The Fractal Feature of the Liquid-Vapor Interface

2004 ◽  
Author(s):  
Danling Zeng ◽  
Deming Wang ◽  
Juanfang Liu
Keyword(s):  
Fractal Dimension ◽  
Smooth Surface ◽  
Fractal Theory ◽  
Dynamics Simulation ◽  
Clear Understanding ◽  
Interfacial Phenomenon ◽  
Interface Tension ◽  
Vapor Interface ◽  
Coexisting Phases ◽  
Simulation Results

Interfacial phenomenon appears frequently in practice. It plays important roles in various fields of science and technology. In order to make a clear understanding on the characteristics of an interface, a molecular dynamics simulation (MDS) was performed. The simulation results show that there exists a transition layer between the coexisting phases in which thermodynamics properties changes continuously. On the other hand, according to the fractal theory it is considered that the interface is not a smooth surface but a fractal one. The fractal dimension of it is calculated in the paper by the aid of the general approach provided in fractal theory. Furthermore, a relation between interface tension and fractal dimension of the interface was advanced. The surface tension thus obtained agrees well with the experiments.

scholarly journals Dynamic characteristics and fractal representations of crack propagation of rock with different fissures under multiple impact loadings

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Bing Sun ◽  
Shun Liu ◽  
Sheng Zeng ◽  
Shanyong Wang ◽  
Shaoping Wang
Keyword(s):  
Fractal Dimension ◽  
Crack Propagation ◽  
Crack Growth ◽  
Impact Test ◽  
Fractal Theory ◽  
Dynamic Change ◽  
Fractal Dimensions ◽  
Peak Stress ◽  
Dynamic Mechanical Properties ◽  
Gravitational Potential Energy

AbstractTo investigate the influence of the fissure morphology on the dynamic mechanical properties of the rock and the crack propagation, a drop hammer impact test device was used to conduct impact failure tests on sandstones with different fissure numbers and fissure dips, simultaneously recorded the crack growth after each impact. The box fractal dimension is used to quantitatively analyze the dynamic change in the sandstone cracks and a fractal model of crack growth over time is established based on fractal theory. The results demonstrate that under impact test conditions of the same mass and different heights, the energy absorbed by sandstone accounts for about 26.7% of the gravitational potential energy. But at the same height and different mass, the energy absorbed by the sandstone accounts for about 68.6% of the total energy. As the fissure dip increases and the number of fissures increases, the dynamic peak stress and dynamic elastic modulus of the fractured sandstone gradually decrease. The fractal dimensions of crack evolution tend to increase with time as a whole and assume as a parabolic. Except for one fissure, 60° and 90° specimens, with the extension of time, the increase rate of fractal dimension is decreasing correspondingly.

scholarly journals Effect of Hydrophobic Silica Nanochannel Structure on the Running Speed of a Colloidal Damper

2021 ◽  
Vol 11 (15) ◽  
pp. 6808
Author(s):  
Gengbiao Chen ◽  
Zhiwen Liu
Keyword(s):  
Fractal Dimension ◽  
Silica Gel ◽  
Fractal Theory ◽  
Percolation Model ◽  
Silica Gels ◽  
Practical Significance ◽  
Running Speed ◽  
Fractal Percolation ◽  
Micropore Structure ◽  
Hydrophobic Silica

A colloidal damper (CD) can dissipate a significant amount of vibrations and impact energy owing to the interface power that is generated when it is used. It is of great practical significance to study the influence of the nanochannel structure of hydrophobic silica gel in the CD damping medium on the running speed of the CD. The fractal theory was applied to observe the characteristics of the micropore structure of the hydrophobic silica gel by scanning electron microscopy (SEM), the primary particles were selected to carry out fractal analysis, and the two-dimensional fractal dimension of the pore area and the tortuous fractal dimension of the hydrophobic silica gel pore structure were calculated. The fractal percolation model of water in hydrophobic silica nanochannels based on the slip theory could thus be obtained. This model revealed the relationship between the micropore structure parameters of the silica gel and the running speed of the CD. The CD running speed increases with the addition of grafted molecules and the reduction in pore size of the silica gel particles. Continuous loading velocity testing of the CD loaded with hydrophobic silica gels with different pore structures was conducted. By comparing the experimental results with the calculation results of the fractal percolation model, it was determined that the fractal percolation model can better characterize the change trend of the CD running velocity for the first loading, but the fractal dimension was changed from the second loading, caused by the small amount of water retained in the nanochannel, leading to the failure of fractal characterization.

scholarly journals Scale Characteristics and Optimization of Park Green Space in Megacities Based on the Fractal Measurement Model: A Case Study of Beijing, Shanghai, Guangzhou, and Shenzhen

