• 한국전산유체공학회:학술대회논문집
• /
• 2008.08a
• /
• pp.33.1-33.1
• /
• 2008

• East Asian mathematical journal
• /
• v.1
• /
• pp.35-42
• /
• 1985

• Journal of the Korean Mathematical Society
• /
• v.32 no.2
• /
• pp.237-250
• /
• 1995

A hopf bifurcation of a free boundary (or an internal layer) occurs in solidification, chemical reactions and combustion. It is a well-known fact that a free boundary usually appear as sharp transitions with narrow width between two materials ([2]).

• Journal of the Korean Mathematical Society
• /
• v.54 no.6
• /
• pp.1853-1878
• /
• 2017

Let $\{U(t,s)\}_{t{\geq}s}$ be a periodic evolutionary process with period ${\tau}$ > 0 on a Banach space X. Also, let L be the generator of the evolution semigroup associated with $\{U(t,s)\}_{t{\geq}s}$ on the phase space $P_{\tau}(X)$ of all ${\tau}$-periodic continuous X-valued functions. Some kind of variation-of-constants formula for the solution u of the equation $({\alpha}I-L)^nu=f$ will be given together with the conditions on $f{\in}P_{\tau}(X)$ for the existence of coefficients in the formula involving the monodromy operator $U(0,-{\tau})$. Also, examples of ODEs and PDEs are presented as its application.

• Communications of the Korean Mathematical Society
• /
• v.9 no.3
• /
• pp.547-564
• /
• 1994

Let X be a real Banach space. We consider the existence of solutions of the abstract nonlinear functional evolution equation : $$ (E) \frac{du(t)}{dt} + A(t)u(t) + F(u)(t) \ni h(t), $$ $$ u(s) = x_o \in D(A(s)), 0 \leq s \leq t \leq T, $$ where u : $[s, T] \to x$ is an unknown function, ${A(t) : 0 \leq t \leq T}$ is a given family of nonlinear (possibly multivalued) operators in X, and $F : C([s, t];X) \to L^{\infty}([s, X];X)$ and $h : [s, T] \to X$ are given functions.

• Interaction and multiscale mechanics
• /
• v.4 no.4
• /
• pp.291-311
• /
• 2011

To simulate the self excited torsional vibrations of rotating drill strings (DSs) in vertical bore-holes, the nonlinear wave models of homogeneous and sectional torsional pendulums are formulated. The stated problem is shown to be of singularly perturbed type because the coefficient appearing before the second derivative of the constitutive nonlinear differential equation is small. The diapasons ${\omega}_b\leq{\omega}\leq{\omega}_l$ of angular velocity ${\omega}$ of the DS rotation are found, where the torsional auto-oscillations (of limit cycles) of the DS bit are generated. The variation of the limit cycle states, i.e. birth (${\omega}={\omega}_b$), evolution (${\omega}_b<{\omega}<{\omega}_l$) and loss (${\omega}={\omega}_l$), with the increase in angular velocity ${\omega}$ is analyzed. It is observed that firstly, at birth state of bifurcation of the limit cycle, the auto-oscillation generated proceeds in the regime of fast and slow motions (multiscale motion) with very small amplitude and it has a relaxation mode with nearly discontinuous angular velocities of elastic twisting. The vibration amplitude increases as ${\omega}$ increases, and then it decreases as ${\omega}$ approaches ${\omega}_l$. Sectional drill strings are also considered, and the conditions of the solution at the point of the upper and lower section joints are deduced. Besides, the peculiarities of the auto-oscillations of the sectional DSs are discussed.

• Korean Journal of Materials Research
• /
• v.8 no.4
• /
• pp.328-336
• /
• 1998

In metal-carbon system with no mutual solubility between matrix and alloying elements as solid or liquid phases, Cu-C-X nanocomposite metal powders were prepared by high energy ball milling for solid-lubricating bronze bearings. Elemental powder mixtures of Cu-lOwt.%C- 5wt. %Fe and Cu- lOwt. %C- 5wt. %Al were mechanically alloyed with an attritor in an argon atmosphere, and then microstructural evolution of the Cu-C-X nanocomposite metal powders was examined. It has been found that after 10 hours of MA, the approximately 10$\mu\textrm{m}$ sized Cu-C- X nanocomposite metal powders can be produced in both compositions. Morphological characteristics and microstructural evolution of the Cu-C-X powders have shown a similar MA procedure compared to those of metal-metal system. As a result of X - ray diffraction analysis, diffraction peaks of Cu and C were broaden and peak intensities were decreased as a function of MA time. Especially, the gradual disappearance of C peaks in the X- ray spectra is proved to be due to the lower atomic scattering factor of C. The calculated Cu crystallite sizes in Cu- C- X nanocomposite metal powders by Williamson- Hall equation were about lOnm size, on the other hand, the observed ones by TEM were in the range of 10 to 30nm.

