Prediction of heat transfer of nanofluid on critical heat flux based on fractal geometry

Analytical expressions for nucleate pool boiling heat transfer of nanofluid in the critical heat flux （CHF） region are derived taking into account the effect of nanoparticles moving in liquid based on the fractal geometry theory. The proposed fractal model for the CHF of nanofluid is explicitly related to the average diameter of the nanoparticles, the volumetric nanoparticle concentration, the thermal conductivity of nanoparticles, the fractal dimension of nanoparticles, the fractal dimension of active cavities on the heated surfaces, the temperature, and the properties of the fluid. It is found that the CHF of nanofluid decreases with the increase of the average diameter of nanoparticles. Each parameter of the proposed formulas on CHF has a clear physical meaning. The model predictions are compared with the existing experimental data, and a good agreement between the model predictions and experimental data is found. The validity of the present model is thus verified. The proposed fractal model can reveal the mechanism of heat transfer in nanofluid.

FRACTAL GEOMETRY STUDY OF CORRELATION BETWEEN IMPACT TOUGHNESS OF STEEL AND PARAMETERS OF FREE-CUTTING PHASE

Studies were made of the calculation of fractal dimension of transverse impact fracture sur- face,and of the correlation between impact toughness of steel and parameters of free-cutting phase by means of the developed fractal geometry model of crack propagation.It is believed that the area fraction,f,of free-cutting phase is negligibly influential to the longitudinal im- pact toughness,as f1 .While the aspect ratio,saying ratio of length to width,of free-cut. ting phase is inversely influential to the transverse impact toughness.This may .be the reason why the transverse impact toughness of free-cutting steel containing more rare earth contrast to sulphur is even higher than the low sulphur containing steel.

Fractal geometry and topology abstracted from hair fibers

Based on the concepts of fractal super fibers, the （3, 9＋2）-circle and （9＋2, 3）-circle binary fractal sets are abstracted form such prototypes as wool fibers and human hairs, with the （3）-circle and the （9＋2）-circle fractal sets as subsets. As far as the （9＋2） topological patterns are concerned, the following propositions are proved： The （9＋2） topological patterns accurately exist, but are not unique. Their total number is 9. Among them, only two are allotropes. In other words, among the nine topological patterns, only two are independent （or fundamental）. Besides, we demonstrate that the （3, 9＋2）-circle and （9＋2, 3）-circle fractal sets are golden ones with symmetry breaking.

Experimental realization of fractal fretwork metasurface for sound anomalous modulation

Natural creatures and ancient cultures are full of potential sources to provide inspiration for applied sciences.Inspired by the fractal geometry in nature and the fretwork frame in ancient culture,here we design the acoustic metasurface to realize sound anomalous modulation,which manifests itself as an incident-dependent propagation behavior:sound wave propagating in the forward direction is allowed to transmit with high efficiency while in the backward direction is obviously suppressed.We quantitatively investigate the dependences of asymmetric transmission on the propagation direction,incident angle and operating frequency by calculating sound transmittance and energy contrast.This compact fractal fretwork metasurface for acoustic anomalous modulation would promote the development of integrated acoustic devices and expand versatile applications in acoustic communication and information encryption.

A Fractal Orifice-Throat Model for Seepage Characteristics of Multiscale Porous Media

The seepage characteristics of multiscale porous media is of considerable significance in many scientific and engineering fields.The Darcy permeability is one of the key macroscopic physical properties to characterize the seepage capacity of porous media.Therefore,based on the statistically fractal scaling law of porous media,fractal geometry is applied to model the multiscale pore structures.And a two-dimensional fractal orifice-throat model with multiscale and tortuous characteristics is proposed for the seepage flow through porous media.The analytical expression for Darcy permeability of porous media is derived,which is validated by comparing with available experimental data.The results show that the Darcy permeability is significantly influenced by porosity,orifice-throat fractal dimension,minimum to maximum diameter ratio,orifice-throat ratio and tortuosity fractal dimension.The present results are helpful for understanding the seepage mechanism of multiscale porous media,and may provide theoretical basis for unconventional oil and gas exploration and development,porous phase transition energy storage composites,CO2 geological sequestration,environmental protection and nuclear waste treatment,etc.

Performance-based fractal fracture model for complex fracture network simulation

The paper presents a novel hydraulic fracturing model for the characterization and simulation of the complex fracture network in shale gas reservoirs. We go beyond the existing method that uses planar or orthogonal conjugate fractures for representing the ＇＇complexity＇＇ of the network. Bifurcation of fractures is performed utilizing the Lindenmayer system based on fractal geometry to describe the fracture propagation pattern, density and network connectivity. Four controlling parameters are proposed to describe the details of complex fractures and stimulated reservoir volume（SRV）. The results show that due to the multilevel feature of fractal fractures, the model could provide a simple method for contributing reservoir volume calibration. The primary-and second-stage fracture networks across the overall SRV are the main contributions to the production, while the induced fracture network just contributes another 20% in the late producing period. We also conduct simulation with respect to different refracturing cases and find that increasing the complexity of the fracture network provides better performance than only enhancing the fracture conductivity.

