• Journal of the Korean Mathematical Society
• /
• v.38 no.1
• /
• pp.25-35
• /
• 2001

In this paper we consider an age dependent branching process whose particles move according to a Markov process with continuous state space. The Markov process is assumed to the stationary with independent increments and positive recurrent. We find some sufficient conditions for he Markov motion process such that the empirical distribution of the positions converges to the limiting distribution of the motion process.

• Journal of applied mathematics & informatics
• /
• v.14 no.1_2
• /
• pp.157-172
• /
• 2004

An age-dependent branching process where disasters occur as a renewal process leading to annihilation or survival of all the cells, is considered. For such a process, the total mean sojourn time of all the cells in the system is analysed using the regeneration point technique. The mean number of cells which die in time t and its asymptotic behaviour are discussed. When the disasters arrival as a Poisson process and the lifetime of the cells follows exponential distribution, elegant inter- relationships are found among the means of (i) the total number of cells which die in time t (ii) the total sojourn time of all cells in the system upto time t and (iii) the number of living cells at time t. Some of the existing results are deduced as special cases for related processes.

• Journal of the Korean Mathematical Society
• /
• v.36 no.6
• /
• pp.1115-1132
• /
• 1999

We consider a supercritical multitype age dependent branching process. We define a stochastic process Zf(t) which is a functional of the empirical age distribution. When the limit of the expectation of this functional vanishes we4 find some sufficient conditions for the asymptotic normality of the mean of f with respect to the empirical age distribution at time t.

• Journal of the Korean Mathematical Society
• /
• v.36 no.1
• /
• pp.139-157
• /
• 1999

Consider a supercritical Bellman-Harris process evolving from one particle. We superimpose on this process the additional structure of movement. A particle whose parent was at x at its time of birth moves until it dies according to a given Markov process X starting at x. The motions of different particles are assumed independent. In this paper we show that when the movement process X is standard Brownian the proportion of particles with position $\leq${{{{ SQRT { t} }}}} b and age$\leq$a tends with probability 1 to A(a)$\Phi$(b) where A(.) and $\Phi$(.) are the stable age distribution and standard normal distribution, respectively. We also extend this result to the case when the movement process is a Levy process.

• Communications for Statistical Applications and Methods
• /
• v.18 no.6
• /
• pp.809-816
• /
• 2011

A tree-indexed autoregressive(AR) process is a time series defined on a tree which is generated by a branching process and/or a deterministic splitting mechanism. This short article is concerned with conditional heteroscedastic structure of the tree-indexed AR models. It has been usual in the literature to analyze conditional mean structure (rather than conditional variance) of tree-indexed AR models. This article pursues to identify quadratic conditional heteroscedasticity inherent in various tree-indexed AR models in a unified way, and thus providing some perspectives to the future works in this area. The identical conditional variance of sisters sharing the same mother will be referred to as the branching heteroscedasticity(BH, for short). A quasilikelihood but preliminary estimation of the quadratic BH is discussed and relevant limit distributions are derived.

• Journal of the Computational Structural Engineering Institute of Korea
• /
• v.24 no.6
• /
• pp.637-643
• /
• 2011

The bond-based peridynamic model is able to capture many of the essential characteristics of dynamic brittle fracture observed in experiments: crack branching, crack-path instability, asymmetries of crack paths, successive branching, secondary cracking at right angles from existing crack surfaces, etc. In this paper we investigate the influence of the stress waves on the crack branching angle and the velocity profile. We observe that crack branching in peridynamics evolves as the phenomenology proposed by the experimental evidence: when a crack reaches a critical stage(macroscopically identified by its stress intensity factor) it splits into two or more branches, each propagating with the same speed as the parent crack, but with a much reduced process zone.

• International Journal of CAD/CAM
• /
• v.12 no.1
• /
• pp.29-37
• /
• 2012

A new algorithm has been developed to construct surface from the contours having branches and the final smooth surface is obtained by the reversible Catmull-Clark subdivision. In branching, a particular layer has more than one contour that correspond with at least one contour at the adjacent layer. In the next step, three-dimensional composite curve is constructed from contours of a layer having correspondence with at least one contour at the adjacent layer by inserting points between them and joining the contours. The points are inserted in such a way that the geometric center of the contours should merge at the center of the contours at the adjacent layer. This process is repeated for all layers having branching problems. Polyhedra are constructed in the next step with the help of composite curves and the contours at adjacent layer. The required smooth surface is obtained in the proposed work by providing the level of smoothness.

• Journal of the Korean Data and Information Science Society
• /
• v.28 no.1
• /
• pp.153-161
• /
• 2017

Branching processes which is used for epidemic dispersion as stochastic process model have advantages to estimate parameters by real data. We have to estimate both mean and dispersion parameter in order to use the negative binomial distribution as an offspring distribution on branching processes. In existing studies on biology and epidemiology, it is estimated using maximum-likelihood methods. However, for most of epidemic data, it is hard to get the best precision of maximum-likelihood estimator. We suggest a Bayesian inference that have good properties of statistics for small-sample. After estimating dispersion parameter we modelled the posterior distribution for 2015 Korea MERS cases. As the result, we found that the estimated dispersion parameter is relatively stable no matter how we assume prior distribution. We also computed extinction probabilities on branching processes using estimated dispersion parameters.

• Transactions of the Korean Society of Mechanical Engineers A
• /
• v.39 no.11
• /
• pp.1137-1143
• /
• 2015

The stage II fretting fatigue crack growth and branching, i.e., the process of fretting fatigue crack growth starting in an inclined direction and then changing to the normal direction, is analyzed using the finite element method. The fretting fatigue experiment data of A7075-T6 are used in the analysis. The applicability of maximum tangential stress intensity factor, maximum tangential stress intensity factor range, and maximum crack growth rate as the crack growth direction criteria is examined. It is revealed that the stage II crack growth before and after the branching cannot be simulated with a single criterion, but can be done when different criteria are applied to the two stages of crack growth. Moreover, a method to determine the crack length at which the branching occurs is proposed.

• Structural Engineering and Mechanics
• /
• v.71 no.1
• /
• pp.65-75
• /
• 2019

In this article, the dynamic fracture instability characteristics, including dynamic crack propagation and crack branching, in PMMA brittle solids under dynamic loading are investigated using the discrete element method (DEM) simulations. The microscopic parameters in DEM are first calibrated using the comparison with the previous experimental results not only in the field of qualitative analysis, but also in the field of quantitative analysis. The calibrating process illustrates that the selected microscopic parameters in DEM are suitable to effectively and accurately simulate dynamic fracture process in PMMA brittle solids subjected to dynamic loads. The typical dynamic fracture behaviors of solids under dynamic loading are then reproduced by DEM. Compared with the previous experimental and numerical results, the present numerical results are in good agreement with the existing ones not only in the field of qualitative analysis, but also in the field of quantitative analysis. Furthermore, effects of dynamic loading magnitude, offset distance of the initial crack and initial crack length on dynamic fracture behaviors are numerically discussed.