• Computers and Concrete
• /
• v.7 no.2
• /
• pp.159-167
• /
• 2010

This paper demonstrates numerical techniques for complex large-scale modeling with microplane constitutive theories for reinforced high strength concrete, which for these applications, is defined to be around the 7000 psi (48 MPa) strength as frequently found in protective structural design. Applications involve highly impulsive loads, such as an explosive detonation or impact-penetration event. These capabilities were implemented into the authors' finite element code, ParaAble and the PRONTO 3D code from Sandia National Laboratories. All materials are explicitly modeled with eight-noded hexahedral elements. The concrete is modeled with a microplane constitutive theory, the reinforcing steel is modeled with the Johnson-Cook model, and the high explosive material is modeled with a JWL equation of state and a programmed burn model. Damage evolution, which can be used for erosion of elements and/or for post-analysis examination of damage, is extracted from the microplane predictions and computed by a modified Holmquist-Johnson-Cook approach that relates damage to levels of inelastic strain increment and pressure. Computation is performed with MPI on parallel processors. Several practical analyses demonstrate that large-scale analyses of this type can be reasonably run on large parallel computing systems.

• The Bulletin of The Korean Astronomical Society
• /
• v.45 no.1
• /
• pp.48.4-49
• /
• 2020

We reconstruct the expansion history of the universe using type Ia supernovae (SN Ia) in a manner independent of any cosmological model assumptions. To do so, we implement a nonparametric iterative smoothing method on the Joint Light-curve Analysis (JLA) data while exploring the SN Ia light-curve hyperparameter space by Markov Chain Monte Carlo (MCMC) sampling. We test to see how the posteriors of these hyperparameters depend on cosmology, whether using different dark energy models or reconstructions shift these posteriors. Our constraints on the SN Ia light-curve hyperparameters from our model-independent analysis are very consistent with the constraints from using different parameterizations of the equation of state of dark energy, namely the flat ΛCDM cosmology, the Chevallier-Polarski-Linder model, and the Phenomenologically Emergent Dark Energy (PEDE) model. This implies that the distance moduli constructed from the JLA data are mostly independent of the cosmological models. We also studied that the possibility the light-curve parameters evolve with redshift and our results show consistency with no evolution. The reconstructed expansion history of the universe and dark energy properties also seem to be in good agreement with the expectations of the standard ΛCDM model. However, our results also indicate that the data still allow for considerable flexibility in the expansion history of the universe. This work is published in ApJ.

• The Journal of the Petrological Society of Korea
• /
• v.8 no.2
• /
• pp.92-105
• /
• 1999

The Cretaceous Chaeyaksan basaltic rocks consist mainly of basaltic tuffs intercalating three layers of basalt. Stratigraphically, the rocks are located between the upper Songnaedong Formation and the lower Geoncheonri Formation and contain plagioclase, augite, hornblende, and a few olivine phenocrysts. Geochemically, they show calc-alkaline characteristics in some immobile element content, but show the alkaline suite feature in the mobile major element composition. The basalts are widely spilitized but some of them is altered to shoshonitic rocks with more calcic plagioclase, calcite, and chlorite, and adularia veinlets are common in the rocks. It is supposed that the post-eruption alteration of the rocks is done through alkali-replacement by hydrothermal solution or vapor rather than by low grade regional metamorphism. It is considered that A1 in hornblende will be available for estimating the pressure of the pre-eruption magma in the reservoir although the plagioclase of the rocks are highly albitized. The crystallization pressure was calculated as 5.7Kb by the equation of Johnson and Rutherford(l989) incorporating of the effect of overestimate of .41T in hornblende in the case of quartz-free rocks. Application of the estimated temperature, pressure and the constituent of phenocrysts of the rocks to the experimental P-T phase diagram for basalts established by Green(1982) indicates the crystallization course and succession of growth of the phenocrysts during of rising and cooling of the magma reservoir; augite + augite and olivine + augite, olivine, and hornblende -+ augite and hornblende+ augite, hornblende, and plagioclase. Such evolution course of the magma may include crystal fractionation by the phenocrysts crystallization and contamination by country rock in lower crust.