We report on the unconventional optical properties exhibited by a two-dimensional array of thin Si nanowires arranged in a random fractal geometry and fabricated using an inexpensive,fast and maskless process compatib...We report on the unconventional optical properties exhibited by a two-dimensional array of thin Si nanowires arranged in a random fractal geometry and fabricated using an inexpensive,fast and maskless process compatible with Si technology.The structure allows for a high light-trapping efficiency across the entire visible range,attaining total reflectance values as low as 0.1%when the wavelength in the medium matches the length scale of maximum heterogeneity in the system.We show that the random fractal structure of our nanowire array is responsible for a strong in-plane multiple scattering,which is related to the material refractive index fluctuations and leads to a greatly enhanced Raman scattering and a bright photoluminescence.These strong emissions are correlated on all length scales according to the refractive index fluctuations.The relevance and the perspectives of the reported results are discussed as promising for Si-based photovoltaic and photonic applications.展开更多
This paper studies the correlation properties of the speckles in the deep Fresnel diffraction region produced by the scattering of rough self-affine fractal surfaces. The autocorrelation function of the speckle intens...This paper studies the correlation properties of the speckles in the deep Fresnel diffraction region produced by the scattering of rough self-affine fractal surfaces. The autocorrelation function of the speckle intensities is formulated by the combination of the light scattering theory of Kirchhoff approximation and the principles of speckle statistics. We propose a method for extracting the three surface parameters, i.e. the roughness w, the lateral correlation length ξ and the roughness exponent α, from the autocorrelation functions of speckles. This method is verified by simulating the speckle intensities and calculating the speckle autocorrelation function. We also find the phenomenon that for rough surfaces with α= 1, the structure of the speckles resembles that of the surface heights, which results from the effect of the peak and the valley parts of the surface, acting as micro-lenses converging and diverging the light waves.展开更多
For a physics system which exhibits memory,if memory is preserved only at points of random self-similar fractals,we define random memory functions and give the connection between the expectation of flux and the fracti...For a physics system which exhibits memory,if memory is preserved only at points of random self-similar fractals,we define random memory functions and give the connection between the expectation of flux and the fractional integral.In particular,when memory sets degenerate to Cantor type fractals or non-random self-similar fractals our results coincide with that of Nigmatullin and Ren et al.展开更多
In 1975, B. B. Mandelbrot presented the Fractal Geometry through careful observation and comprehensive analysis of many irregular bodies with complicated shapes in nature. Metal fracture is a crack propagation process...In 1975, B. B. Mandelbrot presented the Fractal Geometry through careful observation and comprehensive analysis of many irregular bodies with complicated shapes in nature. Metal fracture is a crack propagation process along a zigzag path, while fractured surfaces are approximately fractal, i. e. 'self-similar'. Recently, fractal analysis in metal fractured surfaces has been widely applied, and the relationships between the fractal dimension of the frac-展开更多
In recent years fractal geometry has been widely used for the quantitative analysis of material fracture, and in the theoretical investigation the geometry also has its applications Lung gave the fractal model of inte...In recent years fractal geometry has been widely used for the quantitative analysis of material fracture, and in the theoretical investigation the geometry also has its applications Lung gave the fractal model of intercrystalline fracture propagation in the shape of '∧'. Sudiscussed the influence of crystal angle on the fractal dimension. However, although even distribution of θ was employed, an error deduction was given in ref. [7]. In this note, we calculate the fmctal dimension for even distribution and Gaussian distribution of θ respectively by means of random fractal method and compute the numerical integration. We also make some discussion.展开更多
We study the properties of the intensity profiles scattered from the self-affine fractal random surfaces.We use the mathematical decay function to approximate the duple negative exponent function in the rigorous theor...We study the properties of the intensity profiles scattered from the self-affine fractal random surfaces.We use the mathematical decay function to approximate the duple negative exponent function in the rigorous theory of scattering,by letting them have the same maximum value and half-width,and the expression for the half-widths of the intensity profiles in the whole range of the perpendicular wave vector component is obtained.The previous results in the two extreme cases are included in the results of this paper.In the simulational verification,we propose a method for the generation of self-affine fractal random surfaces,using the square-root of Fourier transform of the correlation function of the surface height.The simulated results conform well with the theory.展开更多
Random iterated function systems (IFSs) is discussed, which is one of the methods for fractal drawing. A certain figure can be reconstructed by a random IFS. One approach is presented to determine a new random IFS, th...Random iterated function systems (IFSs) is discussed, which is one of the methods for fractal drawing. A certain figure can be reconstructed by a random IFS. One approach is presented to determine a new random IFS, that the figure reconstructed by the new random IFS is the image of the origin figure reconstructed by old IFS under a given affine transformation. Two particular examples are used to show this approach.展开更多
Suppose {Xn} is a random walk in time-random environment with state space Z^d, ｜Xn｜ approaches infinity, then under some reasonable conditions of stability, the upper bound of the discrete Packing dimension of the r...Suppose {Xn} is a random walk in time-random environment with state space Z^d, ｜Xn｜ approaches infinity, then under some reasonable conditions of stability, the upper bound of the discrete Packing dimension of the range of {Xn} is any stability index α. Moreover, if the environment is stationary, a similar result for the lower bound of the discrete Hausdorff dimension is derived. Thus, the range is a fractal set for almost every environment.展开更多
In this paper we propose a numerical method to estimate the fractal dimension of stationary Gaussian stochastic processes using the random Euler numerical scheme and based on an analytical formulation of the fractal d...In this paper we propose a numerical method to estimate the fractal dimension of stationary Gaussian stochastic processes using the random Euler numerical scheme and based on an analytical formulation of the fractal dimension for filtered stochastic signals. The discretization of continuous time processes through this random scheme allows us to find, numerically, the expected value, variance and correlation functions at any point of time. This alternative method for estimating the fractal dimension is easy to implement and requires no sophisticated routines. We use simulated data sets for stationary processes of the type Random Ornstein Uhlenbeck to graphically illustrate the results and compare them with those obtained whit the box counting theorem.展开更多
文摘We report on the unconventional optical properties exhibited by a two-dimensional array of thin Si nanowires arranged in a random fractal geometry and fabricated using an inexpensive,fast and maskless process compatible with Si technology.The structure allows for a high light-trapping efficiency across the entire visible range,attaining total reflectance values as low as 0.1%when the wavelength in the medium matches the length scale of maximum heterogeneity in the system.We show that the random fractal structure of our nanowire array is responsible for a strong in-plane multiple scattering,which is related to the material refractive index fluctuations and leads to a greatly enhanced Raman scattering and a bright photoluminescence.These strong emissions are correlated on all length scales according to the refractive index fluctuations.The relevance and the perspectives of the reported results are discussed as promising for Si-based photovoltaic and photonic applications.
