• Title/Summary/Keyword: Length and frequency dependence

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A Numerical Study on the Anisotropic Thermal Conduction by Phonon Mean Free Path Spectrum of Silicon in Silicon-on-Insulator Transistor (실리콘 박막 트랜지스터 내 포논 평균자유행로 스펙트럼 비등방성 열전도 특성에 대한 수치적 연구)

  • Kang, Hyung-sun;Koh, Young Ha;Jin, Jae Sik
    • Transactions of the Korean Society of Mechanical Engineers B
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    • v.40 no.2
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    • pp.111-117
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    • 2016
  • The primary concern of this research is to examine the phonon mean free path (MFP) spectrum contribution to heat conduction. The size effect of materials is determined by phonon MFP, and the size effect appears when the phonon MFP is similar to or less than the characteristic length of materials. Therefore, knowledge of the phonon MFP is essential to increase or decrease the heat conduction of a material for engineering applications, such as micro/nanosystems. In this study, frequency dependence of the phonon transport is considered using the Boltzmann transport equation based on a full phonon dispersion model. Additionally, the phonon MFP spectrums of in-plane and out-of-plane heat transport are investigated by varying the film thickness of the silicon layer from 41 nm to 177 nm. This will increase the understanding of anisotropic heat conduction in a SOI (Silicon-on-Insulator) transistor.

Growth and Survival of Laminaria japonica Areschoug at different densities (밀도에 따른 다시마(Laminaria japonica Areschoug)의 생장과 생존)

  • KANG Rae-Seon;KOH Chul-Hwan
    • Korean Journal of Fisheries and Aquatic Sciences
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    • v.32 no.4
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    • pp.444-451
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    • 1999
  • The effect of individual density on the growth and survival of Laminaria japonica was experimentally evaluated. Four density treatments of young sporophytes (0.63 cm In maximum length) grown in the laboratory were transplanted to the southeastern coast of Korea and their survivorship and growth rate were measured twice a month from January to July, 1996. Plants showed higher survivorship at low density. Final densities at three lowest densities were similar, ranging from 34 to 38 inds${\cdot}100 cm^{-2}$. Planis at the highest density, however, suffered greater decline than at lower densities, and only 21 plants remained at the end of this study. Mean frond size (length and width) fluctuated throughout the study period at four densities. During the first two mouths after outplanting, mean frond size was negatively correlated with initial density, However, the size was density independent after three months. As stand density increased, size-frequency distribution through time tended to be more positively skewed. The 10 largest plants grew faster in frond size and attained larger size in the lower density. There was a positive relationship between plant size and relative growth rate (or survival). The slope of yield-density (Y-D) relationships at four densities ranged from -0.060 to -0.137. The study suggests that density can strongly affect the survival and growth of this alga. The density-dependent survival and growth patterns, however, were not strictly consistent with those of terrestrial plants.

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Evaluation for Rock Cleavage Using Distribution of Microcrack Spacings (I) (미세균열의 간격 분포를 이용한 결의 평가(I))

