Fractal Structure of Debris Flow

One of the most remarkable characteristics of debris flow is the competence for supporting boulders on the surface of flow, which strongly suggests that there should be some structure in the fluid body. This paper analyzed the grain compositions from various samples of debris flows and then revealed the fractal structure. Specifically, the fractality holds in three domains that can be respectively identified as the slurry, matrix, and the coarse content. Furthermore, the matrix fractal, which distinguishes debris flow from other kinds of flows, involves a hierarchical structure in the sense that it might contain ever increasing grains while the total range of grain size increases. It provides a possible mechanism for the boulder suspension.

Fractal Structures and Chaotic Behaviors in a (2+1)-Dimensional Nonlinear System

With a new projective equation, a series of solutions of the （2-J-1）-dimensional dispersive long-water wave system （LWW） is derived. Based on the derived solitary wave solution, we obtain some special fractal localized structures and chaotic patterns.

CRYSTALLIZATION AND FRACTAL STRUCTURE OF MOLYBDENA SINGLE CRYSTALS

When a molybdenum sheet was heated properly at 900℃ in an oxidizing atmosphere, Mo_5O_(14) single crystals will grow.The size of the most coarse single crystal is up to 15×1.1 mm and 310 nm thick as measured by Rutherford backscattering spectrometry.Some fractal structure consisting of many molybdena whiskers were observed after heating at 750℃.An approach to explain the crystal growth and fractal structure has been discussed.

SOME FRACTAL STRUCTURES IN RAPIDLY SOLIDIFIED Al-Mn ALLOY

The fractal structures formed in rapidly quenched Al_(86)Mn_(14)alloy have been observed on SEM.Their fractal dimensions are from 1.46 to 1.97.The principal phase examined by TEM and X-ray diffractometer is icosahedral quasicrystalline one with a small amount of Al phase. It is believed that these fractal structures are formed by many aggregated particles during the rapid-quenching process.

The fractal structure in the ionization dynamics of Rydberg lithium atoms in a static electric field

The ionization rate of Rydberg lithium atoms in a static electric field is examined within semiclassical theory which involves scattering effects off the core. By semiclassical analysis, this ionization process can be considered as the promoted valence electrons escaping through the Stark saddle point into the ionization channels. The resulting escape spectrum of the ejected electrons demonstrates a remarkable irregular electron pulse train in time-dependence and a complicated nesting structure with respect to the initial launching angles. Based on the Poincaré} map and homoclinic tangle approach, the chaotic behaviour along with its corresponding fractal self-similar structure of the ionization spectra are analysed in detail. Our work is significant for understanding the quantum-classical correspondence.

THE FRACTAL STRUCTURE OF ATTRACTOR FOR THE GENERALIZEDKURAMOTO-SIVASHINSKY EQUATIONS

In this paper, the generalized Kuramoto-Sivashinsky equations (GKS) with periodic boundary value problem are considered and the construction of inertial sets in space H-2 is given. Furthermore, this paper gives and proves the fractal structure of attractors for GKS equations, and find out an exponentially approximating sequence of compact fractal localizing sets of the attractors, these results sharpen and improve the conclusions of the inertial sets and attractor for GKS equation in [1,3,5,7], which describe a kind of geometrical structure of the attractors.

