The fractal dimension of the fusion line in different dissimilar welded joints is measured with Box Dimension Method.The non scale region of the fusion line with fractal character is calculated. The fusion line in th...The fractal dimension of the fusion line in different dissimilar welded joints is measured with Box Dimension Method.The non scale region of the fusion line with fractal character is calculated. The fusion line in the dissimilar welded joint is proved to be a fractal structure. The change and influence factors of the fractal dimension of the fusion line are studied.展开更多
A major concern in modern smart-phones and hand-held devices is a way of mitigating the time interval error (TIE) perceived at high-speed digital transits along the traces of the circuit-board (rigid and or flexible) ...A major concern in modern smart-phones and hand-held devices is a way of mitigating the time interval error (TIE) perceived at high-speed digital transits along the traces of the circuit-board (rigid and or flexible) used in baseband infrastructures. Indicated here is a way of adopting a planar fractal inductor configuration to improvise the necessary time-delay in the transits of digital signal phase jitter and reduce the TIE. This paper addresses systematic design considerations on fractal inductor geometry commensurate with practical aspects of its implementation as delaylines in the high-speed digital transports at the baseband operations of smart-phone infrastructures. Experimental results obtained from a test module are presented to illustrate the efficacy of the design and acceptable delay performance of the test structure commensurate with the digital transports of interest.展开更多
A consistent physical and mathematical model of the propagation of electromagnetic waves in an inhomogeneous medium with strong discontinuities of the electromagnetic field at the interface of two media, which is a ro...A consistent physical and mathematical model of the propagation of electromagnetic waves in an inhomogeneous medium with strong discontinuities of the electromagnetic field at the interface of two media, which is a rough surface, was developed. Mathematical modeling of rough surfaces and their profiles was carried out using fractal geometry, which allows us to display the topology of the object as close as possible to reality. For real heterogeneous rough structures, we have developed a through-counting method that takes into account the continuity of the total current at the interfaces of adjacent media, the effect of induced surface charge and surface current. This approach lets one avoid the necessity to set surface impedances depending on the structure of the field being determined and on the material properties.展开更多
In order to monitor and forecast the deformation of the brick-concrete building, by taking a brick-concrete building as research object, fiber grating sensors were used to collect the monitoring data and double logari...In order to monitor and forecast the deformation of the brick-concrete building, by taking a brick-concrete building as research object, fiber grating sensors were used to collect the monitoring data and double logarithmic curve of limit value characteristic and monitoring data were obtained based on the fractal theory. Constant dimension fractal method cannot be used to analyze the data directly. With the method of variable dimension fractal, we accumulate data, and the double logarithmic curve is smooth. Piecewise fractal dimensions are close. The outer interpolation method is used to calculate the fractal dimension of the next point and then back calculate the vertical displacement. The relative errors are calculated by comparing the forecast values and monitoring values, and the maximum relative error is 5.76%. The result shows that the fractal theory is suitable to use in the forecast of the deformation and the accuracy is good.展开更多
Based on the kinematic viewpoint, the concept of proportional movement is abstracted to explain the strange behaviors of fractal snowflakes. A transformation group for proportional movement is defined. Under the propo...Based on the kinematic viewpoint, the concept of proportional movement is abstracted to explain the strange behaviors of fractal snowflakes. A transformation group for proportional movement is defined. Under the proportional movement transformation groups, necessary and sufficient conditions for self-similarity of multilevel structures are presented. The characteristic topology of snowflake-like fractal patterns, identical to the topology of ternary-segment fractal line, is proved. Moreover, the topological evolution of N-segment line is explored. The concepts of limit growth and infinite growth are clarified,and the corresponding growth conditions are derived. The topological invariant properties of N-segment line are exposed. In addition, the proposition that the topological evolution of the N-segment line is mainly controlled by the topological invariant N is verified.展开更多
文摘The fractal dimension of the fusion line in different dissimilar welded joints is measured with Box Dimension Method.The non scale region of the fusion line with fractal character is calculated. The fusion line in the dissimilar welded joint is proved to be a fractal structure. The change and influence factors of the fractal dimension of the fusion line are studied.
文摘A major concern in modern smart-phones and hand-held devices is a way of mitigating the time interval error (TIE) perceived at high-speed digital transits along the traces of the circuit-board (rigid and or flexible) used in baseband infrastructures. Indicated here is a way of adopting a planar fractal inductor configuration to improvise the necessary time-delay in the transits of digital signal phase jitter and reduce the TIE. This paper addresses systematic design considerations on fractal inductor geometry commensurate with practical aspects of its implementation as delaylines in the high-speed digital transports at the baseband operations of smart-phone infrastructures. Experimental results obtained from a test module are presented to illustrate the efficacy of the design and acceptable delay performance of the test structure commensurate with the digital transports of interest.
文摘A consistent physical and mathematical model of the propagation of electromagnetic waves in an inhomogeneous medium with strong discontinuities of the electromagnetic field at the interface of two media, which is a rough surface, was developed. Mathematical modeling of rough surfaces and their profiles was carried out using fractal geometry, which allows us to display the topology of the object as close as possible to reality. For real heterogeneous rough structures, we have developed a through-counting method that takes into account the continuity of the total current at the interfaces of adjacent media, the effect of induced surface charge and surface current. This approach lets one avoid the necessity to set surface impedances depending on the structure of the field being determined and on the material properties.
文摘In order to monitor and forecast the deformation of the brick-concrete building, by taking a brick-concrete building as research object, fiber grating sensors were used to collect the monitoring data and double logarithmic curve of limit value characteristic and monitoring data were obtained based on the fractal theory. Constant dimension fractal method cannot be used to analyze the data directly. With the method of variable dimension fractal, we accumulate data, and the double logarithmic curve is smooth. Piecewise fractal dimensions are close. The outer interpolation method is used to calculate the fractal dimension of the next point and then back calculate the vertical displacement. The relative errors are calculated by comparing the forecast values and monitoring values, and the maximum relative error is 5.76%. The result shows that the fractal theory is suitable to use in the forecast of the deformation and the accuracy is good.
基金Project supported by the National Natural Science Foundation of China(Nos.10872114,11072125,and 11272175)the National Natural Science Foundation of Jiangsu Province(No.SBK201140044)the Fundation of Tutor for Doctor Degree of Higher Education of China(No.20130002110044)
文摘Based on the kinematic viewpoint, the concept of proportional movement is abstracted to explain the strange behaviors of fractal snowflakes. A transformation group for proportional movement is defined. Under the proportional movement transformation groups, necessary and sufficient conditions for self-similarity of multilevel structures are presented. The characteristic topology of snowflake-like fractal patterns, identical to the topology of ternary-segment fractal line, is proved. Moreover, the topological evolution of N-segment line is explored. The concepts of limit growth and infinite growth are clarified,and the corresponding growth conditions are derived. The topological invariant properties of N-segment line are exposed. In addition, the proposition that the topological evolution of the N-segment line is mainly controlled by the topological invariant N is verified.
