Polyadic Cantor superlattices with variable lacunarity

Reflection and transmission properties of polyadic fractal superlattices are formulated, solved analytically, and characterized for variations in stage of growth, fractal dimension, and lacunarity. This is the first time to our knowledge that the effect of lacunarity on wave interactions with such structures has been considered. The results are summarized by families of reflection data that we denote twist plots. A new doubly recursive computational technique efficiently provides the reflection and transmission coefficients for a large class of Cantor superlattices with numerous interfaces.     

纹理高阶分形特征在海面舰船目标检测中的应用

针对复杂海面环境下的舰船目标检测，分析了高阶分形特征缝隙在纹理分类中的应用，提出了一种基于分形维与缝隙的目标检测新方法，并利用该方法对海面舰船目标进行了检测。实验结果表明利用纹理分形维与缝隙特征进行海面舰船目标检测，可以取得较单一分形维检测更高的准确率。     

Identification of two simultaneous partial discharge sources in an oil-pressboard insulation system using acoustic emission techniques

Insulation failure is one of the major causes of catastrophic failure of transformers. It is established that partial discharge (PD) causes insulation degradation and premature failure of insulation. In power apparatus, more than one PD source may be active simultaneously. The nature of insulation degradation for multiple PD sources is different from that due to single PD source. Therefore, it will be helpful for severity assessment of insulation degradation, if the number of active PD sources are identified and classified. This paper presents a method for identification and classification of two simultaneously active PD sources using acoustic emission techniques. The acoustic emission (AE) signals are measured for laboratory simulated PD in an oil-pressboard insulation system for three different electrode systems. The measurements of partial discharge acoustic emission (PDAE) signals are carried out for single PD source and for two simultaneous PD sources. The measured signals are analyzed using discrete wavelet transform (DWT), box counting fractal dimension and lacunarity. Box counting fractal dimension and lacunarity are calculated for DWT decomposed signal of major frequency band. Energy distribution in different frequency bands of DWT decomposed signal along with box counting fractal dimension and lacunarity is used for classification of two simultaneous PD sources.     

Programmable fractal zone plates (FraZPs) with foci finely tuned

We examined the focusing properties of fractal zone plates (FraZPs) in detail based on a liquid crystal on silicon (LCOS) spatial light modulator (SLM). It was shown that the focal length shifted linearly when the lacunarity of first order FraZPs experienced a linear displacement. From the theoretical analysis and the experimental results, we showed the potential to use the FraZPs as a focusing element whose focal length can be tuned finely. In addition, some side effects of this element were also discussed.     

Fractal geometries and Potts Model behaviour

We study the critical behaviour of the ferromagnetic Potts Model on families of fractal lattices called Sierpinski Carpets and Sierpinski Pastry Shells. We find the influence of geometrical parameters on critical temperature and thermal exponents, which confirms lacunarity as a relevant geometrical parameter in the definition of universality classes. We distinguish the inner surface structure from the bulk and study the influence of both structures independently. The phase diagram for the Pastry Shell family exhibit a crossover between bulk and surface behaviour which shows the increasing importance of the surface bonds on the full fractal geometry as the fractal dimension or the lacunarity is lowered.     

Negative refractive index in the near‐UV from Au‐coated CuCl nanoparticle superlattices

Nanoparticle superlattices consisting of CuCl spheres coated with a gold (Au) nanoshell are shown to exhibit negative index of refraction in the near‐UV regime. These predictions are based on calculations of the effective refractive index by use of the extended Maxwell–Garnett theory. The results for the refractive index are supplemented by multiple‐scattering calculations of light‐transmittance curves from finite slabs of nanoparticle superlattices. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

An efficient implementation of the gliding box lacunarity algorithm

Lacunarity is a measure of how data fills space. It complements fractal dimension, which measures how much space is filled. Many researchers use the gliding box algorithm to calculate lacunarity. This paper introduces a fast algorithm for making this calculation. This algorithm is akin to fast box-counting algorithms used by some researchers to estimate fractal dimension. A simplified gliding box measure equation, along with key pseudo code implementations for the algorithm, are presented. Applications for the gliding box lacunarity measure have ranged from biological community modelling to target detection.     

Estimate of lacunarity of vibrational-rotational absorption spectra of water vapor

Optical spectra of vibrational-rotational absorption bands of atmospheric water vapor are interpreted in terms of fractal analysis. The main calculation parameter is the lacunarity of the initial spectrum. The variation in the lacunarity makes it possible to estimate the degree of translational and scale invariance of the entire spectrum as some quasi-random frequency function.     