2021 ◽  
Vol 13 (15) ◽  
pp. 8554
Author(s):  
Zhen Li ◽  
Wanmin Zhao ◽  
Miaoyao Nie
Keyword(s):  
Fractal Dimension ◽  
Evaluation System ◽  
Goodness Of Fit ◽  
Green Space ◽  
Fractal Theory ◽  
Measurement Model ◽  
Scale Structure ◽  
Qualitative Description ◽  
Urban Spatial Structure ◽  
Factors Affecting

This paper applies fractal theory to research of green space in megacity parks due to the lack of a sufficient qualitative description of the scale structure of park green space, a quantifiable evaluation system, and operable planning methods in traditional studies. Taking Beijing, Shanghai, Guangzhou, and Shenzhen as examples, GIS spatial analysis technology and the Zipf model are used to calculate the fractal dimension (q), the goodness of fit (R2), and the degree of difference (C) to deeply interpret the connotation of indicators and conduct a comparative analysis between cities to reveal fractal characteristics and laws. The research results show that (1) the fractal dimension is related to the complexity of the park green space system; (2) the fractal dimension characterizes the hierarchical iteration of the park green space to a certain extent and reflects the internal order of the scale distribution; (3) the scale distribution of green space in megacity parks deviates from the ideal pyramid configuration; and (4) there are various factors affecting the scale structure of park green space, such as natural base conditions, urban spatial structure, and the continuation of historical genes working together. On this basis, a series of targeted optimization strategies are proposed.

Study on Engine Kinematics and Dynamics Simulation Based on COSMOSMotion

2012 ◽  
Vol 503-504 ◽  
pp. 731-734
Author(s):  
Xiao Xu Liu ◽  
Min Chen ◽  
Ai Hua Tang
Keyword(s):  
Virtual Prototype ◽  
Dynamics Simulation ◽  
Kinematics And Dynamics ◽  
Engine Model ◽  
Kinematics Simulation ◽  
Simulation Based ◽  
Calculation Results ◽  
Simulation Results ◽  
Dynamics Simulations

The engine model with 4 cylinders is built by SolidWorks, the kinematics and dynamics simulations of the engine virtual prototype are done by COSMOSMotion, the results of kinematics simulation are checked, there are very small errors between the simulation results and the calculation results according to formulas. The mainly results of dynamics simulation are given. The simulation result consists with the parameters of the engine.

Dynamics Simulation and Analysis of Transition Stage of Tilt-Rotor Aircraft

2016 ◽  
Vol 842 ◽  
pp. 251-258 ◽  
Author(s):  
Muhammad Rafi Hadytama ◽  
Rianto A. Sasongko
Keyword(s):  
Dynamic Response ◽  
Equations Of Motion ◽  
Flight Dynamics ◽  
Dynamics Simulation ◽  
Tilt Rotor ◽  
Vertical Takeoff And Landing ◽  
Improved Stability ◽  
Simulation Results ◽  
Vtol Aircraft ◽  
Vertical Takeoff

This paper presents the flight dynamics simulation and analysis of a tilt-rotor vertical takeoff and landing (VTOL) aircraft on transition phase, that is conversion from vertical or hover to horizontal or level flight and vice versa. The model of the aircraft is derived from simplified equations of motion comprising the forces and moments working on the aircraft in the airplane's longitudinal plane of motion. This study focuses on the problem of the airplane's dynamic response during conversion phase, which gives an understanding about the flight characteristics of the vehicle. The understanding about the flight dynamics characteristics is important for the control system design phase. Some simulation results are given to provide better visualization about the behaviour of the tilt-rotor. The simulation results show that both transition phases are quite stable, although an improved stability can give better manoeuver and attitude handling. Improvement on the simulation model is also required to provide more accurate and realistic dynamic response of the vehicle.

The Study on Young's Modulus of Multilayered Cu/Ni Multilayered Nano Thin Films by Molecular Dynamics Simulation

2014 ◽  
Vol 513-517 ◽  
pp. 113-116
Author(s):  
Jen Ching Huang ◽  
Fu Jen Cheng ◽  
Chun Song Yang
Keyword(s):  
Thin Film ◽  
Thin Films ◽  
Molecular Dynamics ◽  
Molecular Dynamics Simulation ◽  
Strain Rate ◽  
Young’S Modulus ◽  
Potential Function ◽  
Dynamics Simulation ◽  
System Temperature ◽  
Simulation Results

The Youngs modulus of multilayered nanothin films is an important property. This paper focused to investigate the Youngs Modulus of Multilayered Ni/Cu Multilayered nanoThin Films under different condition by Molecular Dynamics Simulation. The NVT ensemble and COMPASS potential function were employed in the simulation. The multilayered nanothin film contained the Ni and Cu thin films in sequence. From simulation results, it is found that the Youngs modulus of Cu/Ni multilayered nanothin film is different at different lattice orientations, temperatures and strain rate. After experiments, it can be found that the Youngs modulus of multilayered nanothin film in the plane (100) is highest. As thickness of the thin film and system temperature rises, Youngs modulus of multilayered nanothin film is reduced instead. And, the strain rate increases, the Youngs modulus of Cu/Ni multilayered nanothin film will also increase.

