Grain size distribution in two dimensions in the long time limit

Pande, C. S.; Cooper, K. P.; McFadden, Geoffrey B.

doi:10.1016/j.actamat.2008.07.008

Cited by 5 publications

(7 citation statements)

References 32 publications

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“…Pande [5] and Pande and coworkers [5][6][7][8][9]11,12] have attempted to develop a more rigorous theory of isothermal grain growth capable of predicting all of the major attributes of grain growth with minimal assumptions by treating it as a stochastic process. Mathematically, a stochastic process in its simplest form is described by a function of two variables, one of which is time, and involves both a deterministic term and a random term.…”

Section: Stochastic Effects In Grain Growthmentioning

confidence: 99%

“…Here we describe in more detail the analysis of the differential equation (11). The point x = 0 is a regular singular point for this equation and there is a regular solution having the expansion:…”

Section: Appendix Amentioning

confidence: 99%

“…An examination of the first three moments of the differential equation (11) gives an analytical relation between A, e and a that must hold in order for the solution to have a finite third moment:…”

Section: Numerical Solutionmentioning

confidence: 99%

“…[6][7][8][9]. (A similar treatment for the 2-D case has been published recently [10,11].) We start by determining the form of the continuity equation for the grain size distribution.…”

Section: Introductionmentioning

confidence: 98%

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Self-similar grain size distribution in three dimensions: A stochastic treatment

Pande

McFadden

2010

Acta Materialia

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Section: Stochastic Effects In Grain Growthmentioning

confidence: 99%

Section: Appendix Amentioning

confidence: 99%

Section: Numerical Solutionmentioning

confidence: 99%

“…[6][7][8][9]. (A similar treatment for the 2-D case has been published recently [10,11].) We start by determining the form of the continuity equation for the grain size distribution.…”

Section: Introductionmentioning

confidence: 98%

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Self-similar grain size distribution in three dimensions: A stochastic treatment

Pande

McFadden

2010

Acta Materialia

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“…C.S. Pande gets the grain-size distribution by both obtaining a numerical solution of Fokker-Planck equation in a stochastic model and performing computer simulations [3]. X.J.…”

Section: Introductionmentioning

confidence: 99%

Quantitative Measuring Analysis Method and Mechanism of Wear Particle Settlement

Zhang

2021

E3S Web Conf.

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The size and distribution of wear particle in lubricating oil, as important numerical information available in ferrography, is one of the key indexes in wear diagnosis. In this paper, a new method for measuring the size and distribution of abrasive particles is proposed. First, all the abrasive fluid is left standing until all the abrasive particles are precipitated to the bottom. Then, the measuring container is inverted and the whole precipitation process of abrasive particles is recorded by magnetic induction instrument. And according to the precipitation analysis of the wear particle, the following results were obtained:1) At the initial stage of the particle settlement, the gravity, the buoyancy and the drag force of the oil achieve balance quickly, the time and distance of the wear particle moving at a constant velocity can be neglected. 2) The settling velocity is related to the diameter and specific gravity of the wear particle as well as the specific gravity and viscosity of the oil, the distribution of the wear particle is proportional to the square of the diameter of the particle, using the magnetic induction technology, the distribution of particle can be measured by settling time for different sizes of wear particles. 3) Measure the wear particle oil directly, there are different sizes of particles settlement in the bottom at the same time, which causes the difficulty in identifying the size of the particle settlement. The particle should be settled first, and then inverted, settling the particle in accordance with the order from large to small, which facilitates the measurement of different sizes of the particles, different times correspond to different sizes of the particles. 4) The bigger the particle is, the more accurate the measurement and counting is, the smaller the particle is, the bigger the error is.

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The role of grain-environment heterogeneity in normal grain growth: A stochastic approach

et al. 2021

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Grain size distribution in two dimensions in the long time limit

Cited by 5 publications

References 32 publications

Self-similar grain size distribution in three dimensions: A stochastic treatment

Self-similar grain size distribution in three dimensions: A stochastic treatment

Quantitative Measuring Analysis Method and Mechanism of Wear Particle Settlement

The role of grain-environment heterogeneity in normal grain growth: A stochastic approach

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