Dynamics of the Magnetic Flux Trapped in Fractal Clusters of a Normal Phase in Percolative Superconductors

The effect of the fractal clusters of a normal phase, which act as pinning centers, on the dynamics of magnetic flux in percolative type-II superconductor is considered. The main features of these clusters are studied in detail: the cluster statistics is analyzed; the fractal dimension of their boundary is estimated; the distribution of critical currents is obtained, and its peculiarities are explored. It is found that there is the range of fractal dimension where this distribution has anomalous statistical properties, specifically, its dispersion becomes infinite. It is examined how the finite resolution capacity of the cluster geometric size measurement affects the estimated value of fractal dimension. The effect of fractal properties of the normal phase clusters on the electric field arisen from magnetic flux motion is investigated for the cluster area distribution of different kinds. The voltage-current characteristics of fractal superconducting structures in the resistive state are obtained for an arbitrary fractal dimension. It is revealed that the fractality of the boundaries of the normal phase clusters intensifies the magnetic flux trapping and thereby raises the critical current of a superconductor.     

Optico-acoustic characterization of the fractal structure of radiation from a laser with unstable resonator

The thermooptical excitation of sound in a liquid by fluctuating laser radiation with sine-modulated intensity is studied theoretically. The intensity is randomly distributed over the beam cross section. It is assumed that the random processes are homogeneous and that the spatial spectrum of intensity fluctuations obeys a power fractal law. Possibilities for the optico-acoustic characterization of the fractal radiation structure of a laser with unstable resonator are discussed.     

Optical free-path-length distribution in a fractal aggregate and its effect on enhanced backscattering

A free-path-length distribution function (FPDF) of multiply backscattered light is theoretically derived for a fractal aggregate of particles. An effective mean-free path-length l(D) is newly introduced as a measure of randomness analogous with a homogeneously random medium. We confirm the validity of the FPDF by demonstrating agreement between the dimensions designed for a particle distribution generated by a random walk based on the derived FPDF and estimated by the radius of gyration method. The FPDF is applied to Monte Carlo simulations for copolarized multiply backscattered light from the fractal aggregate of particles. It is shown that a copolarized intensity peak of enhanced backscattering in the far field decreases in accordance with theta(2-D) and has an angular width of lambda/l(D). This spatial feature of the backscattering enhancement corresponds to that of the copolarized intensity peak produced from a homogeneously random medium with a dimension of D = 3. As a result, the validity of the model for the fractal structure of particle aggregates and the applicability of the derived FPDF are confirmed by the numerical results.     

Thermal striping fatigue damage in multiple edge-cracked geometries

Thermal fatigue striping damage may be caused when incompletely mixed hot and cold fluid streams pass over the surface of a component or structure containing a defect. Stress intensity factor (SIF) fluctuations are developed in response to the surface temperature fluctuations. An existing methodology for the analysis of striping damage in geometries containing a single edge‐crack geometry is extended to such an analysis of multiple edge cracks. SIFs are calculated as functions of crack depth, when an edge‐cracked plate and semi‐infinite solid, each containing multiple cracks, are subjected to thermal striping. The effect of various restraint conditions and striping frequencies on the SIF values for a stainless steel plate is examined. The degree of conservatism is shown when an assessment of thermal fatigue striping damage is based on a single, rather than multiple, crack analysis. Accurate curve fits are developed resulting in practical weight functions for an edge‐cracked plate and semi‐infinite solid.     

Simulated shift work in rats perturbs multiscale regulation of locomotor activity

Motor activity possesses a multiscale regulation that is characterized by fractal activity fluctuations with similar structure across a wide range of timescales spanning minutes to hours. Fractal activity patterns are disturbed in animals after ablating the master circadian pacemaker (suprachiasmatic nucleus, SCN) and in humans with SCN dysfunction as occurs with aging and in dementia, suggesting the crucial role of the circadian system in the multiscale activity regulation. We hypothesized that the normal synchronization between behavioural cycles and the SCN-generated circadian rhythms is required for multiscale activity regulation. To test the hypothesis, we studied activity fluctuations of rats in a simulated shift work protocol that was designed to force animals to be active during the habitual resting phase of the circadian/daily cycle. We found that these animals had gradually decreased mean activity level and reduced 24-h activity rhythm amplitude, indicating disturbed circadian and behavioural cycles. Moreover, these animals had disrupted fractal activity patterns as characterized by more random activity fluctuations at multiple timescales from 4 to 12 h. Intriguingly, these activity disturbances exacerbated when the shift work schedule lasted longer and persisted even in the normal days (without forced activity) following the shift work. The disrupted circadian and fractal patterns resemble those of SCN-lesioned animals and of human patients with dementia, suggesting a detrimental impact of shift work on multiscale activity regulation.     

