithm for recognizing their structure. The use of a neural network prototype in automatic mode is advisable for relatively simple parts (including a flange, hole, chamfer and rounding). However, since the number of simple units from the recognition point of view amounts to about 40% among the nomenclature of manufactured units, the reduction in the development time of the technological process in comparison with the conventional approach comprises only 10–25% of the total time of technological preparation.

Moisture adsorption thermodynamics of wood from fractal-geometry approach

Holzforschung ◽  
2004 ◽  
Vol 58 (3) ◽  
pp. 274-279 ◽  
Author(s):  
J. Cao ◽  
D.P. Kamdem
Keyword(s):  
Thermodynamic Properties ◽  
Moisture Content ◽  
Adsorption Isotherms ◽  
Fractal Geometry ◽  
Moisture Sorption ◽  
Fractal Dimensions ◽  
Future Research ◽  
Differential Heat ◽  
Internal Surfaces ◽  
Differential Heat Of Adsorption

Abstract The fractal-geometry approach was used to calculate the thermodynamic properties of moisture sorption by wood from the adsorption isotherms in this study. The results were compared with those from an isosteric approach and a calorimetric approach. The adsorption isotherms of Southern yellow pine (Pinus spp.) were measured at 4, 15, 30, and 40°C to provide source data for the calculation of both fractal-geometry and isosteric approaches. The results show that the fractal dimensions of the internal surfaces of wood vary between 2.4 and 2.5. The curves of the differential heat of adsorption −∆H against moisture content from the fractal-geometry approach are similar to those from calorimetric measurements in previous research. The −∆H values from the isosteric approach increased with moisture content within a moisture content range up to 3%. And, at moisture contents higher than 3%, the −∆H values from this method are much higher than those from the fractal-geometry approach and calorimetric approach. As a result, the fractal-geometry approach is applicable to calculate the differential thermodynamic properties of moisture sorption by wood in future research.

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