• Journal of the Korean Society of Combustion
• /
• v.9 no.4
• /
• pp.9-21
• /
• 2004

Stability of laminar premixed planar flames inclined in the gravitational field is asymptotically examined. The flame structure is resolved by a large activation energy asymptotics and a long wave approximation. The coupling between hydrodynamics and diffusion processes is included and near-unity Lewis number is assumed. The results show that as the flame is more inclined from the horizontal plane it becomes more unstable due to not only the decrease of stabilizing effect of gravity but also the increase of destabilizing effect of rotational flow. The obtained dispersion relation involves the Prandtl number and shows the destabilizing effect of viscosity. The analysis predicts that the phase velocity of unstable flame wave depends on not only the flame angle but also the Lewis number. For relatively short wave disturbances, still much larger than flame thickness, the most unstable wavelength is nearly independent on the flame angle and the flame can be stabilized by gravity and diffusion mechanism.

• Journal of the Korean Institute of Telematics and Electronics
• /
• v.26 no.10
• /
• pp.1561-1570
• /
• 1989

In this paper, we propose an image coding scheme which combines the Laplacian pyramid structure and a hierarchical finite state classified vector quantizer in the DCT domain, namely FSDCT-CTQ. First, an optimal bit allocation problem for fixed rates DCT-CVQ on the Laplacian pyramid structure is described. In an asymptotic case, with an optimal bit allocation, a coding gain over scalar quantization of each Laplacian plane is derived. Second, it is experimentallhy shown that the Laplacian pyramid structure provides a considerable codng gain in the sense of total MMSE (minimum mean squared error). Finally, we propose an FS-DCT-CVQ which exploits the hierarchicla correlation between the Laplacian planes. Simulation results on real images show that the proposed coding scheme can reconstruct an image with 30.33 dB at 0.192 bpp, 32.45 dB at 0.385 bpp, respectively.

• Bulletin of the Korean Mathematical Society
• /
• v.47 no.1
• /
• pp.29-37
• /
• 2010

We establish the existence of weak solutions in an infinite subsonic channel in the self-similar plane to the two-dimensional Burgers system. We consider a boundary value problem in a fixed domain such that a part of the domain is degenerate, and the system becomes a second order elliptic equation in the channel. The problem is motivated by the study of the weak shock reflection problem and 2-D Riemann problems. The two-dimensional Burgers system is obtained through an asymptotic reduction of the 2-D full Euler equations to study weak shock reflection by a ramp.

• ETRI Journal
• /
• v.35 no.2
• /
• pp.218-225
• /
• 2013

The pull-out frequency of a second-order phase lock loop (PLL) is an important parameter that quantifies the loop's ability to stay frequency locked under abrupt changes in the reference input frequency. In most cases, this must be determined numerically or approximated using asymptotic techniques, both of which require special knowledge, skills, and tools. An approximating formula is derived analytically for computing the pull-out frequency for a second-order Type II PLL that employs a sinusoidal characteristic phase detector. The pull-out frequency of such PLLs can be easily approximated to satisfactory accuracy with this formula using a modern scientific calculator.

• Proceedings of the Korea Institute of Convergence Signal Processing
• /
• 2003.06a
• /
• pp.153-156
• /
• 2003

This short paper suggests a control strategy using a stepwise fuzzy moving sliding surface. The moving surface is a Sugeno-type fuzzy system that has the angle of state error vector and the distance from the origin in the phase plane as inputs and a first-order linear differential equation as an output. The surface initially passes arbitrary initial states and subsequently moves towards a predetermined surface via rotating or shifting. the proposed method reduces the reaching and tracking time and improves robustness. The asymptotic stability of the fuzzy sliding surface is proved. The validity of the proposed control scheme is shown in computer simulation for a second-order nonlinear system.

• Transactions of the Korean Society of Mechanical Engineers
• /
• v.18 no.1
• /
• pp.150-155
• /
• 1994

An Approximate solution for plane two-dimensional incompressible laminar jet issuing from a finite opening with arbitrary initial profile into the same ambient fluid is proposed. For an arbitrary initial velocity profile, the problem is generated from the well known similarity solution for the jet of infinitesimal opening and provides good approximations in the region where the similarity solution cannot be used as an approximation. The asymptotic behavior of this solution is investigated and it is shown that, as goes downstream, the present solution approachs the similarity solution.

• Journal of the Korean Mathematical Society
• /
• v.56 no.2
• /
• pp.523-537
• /
• 2019

We estimate the essential norms of Volterra-type integral operators $V_g$ and $I_g$, and multiplication operators $M_g$ with holomorphic symbols g on a large class of generalized Fock spaces on the complex plane ${\mathbb{C}}$. The weights defining these spaces are radial and subjected to a mild smoothness conditions. In addition, we assume that the weights decay faster than the classical Gaussian weight. Our main result estimates the essential norms of $V_g$ in terms of an asymptotic upper bound of a quantity involving the inducing symbol g and the weight function, while the essential norms of $M_g$ and $I_g$ are shown to be comparable to their operator norms. As a means to prove our main results, we first characterized the compact composition operators acting on the spaces which is interest of its own.