Fractal Laser Cone Structures Proposed to Confine Antimatter

Flat, straight sheets of paper, standing vertically on edge cannot support any load placed upon their top edge, but once formed into fractal tube conic sections, they have been measured to support up to 97.52 (± 2.27) kilograms (215 (± 5) pounds) of weight with strength-per-weight ratio up to 10,336 (± 240). So, strength has been discovered to be an emergent characteristic arising solely from addition of intelligent order. It is proposed to impose such intelligent order upon, preferably, at least 6 laser beams by focusing each of them to form cones of light, arranging the cones to form a wall of a larger fractal cone, and converging all of them to a common focal point inside a vacuum chamber to give them sufficient strength near this focal point to attract, hold, and move neutral antimatter, preferably anti-lithium. This opens the new field of structural engineering of light and re-defines the concept of strength. Means of cancelling out radiation pressure by reflection of laser beams back to the common focal point are proposed to enable laser confinement of particles having low polarizability, such as anti-hydrogen. Counter-circulation of light by reflection at grazing incidence is proposed as a means of returning escaping antimatter back to the common focal point containment area. Means are proposed to inject a stream of matter into the contained antimatter to create a matter-antimatter reactor and propulsion engine. Since anti-lithium is not available, yet, means are proposed to test these structures by confining ordinary lithium, instead, and by hitting it with anti-protons and/or positrons. Means are proposed to modulate the matter-antimatter reaction with information to create modulated gravitational waves for communication. The proposed structures would enable efficient, stable, safe confinement of antimatter, which would allow better study of antimatter, and make possible renewable, clean, safe, matter-antimatter reactor generators and propulsion engines, antimatter-assisted fusion reactors, and modulated gravitational wave generators.

Fractal Dromion,Fractal Lump,and Multiple peakon Excitations in a New （2＋1）—Dimensional Long Dispersive Wave SYstem

By means of variable separation approach, quite a general excitation of the new (2 + 1)-dimensional long dispersive wave system: is derived. Some types of the usual localized excitations such as dromions, lumps, rings, and oscillating soliton excitations can be easily constructed by selecting the arbitrary functions appropriately. Besides these usual localized structures, some new localized excitations like fractal-dromion, fractal-lump, and multi-peakon excitations of this new system are found by selecting appropriate functions.

Effect of Steel Slag and Granulated Blast-furnace Slag on the Mechanical Strength and Pore Structure of Cement Composites

Reuse of solid industrial wastes is an effective approach to develop low-carbon construction materials. This paper examines how two materials, steel slag（ST） and granulated blast-furnace slag（SL） impact the mechanical performance and pore structure of cement-based systems. Analysis was done on the variations of the porosity, pore size, and pore volume distribution with the curing age and replacement content, and the fractal dimensions of pore surfaces. The results suggested that systems with both supplementary materials had lower early strengths than pure cement, but could generally surpass pure cement paste after 90 d; higher SL content was particularly helpful for boosting the late strengths. The addition of ST increased the porosities and mean pore sizes at each age, and both increased with ST content; SL was helpful for decreasing the system＇s late porosity（especially harmless pores below 20 nm）; The lowest porosity and mean pore size were obtained with 20% SL. Both systems had notably fractal characteristics on pore surfaces, with ST systems showing the highest dimensions at 10% ST, and SL systems at 20% SL. Compressive strength displayed a significant linear increase with fractal dimension.

Transmission properties of fractal Cantor distribution with left-handed materials

Transmission properties of fractal Cantor distribution with left-handed materials （LHM） are investigated. The transmittance and reflectance spectra can be calculated by using the optical transmission matrix method. Comparing with the conventional Cantor multilayers, these structures with LHM have double functions of stopbands and defects. Through adjusting the thickness of dielectric layers, the properties of stopbands and defects can be obtained, respectively. For stopbands, a broad stopband filter is studied. For defect modes, multi-frequencies narrow passband filters are proposed.

Lightweight broadband microwave absorbing metamaterial with CB-ABS composites fabricated by 3D printing

The self-similarity,high geometric symmetry and spatial utilization properties of fractal structures provide new methods for the development of absorbing metamaterials.In this paper,the microwave absorption properties of the gradient dendritic fractal metamaterial structure(GDFMs)based on carbon black and acrylonitrile-butadiene-styrene composites were investigated.The optimal metamaterial structure has an effective absorption in the frequency range of 4.5-40 GHz.The rotational-symmetry GDFMs leads to the polarization independence,and the GDFMs exhibits a wide-angle absorption performance for both TE and TM waves.It is expected that the proposed GDFMs has good application prospects in electromagnetic wave absorption.

