We study the global pressure of a one-dimensional polydisperse granular gases system for the first time, in which the size distribution of particles has the fractal characteristic and the inhomogeneity is described by a fractal dimension D. The particles are driven by Gaussian white noise and subject to inelastic mutual collisions. We define the global pressure P of the system as the impulse transferred across a surface in a unit of time, which has two contributions, one from the translational motion of particles and the other from the collisions. Explicit expression for the global pressure in the steady state is derived. By molecular dynamics simulations, we investigate how the inelasticity of collisions and the inhomogeneity of the particles influence the global pressure. The simulation results indicate that the restitution coefficient e and the fractal dimension D have significant effect on the pressure. 相似文献
A precursor polymer PEO‐b‐PEMA that contains anilino moieties is synthesized from EPAEMA by ATRP by using a PEOBr macroinitiator and CuBr/HMTETA catalyst system. The aminoazobenzene‐containing block copolymer PEO‐b‐PCN is obtained by the azo‐coupling reaction between PEO‐b‐PEMA and the diazonium salt of 4‐aminobenzonitrile. Results show that PEO‐b‐PCN has a narrow molecular weight distribution and the repeat unit numbers of the hydrophilic and hydrophobic blocks are 122 and 200, respectively. PEO‐b‐PCN can form uniform spherical aggregates by gradually adding water into its THF solution. Upon irradiation with a linearly polarized Ar+ laser beam, the spherical aggregates can be significantly elongated in the polarization direction of the light.
Iterated Function System (IFS) models have been used to represent discrete sequences where the attractor of the IFS is self-affine
or piecewise self-affine in R2 or R3 (R is the set of real numbers). In this paper, the piecewise hidden-variable fractal model is extended from R3 to Rn (n is an integer greater than 3), which is called the multi-dimensional piecewise hidden variable fractal model. This new model
uses a “mapping partial derivative” and a constrained inverse algorithm to identify the model parameters. The model values
depend continuously on all the hidden variables. Therefore the result is very general. Moreover, the piecewise hidden-variable
fractal model in tensor form is more terse than in the usual matrix form. 相似文献
Three-dimensional fractures of different fractal dimensions have been constructed with successive random addition algorithm,
the applicability of various dimension determination methods at nanometer scale has been studied. As to the metallic fractures,
owing to the limited number of slit islands in a slit plane or limited datum number at nanometer scale, it is difficult to
use the area-perimeter method or power spectrum method to determine the fractal dimension. Simulation indicates that box-counting
method can be used to determine the fractal dimension at nanometer scale. The dimensions of fractures of valve steel 5Cr21Mn9Ni4N
have been determined with STM. Results confirmed that fractal dimension varies with direction at nanometer scale. Our study
revealed that, as to theoretical profiles, the dependence of frsctal dimension with direction is simply owing to the limited
data set number, i.e. the effect of boundaries. However, the dependence of fractal dimension with direction at nanometer scale
in real metallic fractures is correlated to the intrinsic characteristics of the materials in addition to the effect of boundaries.
The relationship of fractal dimensions with the mechanical properties of materials at macrometer scale also exists at nanometer
scale.
Project supported by the National Natural Science Foundation of China (Grant Nos. 59771050 and 59872004) and the Foundation
Fund of Ministry of Metallurgical Industry. 相似文献
According to the fact that many pulverized particles possess fractal characteristic, a fractal model for studying fine particles in granular material flows is first proposed. An expression of particles' fractal distribution is derived to describe the relationship between the particle fractal dimensions and particle velocity distribution function. In accordance with this model, the theoretical particle effective thermal conductivity is derived. The analytical results show that for the small Biot-Fourier number, the effective thermal conductivity increases with the square root of the granular temperature. For very large Biot-Fourier number, the effective thermal conductivity linearly increases with the granular temperature. Numerically calculated results show that the thermal conductivity increases with the particle size fractal dimensions and decreases with the particle surface fractal dimensions. 相似文献