• Journal of the Korean Mathematical Society
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• v.39 no.4
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• pp.543-558
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• 2002

We investigate the fragmentation process developed by Kolmogorov and Filippov, which has been studied extensively by many physicists (independently for some time). One of the most interesting phenomena is the shattering (or disintegration of mass) transition which is considered a counterpart of the well known gelation phenomenon in the coagulation process. Though no masses are subtracted from the system during the break-up process, the total mass decreases in finite time. The occurrence of shattering transition is explained as due to the decomposition of the mass into an infinite number of particles of zero mass. It is known only that shattering phenomena occur for some special types of break-up rates. In this paper, by considering the n-particle system of stochastic fragmentation processes, we find general conditions of the rates which guarantee the occurrence of the shattering transition.

• Bulletin of the Korean Mathematical Society
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• v.42 no.4
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• pp.855-867
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• 2005

Shattering or disintegration of mass is a well known phenomenon in fragmentation processes first introduced by Kol­mogorov and Filippop and extensively studied by many physicists. Though the mass is conserved in each break-up, the total mass decreases in finite time. We investigate this phenomenon in the n particle system. In this system, shattering can be interpreted such that, in uniformly bounded time on n, order n of mass is located in order o(n) of clusters. It turns out that the tagged particle processes associated with the systems are useful tools to analyze the phenomenon. For the newly defined stochastic shattering based on the above ideas, we derive far sharper conditions of fragmentation kernels which guarantee the occurrence of such a phenomenon than our previous work [9].

• Journal of the Korea Institute of Military Science and Technology
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• v.15 no.5
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• pp.712-719
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• 2012

Penetrator with enhanced lateral effect(PELE) is a newconcept projectile, without dynamite and fuze. It consists of high-density jacket, closed at its rear end and filled with a low-density filling material. To study the explosion characteristics of PELE, by AUTODYN-3D code, the calculation models of projectile body and bullet target are established and the process of penetrating aluminum-2024 alloy target of PELE is simulated, and the scattering characteristics after penetrating aluminum-2024 alloy target of PELE are studied by different initial velocity. The explicit finite element analysis of PELE fragmentation was implemented with stochastic failure criterion in AUTODYN-3D code. As expansion of filling, the fragments were obtained velocities and dispersed laterally and further more enhancing the damage area largely. The number and shape of the PELE fragments were different depend on impact velocity and incidence angle of filling which fragment generated during penetration and lateral dispersion process.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.36 no.12
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• pp.1577-1583
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• 2012

Penetrator with enhanced lateral effect (PELE) is a novel projectile that does not require dynamite and a fuse. It comprises a high-density jacket that is closed at its rear end and filled with a low-density filling material. To study the explosion characteristics of PELE using AUTODYN-3D code, the calculation models of the projectile body and the bullet target were developed and the process of penetrating an aluminum-2024 alloy target using PELE was simulated. The scattering characteristics after PELE penetrated the aluminum-2024 alloy target were studied for different filling materials. The explicit finite element analysis of PELE fragmentation was implemented with the stochastic failure criterion in AUTODYN-3D code. As the filling expanded, the fragments gained velocity and dispersed laterally, increasing the damage area considerably. The number and shape of PELE fragments differed depending on the impact pressure of the filling that fragmented during the penetration and lateral dispersion processes.

• Journal of Ecology and Environment
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• v.45 no.3
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• pp.97-104
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• 2021

Background: Asarum sieboldii Miq., a species of forest understory vegetation, is an herbaceous perennial belonging to the family Aristolochiaceae. The metapopulation of A. sieboldii is distributed sparsely and has a short seed dispersal distance by ants as their seed distributor. It is known that many flowers of A. sieboldii depend on self-fertilization. Because these characteristics can affect negatively in genetic structure, investigating habitat structure and assessment of genetic structure is needed. A total of 27 individuals in a valley were sampled for measuring genetic diversity, genetic distance, and genetic differentiation by RAPDPCR. Results: The habitat areas of A. sieboldii metapopulation were relatively small (3.78~33.60 m²) and population density was very low (five to seven individuals in 20×20 m quadrat). The habitat of A. sieboldii was a very shady (relative light intensity = 0.9%) and mature forest with a high evenness value (J = 0.81~0.99) and a low dominance value (D = 0.19~0.28). The total genetic diversity of A. sieboldii was quite high (h = 0.338, I = 0.506). A total of 33 band loci were observed in five selected primers, and 31 band loci (94%) were polymorphic. However, genetic differentiation along the valley was highly progressed (G_st = 0.548, N_m = 0.412). The average genetic distance between subpopulations was 0.387. The results of AMOVA showed 52.77% of variance occurs among populations, which is evidence of population structuring. Conclusions: It is expected that a small-scale founder effect had occurred, an individual spread far from the original subpopulation formed a new subpopulation. However, geographical distance between individuals would have been far and genetic flow occurred only within each subpopulation because of the low density of population. This made significant genetic distance between the original and new population by distance. Although genetic diversity of A. sieboldii metapopulation is not as low as concerned, the subpopulation of A. sieboldii can disappear by stochastic events due to small subpopulation size and low density of population. To prevent genetic isolation and to enhance the stable population size, conservative efforts such as increasing the size of each subpopulation or the connection between subpopulations are needed.