Direct Synthesis of the 2D Copper(II) 5‐Prop‐2‐ynoxyisophthalate MOF: Comment on “Surface Functionalization of Porous Coordination Nanocages Via Click Chemistry and Their Application in Drug Delivery”

Synthesis of metal–organic materials is often dependent on the reaction conditions of suitable solvent/solvent mixture and temperature. A new finding based on a previously described protocol is reported: instead of obtaining metal–organic polyhedra (MOP), a metal–organic framework (MOF) with a 2D layered structure is obtained, following the same reported protocol. The 2D Cu(II)–5‐prop‐2‐ynoxyisophthlate MOF, crystallized in a kagomé‐type structure, is synthesized using different solvent systems at room temperature, as well as under solvothermal (nonhydrothermal) conditions. Under harsh reaction conditions, alkyne functional groups maintain their integrity and the copper does not catalyze the oxidative coupling of the terminal alkyne groups. X‐ray diffraction analyses confirm the structure and phase purity of the product. Based on the present results and the previous work reported by Zhao et al., it seems that two products, namely 0D MOP and 2D MOF, are equally possible when using the same reactants under same reaction conditions. However, the materials obtained in all the trials are MOF instead of MOP. From the structure point of view, there is a difference in connectivity of the initial building units that determines whether the product is MOP or MOF.     

激光大气传输光斑统计概率接收孔径效应

本文综合考虑湍流大气对激光斑纹强度、光束传输方向的调制作用和有限接收孔径的光强起伏、相位起伏平滑作用等因素,从理论上研究了激光斑纹强度、相位起伏概率密度函数和孔径平滑作用,求得了高阶强度矩的孔径平滑因子。     

Fluctuation Spectral Functions and Phase Transitions for Cold Fermi Gases in 2D

We study cold fermions in 2D that are interacting through the s-wave contact potential, using the path-integral formalism. The phase transitions are investigated using the joint solution of the gap and number equations. In the latter ones, the amplitude and phase fluctuations are taken into account within the t-matrix NSR-type formalism. It is shown that convergent solutions for the fermion density in 2D can be obtained even in the lowest-order (quadratic) approximation for fluctuations with a proper determination of the spectral functions. This approach leads, in particular, to a non-coherent quasicondensate which exists between the Berezinskii-Kosterlitz-Thouless (BKT) transition temperature below which the system is superfluid and a transition temperature T _Δ above which the quasicondensate is destroyed.     

Fraunhofer diffraction by cantor fractals with variable lacunarity

Abstract

Optical diffraction by fractal openings is increasingly being studied because it allows the properties and parameters that characterize these objects to be determined. Allain and Cloitre published the first results showing that the resulting analysis of the distribution of intensity obtained from diffraction experiments through fractal deterministic pupils permits the self-similar dimension and other geometrical characteristic of these structures to be obtained directly. In this work the lacunarity effect ?, dimension d and order k of growth of the Cantor fractal about the distribution of intensities of the diffraction pattern are studied, solved analytically and characterized. In particular we note the influence of lacunarity because this is one of the first studies in which this geometric fractal parameter is taken into consideration. The selfsimilarity of the diffraction figure at different orders is also proved. The results of this study allow us to say that an intimate relation exists between the distribution of the diffracted waves and the parameters that describe this kind of fractal geometry.     