PRIMARY RESEARCH ON FRACTAL GEOMETRY OF MERIDIAN THEORY

In meridian theory of traditional Chinese medicine (TCM), the geometrical descriptions can be traced back to the remote ancient times in China, mainly in The Yellow Emperor’s Internal Classic (The Internal Classic in short). Euclid’s geometry, topology and other classic mathematics are all at their wit’s end to explain the high complexity and non clinear phenomenon of the meridian. In recent over 2000 years, the meridian phenomenon has been being the challenge to fundamental mathematics. Fractral geometry, founded by Mandelbrot (1975), is a branch of learning for investigating irregular geometrical curves. It has successfully solved some qualitative and quantitative problems about the topographical structure of molecular Brown’s movement curve and other irregular complicated curves and geometrical characters. The characteristics of geometrical topographical structure of meridian and its phenomenon belong to the research category of Fractal Geometry. The author of this paper believes that Fractal Geometry may provide a useful mathematical tool and a possible way for revealing the enigma of acup moxibustion meridian theory. The human body is of basic characters of Fractal Geometry in structure, while meridian is the expression form of Fractal structure of the human body. The basic Fractal geometrical characters of meridian are: self similarity, self affinity, symmetry, minute structure and self avoidance, which has been applied for thousands of years in clinic, such as “taking the acupoints on the right side of the body in cases of disorders appearing on the left side and vice versa". The basic characters of meridians are 1) symmetry of the 12 regular meridians on the bilateral sides of the body (symmetry); 2) similarity in characters and actions of acupoints of the same one meridian (self similarity); 3) taking acupoints on the lower part of the body when disorders occurring on the upper part of the body; and taking acupoints on the upper part of the body if disorders appearing on the lower part (self affinity); 4) micro acupuncture system including hand acupuncture, foot acupuncture, scalp acupuncture, auricular acupuncture and eye acupuncture (minute structure); and 5) systematical running of needling sensation (self avoidance).

Monte Carlo Simulation of First-Order Diffusion-Limited Reaction within Three-Dimensional Porous Pellets

The Monte Carlo method was employed to simulate diffusion and reaction processes within three-dimensional porous catalyst pellets. The porous pellets used were represented by a Menger sponge and a uniform-pore structure respectively. Results obtained from the fractal pellet showed an intermediate low-slope asymptote in the logarithmic plot of reaction rate and reaction probability. However, the low-slope one did not appear when the reaction occurred within the uniform pellet. Moreover, it was certified that the fractal structure not only generated a new asymptote, but also reduced diffusion resistance of reactants and products.

Metallogenic Districts of Yangtze Cratonic Rim at the Edge of Chaos

Combining the science of complexity with ore geology, the author puts forward a new theory of metallogenesis: “complexity and self organized criticality of metallogenic dynamic systems”, and three fundamental theories are raised for it. The ore genesis and regularity of ore formation of four metallogenic districts around the Yangtze craton in China are studied with this theory. It is found that “metallogenic districts of Yangtze cratonic rim are all at the edge of chaos”. This proposition is expounded by four determinative criteria of the edge of chaos for metallogenic districts of Yangtze cratonic rim.

Inspired by nature:Self-fractal cobalt sulfate composite electrode for sodium ion storage

Generally,the metal sulfide itself has poor conductivity,and the volume expansion occurs when it is converted with sodium,which will destroy the integrity of the electrode structure,resulting in poor cycle performance and rate performance.To solve the problems of low initial coulombic efficiency(ICE)and volume expansion of metal compounds used as anodes in sodium-ion batteries(SIBs).Inspired by nature,the CoSO_(4)/hard carbon/graphene(CHG)fractal structure electrode was designed.Self-fractal structures with electron/ion transport channels and high strain tolerance proved to be an effective strategy to overcome these challenges.The fractal dimension(D)is measured by synchronous Small Angle X-ray scattering,and the D remains stable during charging and discharging.The fractal CHG also showed excellent electrochemical performance,especially 97.4%ICE.Theoretical calculation shows that self-fractal CHG can promote the formation of a thin solid electrolyte interface(SEI).Synchrotron radiation absorption spectrum proved the reaction mechanism of CHG.This study not only proves that cobalt sulfate is a feasible strategy for developing high-performance SIBs anodes but also provides an advanced method for measuring the fractal dimension of energy storage electrode materials.

