• KSCE Journal of Civil and Environmental Engineering Research
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• v.28 no.1B
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• pp.111-114
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• 2008

Explicit solutions of the wave dispersion equation are developed using the recursive relation in terms of the relative water depth. We use the solutions of Eckart (1951), Hunt (1979), and the deep-water and shallow-water solutions for initial values of the solution. All the recursive solutions converge to the exact one except that with the initial value of deep-water solution. The solution with the initial value by Hunt converged much faster than the others. The recursive solutions may be obtained quickly and simply by a hand calculator. For the transformation of linear water waves in whole water depth, the use of the recursive solutions will yield more accurate analytical solutions than use of previously developed explicit solutions.

• Bulletin of the Korean Mathematical Society
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• v.54 no.4
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• pp.1195-1219
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• 2017

In this paper, the limit behavior of solution for the $Schr{\ddot{o}}dinger$ equation with random dispersion and time-dependent nonlinear loss/gain: $idu+{\frac{1}{{\varepsilon}}}m({\frac{t}{{\varepsilon}^2}}){\partial}_{xx}udt+{\mid}u{\mid}^{2{\sigma}}udt+i{\varepsilon}a(t){\mid}u{\mid}^{2{\sigma}_0}udt=0$ is studied. Combining stochastic Strichartz-type estimates with $L^2$ norm estimates, we first derive the global existence for $L^2$ and $H^1$ solution of the stochastic $Schr{\ddot{o}}dinger$ equation with white noise dispersion and time-dependent loss/gain: $idu+{\Delta}u{\circ}d{\beta}+{\mid}u{\mid}^{2{\sigma}}udt+ia(t){\mid}u{\mid}^{2{\sigma}_0}udt=0$. Secondly, we prove rigorously the global diffusion-approximation limit of the solution for the former as ${\varepsilon}{\rightarrow}0$ in one-dimensional $L^2$ subcritical and critical cases.

• Journal of Powder Materials
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• v.24 no.2
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• pp.102-107
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• 2017

Porous polytetrafluoroethylene (PTFE) thin films are fabricated by spin-coating using a dispersion solution containing PTFE powders, and their crystalline properties are investigated after thermal annealing at various temperatures ranging from 300 to $500^{\circ}C$. Before thermal annealing, the film is densely packed and consists of many granular particles 200-300 nm in diameter. However, after thermal annealing, the film contains many voids and fibrous grains on the surface. In addition, the film thickness decreases after thermal annealing owing to evaporation of the surfactant, binder, and solvent composing the PTFE dispersion solution. The film thickness is systematically controlled from 2 to $6.5{\mu}m$ by decreasing the spin speed from 1,500 to 500 rpm. A triboelectric nanogenerator is fabricated by spin-coating PTFE thin films onto polished Cu foils, where they act as an active layer to convert mechanical energy to electrical energy. A triboelectric nanogenerator consisting of a PTFE layer and Al metal foil pair shows typical output characteristics, exhibiting positive and negative peaks during applied strain and relief cycles due to charging and discharging of electrical charge carriers. Further, the voltage and current outputs increase with increasing strain cycle owing to accumulation of electrical charge carriers during charge-discharge.

• Korean Journal of Materials Research
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• v.27 no.9
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• pp.507-511
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• 2017

An optimum route to fabricate oxide dispersion strengthened ferritic superalloy with desired microstructure was investigated. Two methods of high energy ball milling or polymeric additive solution route for developing a uniform dispersion of $Y_2O_3$ particles in Fe-Cr-Al-Ti alloy powders were compared on the basis of the resulting microstructures. Microstructural observation revealed that the crystalline size of Fe decreased with increases in milling time, to values of about 15-20 nm, and that an FeCr alloy phase was formed. SEM and TEM analyses of the alloy powders fabricated by solution route using yttrium nitrate and polyvinyl alcohol showed that the nano-sized Y-oxide particles were well distributed in the Fe based alloy powders. The prepared powders were sintered at 1000 and $1100^{\circ}C$ for 30 min in vacuum. The sintered specimen with heat treatment before spark plasma sintering at $1100^{\circ}C$ showed a more homogeneous microstructure. In the case of sintering at $1100^{\circ}C$, the alloys exhibited densified microstructure and the formation of large reaction phases due to oxidation of Al.

• Textile Coloration and Finishing
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• v.15 no.5
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• pp.321-326
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• 2003

In order for disperse dye based ink to be fitted with the critical requirements of ink jet printing, this study was undertaken to investigate the effects of 6 different dispersants on the milling efficiency of insoluble dye particles and dispersion stability of the final ink. It was found that a polystyrene dispersant with high molecular weight exerted relatively better dispersion stability which may be associated with its steric stabilization effect in the ink solution.