• Journal of The Korean Astronomical Society
• /
• v.36 no.1
• /
• pp.1-12
• /
• 2003

Nonthermal particles can be produced due to incomplete thermalization at collisionless shocks and further accelerated to very high energies via diffusive shock acceleration. In a previous study we explored the cosmic ray (CR) acceleration at cosmic shocks through numerical simulations of CR modified, quasi-parallel shocks in 1D plane-parallel geometry with the physical parameters relevant for the shocks emerging in the large scale structure formation of the universe (Kang & Jones 2002). Specifically we considered pancake shocks driven by accretion flows with $U_o = 1500 km\;s^{-l}$ and the preshock gas temperature of $T_o = 10^4 - 10^8K$. In order to consider the CR acceleration at shocks with a broader range of physical properties, in this contribution we present additional simulations with accretion flows with $U_o = 75 - 1500 km\;s^{-l}$ and $T_o = 10^4K$. We also compare the new simulation results with those reported in the previous study. For a given Mach number, shocks with higher speeds accelerate CRs faster with a greater number of particles, since the acceleration time scale is $t_{acc}\;{\propto}\;U_o^{-2}$. However, two shocks with a same Mach number but with different shock speeds evolve qualitatively similarly when the results are presented in terms of diffusion length and time scales. Therefore, the time asymptotic value for the fraction of shock kinetic energy transferred to CRs is mainly controlled by shock Mach number rather than shock speed. Although the CR acceleration efficiency depends weakly on a well-constrained injection parameter, $\epsilon$, and on shock speed for low shock Mach numbers, the dependence disappears for high shock Mach numbers. We present the 'CR energy ratio', ${\phi}(M_s)$, for a wide range of shock parameters and for $\epsilon$ = 0.2 - 0.3 at terminal time of our simulations. We suggest that these values can be considered as time-asymptotic values for the CR acceleration efficiency, since the time-dependent evolution of CR modified shocks has become approximately self-similar before the terminal time.

• Journal of the Korean Institute of Telematics and Electronics
• /
• v.18 no.5
• /
• pp.35-45
• /
• 1981

An asymptotic solution of electromagnetic waves scattered by a right-angled dielectric wedge for plane wave incidence is obtained. Scattered fields are constructed by waves reflected and refracted from dielectric interfaces (geometric-optical fields) and a cylindrical wave diffracted from the edge. The edge diffracted field is obtained by adding a correction to the edge diffraction of physical optics approximation, where the correction field is calculated by solving a dual series equation amenable to simple numerical calculation. Validity of this result is assured by two limits of relative dielectric constant $\varepsilon$ of the wedge. The total asymptotic field calculated results in a Rawlins' Neumann series solution for small $\varepsilon$, and the edge diffraction pattern is shown to approach that of a perfectly conducting wedge for large $\varepsilon$. Calculated field patterns are presented and the accuracy of physical optics approximation is discussed.

• Structural Engineering and Mechanics
• /
• v.72 no.6
• /
• pp.713-722
• /
• 2019

Micromechanics is a technique for the analysis of composites or heterogeneous materials which focuses on the components of the intended structure. Each one of the components can exhibit isotropic behavior, but the microstructure characteristics of the heterogeneous material result in the anisotropic behavior of the structure. In this research, the general mechanical properties of a 3D anisotropic and heterogeneous Representative Volume Element (RVE), have been determined by applying periodic boundary conditions (PBCs), using the Asymptotic Homogenization Theory (AHT) and strain energy. In order to use the homogenization theory and apply the periodic boundary conditions, the ABAQUS scripting interface (ASI) has been used along with the Python programming language. The results have been compared with those of the Homogeneous Boundary Conditions method, which leads to an overestimation of the effective mechanical properties. According to the results, applying homogenous boundary conditions results in a 33% and 13% increase in the shear moduli G₂₃ and G₁₂, respectively. In polymeric composites, the fibers have linear and brittle behavior, while the resin exhibits a non-linear behavior. Therefore, the nonlinear effects of resin on the mechanical properties of the composite material is studied using a user-defined subroutine in Fortran (USDFLD). The non-linear shear stress-strain behavior of unidirectional composite laminates has been obtained. Results indicate that at arbitrary constant stress as 80 MPa in-plane shear modulus, G₁₂, experienced a 47%, 41% and 31% reduction at the fiber volume fraction of 30%, 50% and 70%, compared to the linear assumption. The results of this study are in good agreement with the analytical and experimental results available in the literature.