Independently tunable multichannel terahertz filters

We numerically demonstrate terahertz multichannel filters with independently tunable defect modes based on fractal photonic crystMs. Single defect and multiple defects models are proposed to fabricate the multichannel terahertz filters. The facts that the wave functions of the defect states do not overlap and their bases are orthogonal lead to the independency among the defect modes. The simulated results theoretically provide the principle for fabricating independently tunable multichannel terahertz filters by utilizing one-dimensional phot（~nic crystals with defects.

Formation and Aggregation Kinetics of Mixed Metal Hydroxides Agglomerates

The aggregation and fractal structure of mixed metal hydroxides ( MMH ) agglomerates with increasing ionic strength have been studied by dynamic light scattering ( DLS ) and SEM techniques. The experiments indicate that the MMH agglomerates have two different structures in RLA regime and DLA regime, and also give the proof that the transition region between RLA and DLA may occur.

Lattice Boltzmann simulation of fluid flow through coal reservoir's fractal pore structure

The influences of fractal pore structure in coal reservoir on coalbed methane(CBM) migration were analyzed in detail by coupling theoretical models and numerical methods.Different types of fractals were generated based on the construction thought of the standard Menger Sponge to model the 3D nonlinear coal pore structures.Then a correlation model between the permeability of fractal porous medium and its pore-size-distribution characteristics was derived using the parallel and serial modes and verified by Lattice Boltzmann Method(LBM).Based on the coupled method,porosity(ф),fractal dimension of pore structure(Db),pore size range(rmin,rmax) and other parameters were systematically analyzed for their influences on the permeability(ф) of fractal porous medium.The results indicate that:① the channels connected by pores with the maximum size(rmax) dominate the permeability,approximating in the quadratic law;② the greater the ratio of r max and r min is,the higher is;③ the relationship between D b and follows a negative power law model,and breaks into two segments at the position where Db ≌2.5.Based on the results above,a predicting model of fractal porous medium permeability was proposed,formulated as k=cfrnmax,where C and n(approximately equal to 2) are constants and f is an expression only containing parameters of fractal pore structure.In addition,the equivalence of the new proposed model for porous medium and the Kozeny-Carman model k=Crn was verified at Db =2.0.

Complexity and Self-Organized Criticality of Solid Earth System(Ⅰ)

The author puts forward the proposition of Complexity and Self Organized Criticality of Solid Earth System in the light of: (1) the science of complexity studies the mechanisms of emergence of complexity and is the science of the 21st century, (2) the study of complexity of the earth system would be one of the growing points occupying a strategic position in the development of geosciences in the 21st century. By the proposition we try to cogitate from a new viewpoint the ancient yet ever new solid earth system. The author abstracts the fundamental problem of the solid earth system from the essence of the generalized geological systems and processes which reads: the complexity and self organized criticality of the global nature, structure and dynamical behavior of the whole solid earth system emerging from the multiple coupling and superposition of non linear interactions among the multicomponents of the earths material and the multiple generalized geological (geological, geophysical, and geochemical) processes . Starting from this cognizance the author proposes eight major themes and the methodology of researches on the complexity and self organized criticality of the solid earth system.

一种具有分形结构的弹黏塑性材料建模及其求解方法

本文建立了一种具有分形结构的元件模型,用于描述材料弹粘塑性特性,并可以在无需求解相应的无限阶微分方程的情况下获得各载荷作用下模型的力学反应.首先,基于这种建模方法,建立了表征具有复杂无限阶分形结构材料弹黏塑性特性的混联元件模型(L-R模型).然后,利用MATLAB/Simulink,借助弹簧(弹性)、黏壶(黏性)和塑性体(塑性)单元的本构关系来描述材料的基本力学性能.之后,将宾厄姆模型作为基本模型按照分形理论进行迭代,通过求解得到描述材料在各种载荷作用下的力学(弹黏塑性)反应.最后,为了验证该建模方法及其求解结果的可靠性,在钢、板岩、煤、红砂岩和盐岩五种不同分形结构的材料上进行了循环载荷实验.将实验结果与求解结果进行比较,表明所建立的模型能够有效地描述材料的弹黏塑性性能.