• Natural Product Sciences
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• v.27 no.1
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• pp.36-44
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• 2021

The essential oils from the aerial parts (leaves and flowers) of Spiraea hypericifolia L. (Rosaceae), collected in Northern Kazakhstan, were obtained by distillation in two dispersion media (distilled water and 15% NaCl solution). The chemical composition of the essential oils was evaluated by GC-MS for the first time. The yield of the essential oil was 0.04% (in fresh growth conditions) and 0.02% (in dry growth conditions) respectively regardless of which dispersion media (H2O or 15% NaCl solution) was used at the isolation of essential oil. The main compounds were aliphatic hydrocarbons (alkanes) (40.6-53.2%), aldehydes (8.4-17.4%), diterpenoids (9.1-16.7%) and ketones (6.2-8.7%). Content of monoterpenoids was depended on dispersion media (2.2-3.6% where H2O was dispersion media and 8.4-8.5% where 15% NaCl solution was dispersion media). n-Heneicosane (17.4-34.1%) and n-tricosane (14.3-19.5%) were the main constituents of the essential oil of S. hypericifolia. There were many insects from different classes in S. hypericifolia at flowering. Important components such as α-methylene-γ-butyrolactone (0.8-2.8%), benzyl cyanide (0.7-1.1%), β-damascenone (1.2-2.9%), (E,E)-4,8,12-trimethyl-1,3,7,11-tridecatetraene (1.8-2.7%), β-ionone (0.5-1.8%) and others were detected in small amounts.

• Journal of the Korean institute of surface engineering
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• v.41 no.5
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• pp.194-198
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• 2008

Several methods for improving dispersion of carbon nanotubes (CNTs) have been investigated. CNTs modified by acids and hydrogen peroxide ($H_2O_2$) showed improved dispersion. From SEM micrographs and photos of dispersion, CNTs modified with nitric acid and $H_2O_2$, showed no agglomeration in solution even standing for 4 months, which means successfully improved dispersion property. TEM micrographs of surface modified single CNT treated with 69% $HNO_3$ in boiling acid solution as the optimum method were obtained. For confirmation of CNTs' application to EDLC electrode materials, characteristics of EDLC have been analyzed by cyclic voltammetry curve, specific capacitance of unit cell, electrode discharge curves and AC impedance curve. From the results, it could be confirmed that electrochemical properties of CNTs were enhanced after surface modification with 69% $HNO_3$ acid treatment.

• Journal of Korean Society for Atmospheric Environment
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• v.15 no.6
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• pp.757-765
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• 1999

Lagrangian particle dispersion model(LPDM) is an effective tool to calculate the dispersion from a point source since it dose not induce numerical diffusion errors in solving the pollutant dispersion equation. Fictitious particles are released to the atmosphere from the emission source and they are then transported by the mean velocity and diffused by the turbulent eddy motion in the LPDM. The concentration distribution from the dispersed particles in the calculation domain are finally estimated by applying a particle count method or a Gaussian kernel method. The two methods for calculating concentration profiles were compared each other and tested against the analytic solution and the tracer experiment to find the strength and weakness of each method and to choose computationally time saving method for the LPDM. The calculated concentrations from the particle count method was heavily dependent on the number of the particles released at the emission source. It requires lots fo particle emission to reach the converged concentration field. And resulting concentrations were also dependent on the size of numerical grid. The concentration field by the Gaussian kernel method, however, converged with a low particle emission rate at the source and was in good agreement with the analytic solution and the tracer experiment. The results showed that Gaussian kernel method was more effective method to calculate the concentrations in the LPDM.

• Coupled systems mechanics
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• v.13 no.3
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• pp.247-275
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• 2024

The paper studies the influence of the fluid flow velocity and flow direction in the initial state on the dispersion of the axisymmetric waves propagating in the inhomogeneously pre-stressed hollow cylinder containing this fluid. The corresponding eigenvalue problem is formulated within the scope of the three-dimensional linearized theory of elastic waves in bodies with initial stresses, and with linearized Euler equations for the inviscid compressible fluid. The discrete-analytical solution method is employed, and analytical expressions of the sought values are derived from the solution to the corresponding field equations by employing the discrete-analytical method. The dispersion equation is obtained using these expressions and boundary and related compatibility conditions. Numerical results related to the action of the fluid flow velocity and flow direction on the influence of the inhomogeneous initial stresses on the dispersion curves in the zeroth and first modes are presented and discussed. As a result of the analyses of the numerical results, it is established how the fluid flow velocity and flow direction act on the magnitude of the influence of the initial inhomogeneous stresses on the wave propagation velocity in the cylinder containing the fluid.

• Proceedings of the IEEK Conference
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• 2001.06a
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• pp.81-84
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• 2001

We propose the cascade FBG(Fiber Bragg Grating)s to compensate the dispersion, discuss the dispersion characteristics of such cascaded FBGs, compare with the single FBG dispersion compensator. For these, we theoretically consider the sencond- and third-order group-velocity dispersion(GVD) in the single fiber grating using plane wave solution and the coupled mode equation. We also theoretically find the group-velocity dispersion in the cascaded fiber gratings from the results in the single fiber grating and present the optimum disign data of the cascaded FBGs dispersion compensator in the N-channel WDM system through the numerical simulation.