Dresselhaus spin-orbit coupling induced spin-polarization and resonance-split in n-well semiconductor superlattices

Using the transfer matrix method, we investigate the electron transmission over multiple-well semiconductor superlattices with Dresselhaus spin-orbit coupling in the potential-well regions. The superlattice structure enhances the effect of spin polarization in the transmission spectrum. The minibands of multiple-well superlattices for electrons with different spin can be completely separated at the low incident energy, leading to the 100% spin polarization in a broad energy windows, which may be an effective scheme for realizing spin filtering. Moreover, for the transmission over n-quantum-well, it is observed that the resonance peaks in the minibands split into n-folds or (n−1)-folds depending on the well-width and barrier-thickness, which is different from the case of tunneling through n-barrier structure.     

Lacunar fractal photon sieves

We present a new family of diffractive lenses whose structure is based on the combination of two concepts: photon sieve and fractal zone plates with variable lacunarity. The focusing properties of different members of this family are examined. It is shown that the sieves provide a smoothing effect on the higher order foci of a conventional lacunar fractal zone plate. However, the characteristic self-similar axial response of the fractal zone plates is always preserved.     

Fractal properties of aggregates of metal nanoclusters on solid surface

AFM images are used to determine and analyze fractal characteristics (cluster fraction dimension and lacunarity) of aggregates of Au and Ag nanoclusters on metal films of the same metal produced with the aid of thermal vacuum deposition on mica surface. A fractal dimension of 1.6 that corresponds to typical samples with relatively uniform distribution of nanoclusters on the film surface is in agreement with the mean value calculated from experimental data of Belko et al., who studied the fractal dimension of Au nanoclusters on a different dielectric (quartz) surface. When a compact single aggregate of Au nanoclusters is formed on a certain active center or defect, the fractal cluster dimension decreases to 1.4. The experimental data are compared with the results of existing theoretical models of association of nanoclusters in 2D systems.     

Cosmic lacunarity

The present distribution of galaxies in space is a remnant of their formation and interaction. On a large enough scale, we may represent the galaxies as a set of points and quantify the structures in this set by its generalized dimensions [Beck and Schlogl, Thermodynamics of Chaotic Systems (Cambridge University Press, Cambridge, 1986); Paladin and Vulpiani, Phys. Rep. 156, 147 (1987)]. The results of such evaluation are often taken to be evidence of a fractal (or multifractal) distribution of galaxies. However, those results, for some scales, may also reveal the presence of singularities formed in the gravitational processes that produce structure in the galaxy distribution. To try to make some decision about this issue, we look for the more subtle galactic lacunarity. We believe that this quantity is discernible in the currently available data and that it provides important evidence on the galaxy formation process. (c) 1997 American Institute of Physics.     

Fractal model of the atom and some properties of the matter through an extended model of scale relativity

The scale relativity model was extended for the motions on fractal curves of fractal dimension D _F and third order terms in the equation of motion of a complex speed field. It results that, in a fractal fluid, the convection, dissipation and dispersion are compensating at any scale (differentiable or non-differentiable), whereas a generalized Schrödinger type equation is obtained for an irrotational movement of the fractal fluid. For D _F = 2 and the dissipative approximation of the motions, the fractal model of atom is build: the real part of the complex speed field describes the electron motion on stationary orbits according to a quantification condition, while the imaginary part of the complex speed field gives the electron energy quantification. For D _F = 3 and the dispersive approximation of motions, some properties of the matter are explained: at the differentiable scale the flowing regimes (non-quasi-autonomous and quasi-autonomous) of the fractal fluids are separated by the experimental “0.7 structure”, while for the non-differentiable scale the fractal potential acts as an energy accumulator and controls through coherence the transport phenomena. Moreover, the compatibility between the differentiable and non-differentiable scales implies a Cantor space-time, and consequently a fractal at any scale. Thus, some properties of the matter (the anomaly of nano-fluids thermal conductivity, the superconductivity etc.) can be explained by this model.     

