Fractal Characteristic Evolution of Coastal Settlement Land Use: A Case of Xiamen, China

Coastal settlements in urban areas show certain degrees of spatial complexity. Understanding the evolution law of fractal settlements is practically important for marine engineering and urban planning. In this paper, we investigate the fractal evolution of coastal settlement land use based on fractal theory. The fractal dimensions of the land uses for three typically coastal settlements in Xiamen city, China, are obtained to quantify their spatial complexity. The results reveal the fractal characteristics and regional differences of the coastal settlements. Furthermore, nonlinear modeling is applied to describe the fractal dimension evolution of the coastal settlement land uses from 2000 to 2018. Three settlements in rapid urbanization show different nonlinear evolution equations of the fractal dimension due to their different land uses. This study might provide a theoretical basis for understanding the fractal characteristic evolution of coastal settlements in urban areas and show its potential application in urban geography.

Review about the Application of Fractal Theory in the Research of Packaging Materials

The work is intended to summarize the recent progress in the work of fractal theory in packaging material to provide important insights into applied research on fractal in packaging materials. The fractal analysis methods employed for inorganic materials such as metal alloys and ceramics, polymers, and their composites are reviewed from the aspects of fractal feature extraction and fractal dimension calculation methods. Through the fractal dimension of packaging materials and the fractal in their preparation process, the relationship between the fractal characteristic parameters and the properties of packaging materials is discussed. The fractal analysis method can qualitatively and quantitatively characterize the fractal characteristics, microstructure, and properties of a large number of various types of packaging materials. The method of using fractal theory to probe the preparation and properties of packaging materials is universal; the relationship between the properties of packaging materials and fractal dimension will be a critical trend of fractal theory in the research on properties of packaging materials.

FRACTAL CHARACTERISTIC AND DOMAIN EXTENSION FACTOR STUDY ON CONTACT MODEL OF ROUGH SURFACE

Machine joint surface has an important impact on the performance of mechanical systems. Based on fractal theory, joint surface is assumed to be the contact between absolute smooth surface and rough surface. Through the analysis of the contact process, the contact mechanics model, the contact stiffness model and the three-dimensional surface micro-contact model are studied. To obtain fractal characteristic, the factors and laws affecting the contact characteristics are indicated through digital simulation. The concept of micro-convex body hierarchy is proposed. The critical values are related to the scale of micro-convex bodies and affected by the property parameters of the material. It is proved that the critical point is smooth and continuous, the parameter characteristics of the critical point are determined and the error between prediction and practice is reduced. In the integral calculation of the model, the experimental constants are also established to facilitate the calculation. The results show that the contact process of rough surface is consistent with the actual contact. It makes up the deficiency of KE model by considering the interaction between micro-convex bodies.

An index of the fractal characteristic of an airway tree is associated with airflow limitations and future body mass index reduction in COPD patients

An airway tree is a fractal object. We showed that the distribution of minimal inner cross-sectional area (iCSA) of airway branches can be expressed by a fractal index, D, of minimal iCSA. This D was correlated with airflow limitation and future body mass index reduction in chronic obstructive pulmonary disease patients, as predicted by Hess–Murray’s law.

Study on the relation between damage and permeability of sandstone at depth under cyclic loading

The damage and permeability evolution of rock under stress is of great significance to engineering safety. In this paper, the evolution law of rock damage and permeability is studied by means of acoustic emission (AE) seepage experiment on deep roof sandstone with cyclic loading. Characterization of damage uses the changes in acoustic emission fractal characteristics and compression parameter which based on elastic modulus. The experimental results show that the AE events has fractal characteristic, in which the AE b-value and correlation dimension can represent the damage of rock. When the fractal characteristic value of AE increases, it indicates that the rock is in the compaction stage and the damage is not obvious. When the fractal characteristic value of AE drops, it indicates that the rock was damaged, and the permeability increase. Under the cyclic load increasing step by step, the elastic modulus first increases and then decrease. Introducing compression parameter C to characterize the state of compaction and damage, it is obtained that the rock damage state and hydrostatic permeability show a power law function relationship with porosity and have the same monotonicity. When compression parameter is less than zero, the evolution law of permeability and damage can be described by functional relationship between hydrostatic permeability K and compression parameter C.

Analysis of rupture mode and acoustic emission characteristic of rock and coal samples with holes

In order to understand the rupture mechanism of rock and coal samples with holes, the acoustic emission (AE) tests of rock and coal samples with holes under uniaxial compression are done. Through the AE tests, the basic mechanical and AE variation rule of two samples in the total rupture process are obtained, the dynamic rupture process was observed and finally the spatial evolution and multi-fractal characteristic of AE are analyzed. The results show that the variation rule of AE events of two samples are coincident with the variation rule of stress. The uniaxial compressive strength of a rock sample with a hole is about five times than that of a coal sample with a hole, and the maximum AE pulsing counts (AEPC) of a rock sample with a hole is much larger than that of a coal sample with a hole. Due to the variation of lithology, the dynamic rupture process and the spatial evolution rule of AE events of rock and coal samples with holes are obviously different. But the distributions of the three-dimensional locations of the two samples are coincident with the macroscopic rupture morphology. Both of them have multi-fractal characteristic in the process of rupture, the multi-fractal spectrum width Δf(α) at the time of rupture is smaller than that before rupture and the Δf(α) before rupture is smaller than that after rupture. This indicates that the energy (E) before and after rupture is smaller than that at the time of rupture, the E after rupture is smaller than that before rupture and the E of a coal sample with a hole in each stage is less than that of the corresponding stages of a rock sample with a hole.