  • Park, Deok-Won
    • The Journal of the Petrological Society of Korea
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    • v.25 no.1
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    • pp.13-27
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    • 2016
  • The characteristics of the rock cleavage inherent in Jurassic granite from Geochang were analysed. The phases of distribution of microcrack spacings were derived from the enlarged photomicrographs(${\times}6.7$) of the thin section. The evaluation for the six directions of rock cleavages was performed using nine parameters such as (1) frequency of microcrack spacing(N), (2) frequency ratio(${\leq}1mm$ and 4 mm >) to total spacing frequency(N:191), (3) spacing ratio(${\leq}1mm$) to total spacing(118.49 mm), (4) mean spacing($S_{mean}$), (5) difference value($S_{mean}-S_{median}$) between mean spacing and median spacing($S_{median}$), (6) density of spacing, (7) median spacing, (8) reduction ratio of spacing frequency to length frequency and (9) magnitude of exponent(${\lambda}$ and b) related to the distribution type of diagram. Especially the close dependence between the above spacing parameters and the parameters from the spacing-cumulative frequency diagrams was derived. The results of correlation analysis between the values of parameters for three rock cleavages and those for three planes are as follows. The values of (I) parameters(1, 2 and 3), (II) parameters(4, 5 and 6), (III) parameter(7), (IV) parameter(8) and (V) parameter(9) show the various orders of H(hardway, H1+H2) < G(grain, G1+G2) < R(rift, R1+R2), R < G < H, R < H < G, G < H < R and H < G < R, respectively. On the contrary, the values of the above four groups(I~IV) of parameters for three planes show reverse orders. This type of correlation analysis is useful for discriminating three quarrying planes. Six spacing-cumulative frequency diagrams were arranged in increasing order on the value of main parameter($S_{mean}-S_{median}$). These diagrams show an order of R2 < R1 < G2 < G1 < H2 < H1 from the related chart. In other words, the above six diagrams can be summarized in order of rift(R1+R2) < grain(G1+G2) < hardway(H1+H2). These results indicate a relative magnitude of rock cleavage related to microcrack spacing. Especially, the above main parameter could provide advanced information for prediction the order of arrangement among the diagrams.

Evaluation for Rock Cleavage Using Distributional Characteristics of Microcracks and Brazilian Tensile Strengths (미세균열과 압열인장강도의 분포 특성을 이용한 결의 평가)

  • Park, Deok-Won
    • Korean Journal of Mineralogy and Petrology
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    • v.33 no.2
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    • pp.99-114
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    • 2020
  • The characteristics of the Brazilian tensile strengths(σt) parallel to the rock cleavages in Jurassic granite from Geochang were analysed. The evaluation for the six directions of rock cleavages was performed using the parameter values on microcrack length and the above strength. The strength values of the five test specimens belonging to each direction were classified into five groups. The strength values of these five groups increase in order of group A < B < C < D < E. The close dependence between the above microcrack and strength was derived. The analysis results of this study are summarized as follows. First, the chart showing the variation and characteristics of strength among the three rock cleavages were made. In the above chart, the strength values of six directions belonging to each group were arranged in order of rift(R1 and R2), grain(G1 and G2) and hardway(H1 and H2). The strength distribution lines of the five groups concentrate in the direction of R1. And the widths among the above five lines indicating strength difference(Δσt) are the most narrowest in R1 direction. From the related chart, the variation characteristics among the two directions forming each rock cleavage were derived. G2(2)-test specimen shows higher value and lower value of the difference in strength compared to the case of G1(1)-test specimen. These kinds of phenomena are the same as the case between the test specimen H2(2) and H1(1). The strength characteristics of the above test specimens (2) suggest lower microcrack density value and higher degree of uniformity in the distribution of microcracks arrayed parallel to the loading direction compared to those of test specimens (1). The six strength values belonging to each group were arranged in increasing order in the above chart. The strength values of the test specimens belonging to both group D and E appear in order of R1 < R2 < G1 < H1 < G2 < H2. Therefore, the strength values of group D and E can be indicator values for evaluating the six directions of rock cleavages. Second, the correlation chart between slope angle(θ) and strength difference(Δσt) were made. The values of the above two parameters were obtained from the five strength distribution lines connecting between the two directions. From the chart related to rift plane(G1-H1, R'), grain plane(R1-H2, G') and hardway plane(R2-G2, H'), the slope values of linear functions increase in order of R'(0.391) < G'(0.470) < H'(0.485). Among three planes, the charts related to hardway plane show the highest distribution density among the five groups. From the related chart for rift(R1-R2, R), grain(G1-G2, G) and hardway(H1-H2, H), the slope values of linear functions increase in order of rift(0.407) < hardway(0.453) < grain(0.460). Among three rock cleavages, the charts related to rift show the highest frequency of groups belonging to the lower region. Taken together, the width of distribution of the slope angle among the three planes and three rock cleavages increase in order of H' < G < R' < R < G' < H. Third, the correlation analysis among the parameters related to microcrack length and the tensile strengths was performed. These parameters may include frequency(N), total length(Lt), mean length(Lm), median length(Lmed) and density(ρ). The correlation charts among individual parameters on the above microcrack(X) and corresponding five levels of tensile strengths for the five groups(Y) were made. From the five kinds of correlation charts, the values of correlation coefficients(R2) increase along with the five levels of strengths. The mean values of the five correlation coefficients from each chart increase in order of 0.22(N) < 0.34(Lt) < 0.38(ρ) < 0.57(Lmed) < 0.58(Lm). Fourth, the correlation chart among the corresponding maximum strength for group E(X) and the above five parameters(Y) were made. From the related chart, the values of correlation coefficient increase in order of 0.61(N) < 0.81(Lt) < 0.87(ρ) < 0.93(Lm) < 0.96(Lmed). The two parameters that have the highest correlations are median length with maximum strength. Through the above correlation analysis between microcrack and strength, the credibility for the results from this study can be enhanced.