Quasiparticle states in superconducting superlattices

The energy bands and the global density of states are computed for superconductor / normal-metal superlattices in the clean limit. Dispersion relations are derived for the general case of insulating interfaces, including the mismatch of Fermi velocities and effective band masses. We focus on the influence of finite interface transparency and compare our results with those for transparent superlattices and trilayers. Analogously to the rapid variation on the atomic scale of the energy dispersion with layer thicknesses in transparent superlattices, we find strong oscillations of the almost flat energy bands (transmission resonances) in the case of finite transparency. In small-period transparent superlattices the BCS coherence peak disappears and a similar subgap peak is formed due to the Andreev process. With decreasing interface transparency the characteristic double peak structure in the global density of states develops towards a gapless BCS-like result in the tunnel limit. This effect can be used as a reliable STM probe for interface transparency.     

Influence of Deviation on Optical Transmission through Aperiodic Superlattices

We propose a deviation model and study the influences of the relative error and sensitivity of a machine on the transmission coefficients （TCs） of Fibonacci superlattices. It is found that for a system with fewer layers, the influence of deviation can be ignored. When superlattices become more complicated, they may be fabricated by a machine with suitable relative error and possess the designed value of TO. However, when the number of system layers exceeds some critical value, superlattices should be manufactured only by precise machines. The influence of the sensitivity is also discussed.     

Spin waves propagation in Fibonacci quasiperiodic metamagnet superlattices

In this work we present a fractal analysis of the spin wave modes propagating in a Fibonacci quasiperiodic metamagnetic superlattices consisting of a ferromagnetic material (layer A being Fe) and a metamagnetic material (layer B being FeBr₂). The spin wave modes are obtained in the exchange regime, using the transfer matrix technique. Our numerical results show that the power law for this system is independent of the dimensionless in-plane wavevector kxa$k_{x}a$, and that the spectrum present a multifractal characteristic, exhibiting several scale invariant windows for a fixed value of the in-plane wavevector. The results reported here can be experimentally observed by light scattering techniques.     

On the two dimensional effective electron mass in quantum wells,inversion layers and NIPI superlattices of Kane type semiconductors in the presence of strong light waves: Simplified theory and relative comparison

An attempt is made to study the two dimensional (2D) effective electron mass (EEM) in quantum wells (Qws), inversion layers (ILs) and NIPI superlattices of Kane type semiconductors in the presence of strong external photoexcitation on the basis of a newly formulated electron dispersion laws within the framework of k.p. formalism. It has been found, taking InAs and InSb as examples, that the EEM in Qws, ILs and superlattices increases with increasing concentration, light intensity and wavelength of the incident light waves, respectively and the numerical magnitudes in each case is band structure dependent. The EEM in ILs is quantum number dependent exhibiting quantum jumps for specified values of the surface electric field and in NIPI superlattices; the same is the function of Fermi energy and the subband index characterizing such 2D structures. The appearance of the humps of the respective curves is due to the redistribution of the electrons among the quantized energy levels when the quantum numbers corresponding to the highest occupied level changes from one fixed value to the others. Although the EEM varies in various manners with all the variables as evident from all the curves, the rates of variations totally depend on the specific dispersion relation of the particular 2D structure. Under certain limiting conditions, all the results as derived in this paper get transformed into well known formulas of the EEM and the electron statistics in the absence of external photo-excitation and thus confirming the compatibility test. The results of this paper find three applications in the field of microstructures.     

Measures of complexity for 3D image analysis of trabecular bone

Based on fractal properties and spatial auto-correlation, the measures of complexity lacunarity, Moran's I and Geary's C index are defined for 3D image analysis. Their abilities to investigate translational invariance, characteristic length scales, spatial correlation and shapes of 3D micro-structures are demonstrated on proto-typical examples. Finally, using these measures of complexity, 3D images of trabecular bone are analysed. The main findings are that the complexity of the trabecular structure decreases and the plate-like shapes of the trabeculae change to mainly rod-like shapes during bone loss. These results and the proposed measures could have a great impact for medicine and for space exploration.     

基于边缘链码高阶分形特征的舰船目标检测算法

针对舰船目标和海杂波轮廓结构的不同,提出了基于边缘链码高阶分形特征的舰船目标检测算法,算法利用相对链码对5类舰船目标轮廓进行编码,分别计算分形维和缝隙,得到了舰船目标的4个分形特征的范围。实验结果表明边缘链码的4个分形特征能有效区分舰船目标和海杂波。     

The effects of photoexcitation on excitons in semiconductor doping superlattices

Calculations of the properties of excitons in doping superlattices have been made as a function of doping density using a variational approach. Interesting new features are obtained when the exciton energy becomes comparable to the superlattice potential energy. These results are compared to recent experimental data on GaAs doping superlattices.