Runoff Fractal Dimension of Songhua River Basin in Harbin Station Based on Db4 Wavelet

2012 ◽  
Vol 550-553 ◽  
pp. 2537-2540
Author(s):  
Hai Yan Gu ◽  
Yong Wang ◽  
Lei Yu
Keyword(s):  
Time Series ◽  
Fractal Dimension ◽  
River Basin ◽  
Fractal Theory ◽  
Measurement Methods ◽  
Self Similarity ◽  
Songhua River ◽  
Songhua River Basin ◽  
The Songhua River Basin ◽  
The Songhua River

The wavelet analysis and fractal theory into the analysis of hydrological time series, fluctuations in hydrological runoff sequence given the complexity of the measurement methods--- fractal dimension. The real monthly runoffs of 28 years from Songhua River basin in Harbin station are selected as research target. Wavelet transform combined with spectrum method is used to calculate the fractal dimension of runoff. Moreover, the result demonstrates that the runoff in Songhua River basin has the characteristic of self-similarity, and the complexity of runoff in the Songhua River basin in Harbin station is described quantificationally.

scholarly journals Effective Thermal Conductivity of Open Cell Polyurethane Foam Based on the Fractal Theory

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Kan Ankang ◽  
Han Houde
Keyword(s):  
Thermal Conductivity ◽  
Fractal Dimension ◽  
Effective Thermal Conductivity ◽  
Polyurethane Foam ◽  
Solid Phase ◽  
Fractal Theory ◽  
Heat Radiation ◽  
Total Thermal Conductivity ◽  
Equivalent Thermal Conductivity ◽  
Open Cell

Based on the fractal theory, the geometric structure inside an open cell polyurethane foam, which is widely used as adiabatic material, is illustrated. A simplified cell fractal model is created. In the model, the method of calculating the equivalent thermal conductivity of the porous foam is described and the fractal dimension is calculated. The mathematical formulas for the fractal equivalent thermal conductivity combined with gas and solid phase, for heat radiation equivalent thermal conductivity and for the total thermal conductivity, are deduced. However, the total effective heat flux is the summation of the heat conduction by the solid phase and the gas in pores, the radiation, and the convection between gas and solid phase. Fractal mathematical equation of effective thermal conductivity is derived with fractal dimension and vacancy porosity in the cell body. The calculated results have good agreement with the experimental data, and the difference is less than 5%. The main influencing factors are summarized. The research work is useful for the enhancement of adiabatic performance of foam materials and development of new materials.

Dynamics Equations of Robots Mounted on Moving Bases

1991 ◽  
Author(s):  
R. W. Toogood
Keyword(s):  
Angular Velocity ◽  
Control Systems ◽  
Linear Acceleration ◽  
Computer Code ◽  
Dynamics Simulation ◽  
Simulation Studies ◽  
Flexible Link ◽  
Paper Briefly ◽  
Simulation Results ◽  
Simplification Techniques

Abstract A number of programs have been developed for the automatic symbolic generation of efficient computer code for the dynamic analysis of serial rigid and flexible link manipulators. Code for both the inverse and the direct dynamics computations can be generated. The symbolic generators allow the robot base to be given an arbitrary linear acceleration anchor angular velocity and acceleration. The efficiency of the generated code is an important consideration for simulation studies and/or implementation in control systems. This paper briefly describes the symbolic generation and simplification techniques. The added computational load due to including the base motion is discussed. Some dynamics simulation results are presented for a 3R rigid link manipulator mounted on an oscillating base, which graphically illustrates the effect of the base movement on the dynamics.

scholarly journals Thermal and Wet Comfort of Fabrics Based on Fractal Dimension of Silicone Coating

2018 ◽  
Vol 13 (1) ◽  
pp. 155892501801300
Author(s):  
Yunlong Shi ◽  
Liang Wang ◽  
Wenhuan Zhang ◽  
Xiaoming Qian
Keyword(s):  
Fractal Dimension ◽  
Thermal Insulation ◽  
Coating Layer ◽  
Fractal Theory ◽  
Barrier Effect ◽  
Evaporative Resistance ◽  
Silicone Coating ◽  
Self Similar ◽  
Warmth Retention ◽  
Coated Fabrics

In this paper, thermal and wet comforts of silicone coated windbreaker shell jacket fabrics were studied. Both thermal insulation and evaporative resistance of fabric increased with an increase in coating area due to the barrier effect of the silicone coating layer. Moreover, the coated fabrics with self-similar structures showed different thermal insulation and evaporative resistance under the same total coating area. Fractal theory was used to explain this phenomenon. Optimal thermal-wet comfort properties were obtained when the fractal dimension (D=1.599) was close to the Golden Mean (1.618). When the fractal dimension of coating was lower than 1.599, fabric warmth retention was not high enough. In contrast, fabric evaporative resistance was beyond the value at which people would feel comfortable when the fractal dimension was greater than 1.599.

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