Dual-band and polarization-insensitive terahertz absorber based on fractal Koch curves

We report the design, fabrication, and characterization of a dual-band and polarization-insensitive metamaterial ab-sorber （MA）, which consists of periodically arranged fractal Koch curves acting as the top resonator array and a metallic ground plane separated by a dielectric spacer. Compared with conventional MAs, a more compact size and multi-frequency operation are achieved by using fractal geometry as the unit cell of the MA. Both the effective medium theory and the multi- reflection interference theory are employed to investigate the underlying physical mechanism of the proposed terahertz MA, and results indicate that the latter theory is not suitable for explaining the absorption mechanism in our investigated struc-ture. Two absorption peaks are observed at 0.226 THz and 0.622 THz with absorptivities of 91.3% and 95.6% respectively and good agreements between the full-wave simulation and experimental results are achieved.

Quantum Dark Energy from the Hyperbolic Transfinite Cantorian Geometry of the Cosmos

The quintessence of hyperbolic geometry is transferred to a transfinite Cantorian-fractal setting in the present work. Starting from the building block of E-infinity Cantorian spacetime theory, namely a quantum pre-particle zero set as a core and a quantum pre-wave empty set as cobordism or surface of the core, we connect the interaction of two such self similar units to a compact four dimensional manifold and a corresponding holographic boundary akin to the compactified Klein modular curve with SL(2,7) symmetry. Based on this model in conjunction with a 4D compact hy- perbolic manifold M(4) and the associated general theory, the so obtained ordinary and dark en- ergy density of the cosmos is found to be in complete agreement with previous analysis as well as cosmic measurements and observations such as WMAP and Type 1a supernova.

Application of fractal theory to size effect of disordered materials

For disordered materials it is impossible to measure constant material properties using the Euclidian geometrical dimension of the test specimens. Based on the theory of fractal geometry, the fractal dimension of the damaged microstructure is applied to measure the strength and fracture toughness of imitation marbles, which turn out to be scale invariant material constants. In this paper, the experimental data are treated and interpreted by the theory of fractal geometry. Reasonable results are obtained and the size effects on strength and fracture energy are observed.

Fractal Description of the Shearing-Surface of Tools

In this paper, the basic methods are introduced to calculate the fractaldimensions of the shearing surface of some tools. The fractal dimension of the shearing surface ofexperimental sampling is obtained and the fractal characteristics are also discussed. We can applythe fractal method to identify types of tools used by burglars and to do the job of individualrecognition. New theories and methods are provided to measure and process the shearing surfaceprofile of tools.

THE THEORY OF FRACTAL INTERPOLATED SURFACE AND ITS APPLICATIONS

In this paper, the principle of construction of a fractal surface is introduced, interpolation functions for a fractal interpolated surface are discussed, the theorem of the uniqueness of an iterated function system of fractal interpolated surface is proved, the theorem of fractal dimension of fractal interpolated surface is derived, and the case that practical data are used to interpolate fractal surface is studied.

A Study on Application of Fractal Theory in Examination of Striation Marks

Use scissors and cutting pliers to produce some striation marks. The data collection apparatus is used to collect the surface data of such marks produced by scissors and cutting pliers, and then get the profile curve that is vertical to the surface of striation marks. In tha application of fractal theory, the fractal dimension of such a profile curve is then calculated, and further studies are made on its fractal characteristics. As an exploration on tool types and individual identification, this is aimed to provide a new theory and approach to examination and identification of striation tool marks.

INVESTIGATION INTO EFFECT OF SPRING PRESSURE ON PERFORMANCE OF BALANCED MECHANICAL SEALS

The loads acting on the sealing elements of balanced mechanical seals are analyzed. When the balance factor approaches the back pressure factor, the spring pressure will become main part of the face pressure. The leakage model of balanced mechanical seals is established on the base of M-B model for rough surface. Several GY-70 type balanced mechanical seals are tested. The influences of the spring pressure both on the leakage rate and on the friction characteristic of balanced mechanical seals are investigated. The research results indicate that as spring pressure increases, both the clear-ance between two end faces and the leakage rate will decrease, and the friction will be more serious because lubrication medium between the rotating ring and the stationary ring reduces, though the increase of the spring pressure may not be enough to change the face friction state of mechanical seals. There exists an optimum spring pressure for mechanical seal operation. Under this spring pres-sure, not only leakage rate is small, but also the seal end surfaces have a fine friction characteristic. Under different operating conditions, identical type mechanical seals may possess different spring pressure. Appropriate selection of spring pressure is valuable to realize long-period and small leakage rate operating of balanced mechanical seals.