Fraunhofer Diffraction by Koch Fractals

Abstract

Analytical expressions are derived for the complex amplitude in the Fraunhofer diffraction field of an arbitrary Koch fractal with a finite range of self-similarity. Results of the numerical evaluation for the intensity distribution of Fraunhofer diffraction patterns are compared with those obtained experimentally. It is shown that the diffraction pattern of the Koch fractal can be divided into two areas, a central fractal area and a periodic area, and that the former is surrounded by the latter. The existence of the periodic area is a consequence of the finite inner cut-off of the self-similarity of the object fractal. On the other hand, the outer cut-off gives rise to a small core area at the centre of the diffraction pattern.     

Atmospheric-turbulence-induced power-fade statistics for a multiaperture optical receiver

To estimate the probability distributions of power fades, we consider two basic types of disturbance in electromagnetic wave propagation through atmospheric turbulence: wave-front intensity fluctuations and wave-front distortion. We assess the reduction in the cumulative probability of losses caused by these two effects through spatial diversity by using a multiaperture receiver configuration. Degradations in receiver performance are determined with fractal techniques used to simulate the turbulence-induced wave-front phase distortion, and a log normal model is assumed for the collected power fluctuations.     

Fractal research on AFM images of polycrystalline aluminum surface with adsorption film of SDS inhibitor

We propose a new method of fractal analysis of the phase images obtained by the atomic-force microscopy (AFM) to study the properties of molecular adsorption films of corrosion inhibitors on the coarse polycrystalline surface, which can hardly be distinguished by using AFM height images due to the roughness of the surface. The system of polycrystalline aluminum and SDS (Sodium Dodecyl Sulfate) inhibitor is chosen as the research object. The electrochemical measurements of aluminum electrodes precoated with SDS films are carried out in HCl solutions, and the results show that the inhibition efficiency increases with the concentration of SDS in the prefilming solution and then remains nearly constant as the CMC (critical micelle concentration) of SDS is exceeded. The fractal analysis of the AFM images of prefilmed aluminum surfaces obtained in SDS solutions is performed and demonstrates that, as the SDS concentration increases, no obvious changes are observed for the fractal dimensions of height images, whereas the phase images present regular changes in the values of fractal dimensions, thus displaying the consistent alteration rule as revealed by electrochemical tests. The results prove the feasibility of the fractal analysis of AFM phase images in characterizing the adsorption behavior of the corrosion inhibitor on polycrystalline coarse surfaces.     

Moiré by fractal structures

Abstract

The theoretical and experimental results of the Moiré effect observed by superposing two grids containing fractal Cantor structures are presented in this paper. It is also analysed the equivalence between the information obtained by the Fraunhofer diffraction through those fractal grids and that obtained through Moiré. In a recently published paper [1] it was verified that the diffraction pattern is highly sensitive to variations in dimension, order of growth and lacunarity of the Cantor fractal, becoming a powerful tool to analyse and determine these parameters. So, in this paper it is intended to determine the effect that the order of growth, the dimension, and the lacunarity of one-dimensional fractal Cantor structures have over the Moiré patterns that result from superposing these structures over replicas of themselves which have been rotated through a small angle α. The main goal is to verify if there exists an intimate relation between the resulting Moiré pattern and the parameters that describe this fractal structure, as occurs in the case of the diffraction pattern.     

Gas-liquid two phase flow pattern evolution characteristics based on detrended fluctuation analysis

In this paper, we first extract a nonlinear time series from the Weierestrass function as a toy model and investigate the anti-noise ability of six different fractal scale algorithm. The results indicate that the fractal scales calculated from Detrended Fluctuation Analysis(DFA) are robust with respect to variation in noise level. Based on the conductance fluctuating signals measured from vertical gas-liquid two phase flow experiment, we calculate the fractal scales of five typical flow patterns. The results show that when the water superficial velocity ranging from 0.0453ms⁻¹ to 0.226 ms⁻¹ and the gas superficial velocity ranging from 0.0043ms⁻¹ to 3.43 ms⁻¹, the values of the fractal scale of bubble flow are lowest corresponding to the random complex dynamic behavior, while the values of slug flow are highest corresponding to the alternatively periodic motions between gas slug and liquid slug, and the values of churn flow lies between them indicating the relatively complex dynamic behavior. Our main result is that the fractal scales obtained from conductance fluctuating signals can not only effectively characterize the dynamic characteristics of gas-liquid two phase flow patterns, but also further provide valuable reference for understanding the transitions of different gas-liquid two phase flow patterns.     