基金Project supported by the National Natural Science Foundation of China （Grant No 69978012）, and by the National Key Basic Research Special Foundation （NKBRSF） of China （Grant No G1999075200）.
文摘This paper studies the correlation properties of the speckles in the deep Fresnel diffraction region produced by the scattering of rough self-affine fractal surfaces. The autocorrelation function of the speckle intensities is formulated by the combination of the light scattering theory of Kirchhoff approximation and the principles of speckle statistics. We propose a method for extracting the three surface parameters, i.e. the roughness w, the lateral correlation length ξ and the roughness exponent α, from the autocorrelation functions of speckles. This method is verified by simulating the speckle intensities and calculating the speckle autocorrelation function. We also find the phenomenon that for rough surfaces with α= 1, the structure of the speckles resembles that of the surface heights, which results from the effect of the peak and the valley parts of the surface, acting as micro-lenses converging and diverging the light waves.
文摘For a physics system which exhibits memory,if memory is preserved only at points of random self-similar fractals,we define random memory functions and give the connection between the expectation of flux and the fractional integral.In particular,when memory sets degenerate to Cantor type fractals or non-random self-similar fractals our results coincide with that of Nigmatullin and Ren et al.
文摘In 1975, B. B. Mandelbrot presented the Fractal Geometry through careful observation and comprehensive analysis of many irregular bodies with complicated shapes in nature. Metal fracture is a crack propagation process along a zigzag path, while fractured surfaces are approximately fractal, i. e. 'self-similar'. Recently, fractal analysis in metal fractured surfaces has been widely applied, and the relationships between the fractal dimension of the frac-
文摘In recent years fractal geometry has been widely used for the quantitative analysis of material fracture, and in the theoretical investigation the geometry also has its applications Lung gave the fractal model of intercrystalline fracture propagation in the shape of '∧'. Sudiscussed the influence of crystal angle on the fractal dimension. However, although even distribution of θ was employed, an error deduction was given in ref. [7]. In this note, we calculate the fmctal dimension for even distribution and Gaussian distribution of θ respectively by means of random fractal method and compute the numerical integration. We also make some discussion.
文摘We study the properties of the intensity profiles scattered from the self-affine fractal random surfaces.We use the mathematical decay function to approximate the duple negative exponent function in the rigorous theory of scattering,by letting them have the same maximum value and half-width,and the expression for the half-widths of the intensity profiles in the whole range of the perpendicular wave vector component is obtained.The previous results in the two extreme cases are included in the results of this paper.In the simulational verification,we propose a method for the generation of self-affine fractal random surfaces,using the square-root of Fourier transform of the correlation function of the surface height.The simulated results conform well with the theory.
文摘Random iterated function systems (IFSs) is discussed, which is one of the methods for fractal drawing. A certain figure can be reconstructed by a random IFS. One approach is presented to determine a new random IFS, that the figure reconstructed by the new random IFS is the image of the origin figure reconstructed by old IFS under a given affine transformation. Two particular examples are used to show this approach.
基金Project supported by NNSF of China (10371092)Foundation of Wuhan University
文摘Suppose {Xn} is a random walk in time-random environment with state space Z^d, ｜Xn｜ approaches infinity, then under some reasonable conditions of stability, the upper bound of the discrete Packing dimension of the range of {Xn} is any stability index α. Moreover, if the environment is stationary, a similar result for the lower bound of the discrete Hausdorff dimension is derived. Thus, the range is a fractal set for almost every environment.
文摘In this paper we propose a numerical method to estimate the fractal dimension of stationary Gaussian stochastic processes using the random Euler numerical scheme and based on an analytical formulation of the fractal dimension for filtered stochastic signals. The discretization of continuous time processes through this random scheme allows us to find, numerically, the expected value, variance and correlation functions at any point of time. This alternative method for estimating the fractal dimension is easy to implement and requires no sophisticated routines. We use simulated data sets for stationary processes of the type Random Ornstein Uhlenbeck to graphically illustrate the results and compare them with those obtained whit the box counting theorem.