Pulse-to-pulse periodic signal sorting features and feature extraction in radar emitter pulse sequences

A novel class of periodically changing features hidden in radar pulse sequence environment,named G features,is proposed.Combining fractal theory and Hilbert-Huang transform,the features are extracted using changing characteristics of pulse parameters in radar emitter signals.The features can be applied in modern complex electronic warfare environment to address the issue of signal sorting when radar emitter pulse signal parameters severely or even completely overlap.Experiment results show that the proposed feature class and feature extraction method can discriminate periodically changing pulse sequence signal sorting features from radar pulse signal flow with complex variant features,therefore provide a new methodology for signal sorting.

ELASTIC-PLASTIC ADHESION MODEL FOR SINGLE ASPERICAL ASPERITY MICROCONTACT

The adhesion of single asperity contacting with a rigid flat is investigated. The microcontact model of the deformable asperity is established utilizing fractal geometry, which makes the resuRed adhesion model to relate with the surface characteristics that the asperity belongs to. The Dugdale approximation is utilized to consider the adhesive interaction within and outside the contact area. Then the model for solving the elastic-plastic adhesion of single asperity is presented by combing the Maugis-Dugdale（MD） model. To illustrate the necessity of considering the plastic deformation in microcontact, simulations of the relationship between the adhesive contact load and the interference of the asperity are performed. The result shows that the presented model is more suitable for the solution of the elastic-plastic microcontact of spherical asperity due to intermolecular adhesive interactions.

Advances in experimental methods for root system architecture and root development

Plant roots play important roles in acquisition of water and nutrients, storage, anchoring, transport, and symbiosis with soil microorganisms, thus quantitative researches on root developmental processes are essential to understand root functions and root turnover in ecosystems,and at the same time such researches are the most difficult because roots are hidden underground. Therefore, how to investigate efficiently root functions and root dynamics is the core aspect in underground ecology. In this article, we reviewed some experimental methods used in root researches on root development and root system architecture, and summarized the advantages and shortages of these methods. Based on the analyses, we proposed three new ways to more understand root processes：（1） new experimental materials for root development;（2） a new observatory system comprised of multiple components, including many observatory windows installed in field, analysis software,and automatic data transport devices;（3） new techniques used to analyze quantitatively functional roots.

Simulation of tree and its swaying with wind generated by L-system

This paper constructs a tree model by using the 3D stochastic and L system with brackets. Adjusting the range of the parameters, the present method ensures a favorable randomness and reflects the reality and the real time. Based on a simple mechanical model, the simulation of the phenomenon of wind swaying trees satisfies visual effects well.

Receiver tube heat transfer analysis of a CCP collector designed based on branched fractals geometry

For the development of systems related to renewable energy and specifically for thermo-solar energy,it is essential to study and analyze the different thermal phenomena of heat transfer,in search of the best conditions that allow strengthening the designs.Phenomena such as radiation,convection,and conduction are highly studied,from the field of materials to the field of infrastructure,finding day to day optimal solutions that guarantee a great use of the solar resource available on the earth's surface.This study presented the results of heat transfer analysis on a receiver pipe in a CCP;designed using the theory of branched fractal geometry to improve the heat transfer associated with concentrating solar capture systems.A fractal structure as a branch or arboreal fractal type network,influenced thermal and electrical parameters,as electrical resistance,thermal resistance,and convective heat transfer,so increasing the level branch heat transfer can be enhancement along of the pipe.The use of renewable energies in agriculture benefits the industrial processes that require a continuous power system,due to climatic conditions and geographical location is not a guarantee in food production fields,which reason solar capture systems contribute to food dehydration processes,water heating,refrigeration,and energy production.

Tree-inspired dendriforms and fractal-like branching structures in architecture： A brief historical overview

The shapes of trees are complex and fractal-like, and they have a set of physical, mechanical and biological functions. The relation between them always draws attention of human beings throughout history and, focusing on the relation between shape and structural strength, architects have designed a number of treelike structures, referred as dendriforms. The replication and adoption of the treelike patterns for constructing architectural structures have been varied in different time periods based on the existing and advanced knowledge and available technologies. This paper, by briefly discussing the biological functions and the mechanical properties of trees with regard to their shapes, overviews and investigates the chronological evolution and advancements of dendriform and arboreal structures in architec- ture referring to some important historical as well as contemporary examples.

Hlder Norm Estimate for a Hilbert Transform in Hermitean Clifford Analysis

A Hilbert transform for H61der continuous circulant （2 × 2） matrix functions, on the d- summable （or fractal） boundary F of a Jordan domain Ω in R2n, has recently been introduced within the framework of Hermitean Clifford analysis. The main goal of the present paper is to estimate the HSlder norm of this Hermitean Hilbert transform. The expression for the upper bound of this norm is given in terms of the HSlder exponents, the diameter of F and a specific d-sum （d 〉 d） of the Whitney decomposition of Ω. The result is shown to include the case of a more standard Hilbert transform for domains with left Ahlfors-David regular boundary.