基于分形理论的人工挖孔嵌岩桩承载特性分析

嵌岩长桩的承载性能主要取决于桩-岩接触面的剪切强度。基于岩体结构面强度的研究方法,引入分形维数描述的两相接触介质粗糙表面的抗剪强度公式,建立了以分维数表示的嵌岩桩侧摩阻力传递模型,求得了弹性条件下的桩侧摩阻力及桩身轴力的解析式。基于所获得的解答,深入地探讨了分形维数D对桩侧摩阻力?、桩身轴力P及桩端荷载分担比Pb/Pd的影响规律。研究表明:同等条件下一定范围内粗糙分维值D越大,桩侧摩阻力在桩身上部分布越集中,荷载传递深度越小,桩端荷载分担比Pb/Pd也越小;长径比l/d越小,桩端荷载分担比越大,反之越小。工程算例对比分析表明:理论计算与实测结果吻合较好,对嵌岩桩设计有一定参考价值。     

Local strain in a 3D nano-crystal revealed by 2D coherent X-ray diffraction imaging

The coherent X-ray diffraction from an isolated strained nano-crystal is given by the Fourier transform of a complex-valued electron density where the modulus and phase are linked to the physical electron density and the displacement field, respectively. The possibility to reconstruct a complex-valued object from a coherent diffraction pattern is demonstrated using iterative algorithms. In the case of a 2D intensity slice, the reconstructed 2D object is strongly dependent on the distribution function of the displacement field values along the direction perpendicular to the observation plane. It is shown that valuable 3D information can, however, still be extracted. This work is of particular interest as soon as the complete 3D measurement is not accessible.     

The possibility of using platinum foils with a rippled surface as diffraction gratings

The atomic structure and surface relief of thin cold-rolled platinum foils upon recrystallization annealing and loading under ultrahigh vacuum conditions have been studied by low energy electron diffraction (LEED), atomic force microscopy (AFM), and scanning tunneling microscopy (STM). The surface of samples upon high-temperature annealing and subsequent uniaxial extension of recrystallized Pt foils represents a fractal structure of unidirectional ripples on various spatial scales. The total fractal dimension of this surface is D _GW = 2.3, while the fractal dimensions along and across ripples are D _‖ ≈ 1 and D _⊥ ≈ 1.3, respectively. The optical spectra of a halogen lamp and a PRK-2 mercury lamp were recorded using these rippled Pt foils as reflection diffraction gratings. It is shown that Pt foils with this surface relief can be used as reflection diffraction gratings for electromagnetic radiation in a broad spectral range.     

Synthesis, structure, and physical properties of carbon, iron, and chromium deposits possessing a fractal structure

A carbon deposit formed during graphite spraying in an electric arc, as well as iron and chromium particles obtained by electrochemical deposition under certain conditions, possess fractal structures. Data on some physical properties, the size of fractal aggregates, and the fractal dimension D of carbon, iron, and chromium deposits are presented. Relations between the fractal dimensions and physical properties of deposits are considered. A possible mechanism of the fractal structure formation is discussed.     

Isothermal crystallization kinetics and morphology of biodegradable poly(3-hydroxybutyrate-co-4-hydroxybutyrate)

Isothermal crystallization kinetics and morphology of poly(3-hydroxybutyrate-co-4-hydroxybutyrate) [P(3HB-co-4HB)] with different 4-hydroxybutyrate (4HB) molar fraction were investigated by differential scanning calorimetry (DSC), wide angle X-ray diffraction (WAXD), and polarized optical microscopy (POM). The results show that the crystallization mechanism and crystal structure of P(3HB-co-4HB) copolymers are the similar as those of poly(3-hydroxybutyrate) (PHB). While the equilibrium melting point and crystallization rate decrease with the increase of 4HB molar fraction. Banded spherulites are observed in neat PHB and P(3HB-co-4HB) copolymers, and morphology is influenced apparently by the crystallization temperature and 4HB unit.