Aim The particle texture from diesel engine was imitated by use of computer. Methods The theory of fractal geometry and the diffusion limited aggregation model were used to simulate the micron texture. Results The...Aim The particle texture from diesel engine was imitated by use of computer. Methods The theory of fractal geometry and the diffusion limited aggregation model were used to simulate the micron texture. Results The fractal dimensions of granule distribution and corpuscle superficial area are quite conformed with those of measurement. Conclusion The texture parameters of engine particle cluster can be obtained precisely by use of fractal theory.展开更多
The optimal filter 7r = {π,t ∈ [0, T]} of a stochastic signal is approximated by a sequence {Try} of measure-valued processes defined by branching particle systems in a random environment （given by the observation ...The optimal filter 7r = {π,t ∈ [0, T]} of a stochastic signal is approximated by a sequence {Try} of measure-valued processes defined by branching particle systems in a random environment （given by the observation process）. The location and weight of each particle are governed by stochastic differential equations driven by the observation process, which is common for all particles, as well as by an individual Brownian motion, which applies to this specific particle only. The branching mechanism of each particle depends on the observation process and the path of this particle itself during its short lifetime δ = n-2α, where n is the number of initial particles and ~ is a fixed parameter to be optimized. As n → ∞, we prove the convergence of π to πt uniformly for t ∈ [0, T]. Compared with the available results in the literature, the main contribution of this article is that the approximation is free of any stochastic integral which makes the numerical implementation readily available.展开更多
The problem of fragmentation(disintegration) process is theoretically studied with allowance for the initial particle volume. An exact analytical solution of integro-differential model governing the fragmentation phen...The problem of fragmentation(disintegration) process is theoretically studied with allowance for the initial particle volume. An exact analytical solution of integro-differential model governing the fragmentation phenomenon is obtained. The key role of a finite initial volume of particles leading to substantial changes of the particle-size distribution function is demonstrated.展开更多
文摘Aim The particle texture from diesel engine was imitated by use of computer. Methods The theory of fractal geometry and the diffusion limited aggregation model were used to simulate the micron texture. Results The fractal dimensions of granule distribution and corpuscle superficial area are quite conformed with those of measurement. Conclusion The texture parameters of engine particle cluster can be obtained precisely by use of fractal theory.
基金supported by US National Science Foundation(Grant No. DMS-0906907)
文摘The optimal filter 7r = {π,t ∈ [0, T]} of a stochastic signal is approximated by a sequence {Try} of measure-valued processes defined by branching particle systems in a random environment （given by the observation process）. The location and weight of each particle are governed by stochastic differential equations driven by the observation process, which is common for all particles, as well as by an individual Brownian motion, which applies to this specific particle only. The branching mechanism of each particle depends on the observation process and the path of this particle itself during its short lifetime δ = n-2α, where n is the number of initial particles and ~ is a fixed parameter to be optimized. As n → ∞, we prove the convergence of π to πt uniformly for t ∈ [0, T]. Compared with the available results in the literature, the main contribution of this article is that the approximation is free of any stochastic integral which makes the numerical implementation readily available.
基金Supported by the Russian Science Foundation under Grant No.16-11-10095
文摘The problem of fragmentation(disintegration) process is theoretically studied with allowance for the initial particle volume. An exact analytical solution of integro-differential model governing the fragmentation phenomenon is obtained. The key role of a finite initial volume of particles leading to substantial changes of the particle-size distribution function is demonstrated.