Evaluation for Rock Cleavage Using Distribution of Microcrack Spacings (III) (미세균열의 간격 분포를 이용한 결의 평가 (III))

  • Park, Deok-Won
    • The Journal of the Petrological Society of Korea
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    • v.25 no.4
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    • pp.311-324
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    • 2016
  • The characteristics of the rock cleavage in Jurassic granite from Geochang were analysed. The evaluation for three quarrying planes and three rock cleavages was performed using the parameters such as (1) reduction ratio between the value of spacing and the value of length, (2) microcrack spacing frequency(N), (3) total spacing($1mm{\geq}$), (4) exponential constant(a), (5) magnitude of exponent(${\lambda}$), (6) mean spacing($S_{mean}$), (7) difference value($S_{mean}-S_{median}$) between mean spacing and median spacing($S_{median}$) and (8) density of spacing. Especially the close dependence between the above spacing parameters and the parameters from the spacing-cumulative frequency diagrams was derived. The discrimination factors representing three quarrying planes and three rock cleavages were acquired through these mutual contrast. The analysis results of the research are summarized as follows. First, the reduction ratios of frequency(N), mean value, median value, the above difference value($S_{mean}-S_{median}$) and density for three rock cleavages are in orders of G(grain, (G1 + G2)/2) < H(hardway, (H1 + H2)/2) < R(rift, (R1 + R2)/2), H < G $\ll$ R, H < G $\ll$ R, H < G < R and H < G $\ll$ R. The values of the above five parameters for three planes show the various orders of R'(rift plane) $\ll$ H'(hardway plane) < G'(grain plane), R' $\ll$ G' < H', R' < H' < G', R' < G' < H' and R' $\ll$ H' < G', respectively. Second, the values of (I) parameters(2, 3, 4 and 5) and (II) parameters(6, 7 and 8) are in orders of (I) H < G < R and (II) R < G < H. On the contrary, the values of the above two groups(I~II) of parameters for three planes show reverse orders. Third, to review the overall characteristics of the arrangement among the six diagrams, these diagrams show an order of R2 < R1 < G2 < G1 < H2 < H1 from the related chart. In other words, above six diagrams can be summarized in order of rift(R1 + R2) < grain(G1 + G2) < hardway(H1 + H2). These results indicate a relative magnitude of rock cleavage related to microcrack spacing. Especially, two parameters for each diagram, the above difference value($S_{mean}-S_{median}$) and mean spacing, could provide advanced information for prediction the order of arrangement among the diagrams. Finally, the general chart for three planes and three rock cleavages were made. From the related chart, three exponential straight lines for three rock cleavages show an order of R(R1 + R2) < G(G1 + G2) < H(H1 + H2). On the contrary, three lines for three planes show an order of H'(R2 + G2) < G'(R1 + H2) < R'(G1 + H1). Consequently, correlation of the mutually reverse order between three planes and three rock cleavages can be drawn from the related chart.