• Biotechnology and Bioprocess Engineering:BBE
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• v.7 no.6
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• pp.362-366
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• 2002

A mathematical model has been developed for describing the oxygen concentration during the exponential growth of microorganisms, in a static solid substrate bed supported on a tray fermentor. The model equations comprise of one partial differential equation for mass transfer and an ordinary differential equation of growth. After nondimensionlisation, analytical solution tn the model has been obtained by the method of Laplace transforms. An expression for critical thickness of bed is deduced from the model equation. The significance of the model in the design of tray fermentors is discussed. The validity of the discussion is verified by taking an illustration from the literature.

• JSTS:Journal of Semiconductor Technology and Science
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• v.5 no.3
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• pp.173-181
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• 2005

A new two dimensional (2-D) model for the potential distribution of fully depleted short-channel ion-implanted silicon MESFET's has been presented in this paper. The solution of the 2-D Poisson's equation has been considered as the superposition of the solutions of 1-D Poisson's equation in the lateral direction and the 2-D homogeneous Laplace equation with suitable boundary conditions. The minimum bottom potential at the interface of the depletion region due to the metal-semiconductor junction at the Schottky gate and depletion region due to the substrate-channel junction has been used to investigate the drain-induced barrier lowering (DIBL) and its effects on the threshold voltage of the device. Numerical results have been presented for the potential distribution and threshold voltage for different parameters such as the channel length, drain-source voltage, and implanted-dose and silicon film thickness.

• Journal of Korean Institute of Industrial Engineers
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• v.5 no.2
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• pp.2-7
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• 1979

The fundamental stochastic duel of Williams and Ancker is combined with the probabilistic linear, square and mixed laws of Brown and Smith when the battle time is limited and interfiring times are continuous. The Probability of a given side's winnig or a draw is derived in a recursive equation with Laplace transforms. Examples with negative exponential firing times are given. In linear law an exact closed form solution is obtained, whereas for square and mixed laws only square ($2{\times}2$) duels are considered.

• Journal of electromagnetic engineering and science
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• v.14 no.3
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• pp.273-277
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• 2014

In this research, integral transform technique for electromagnetic scattering formulation is reviewed. Electromagnetic boundary-value problems are presented to demonstrate how the integral transforms are utilized in electromagnetic propagation, antennas, and electromagnetic interference/compatibility. Various canonical structures of slotted conductors are used for illustration; moreover, Fourier transform, Hankel transform, Mellin transform, Kontorovich-Lebedev transform, and Weber transform are presented. Starting from each integral transform definition, the general procedures for solving Helmholtz's equation or Laplace's equation for the potentials in the unbounded region are reviewed. The boundary conditions of field continuity are incorporated into particular formulations. Salient features of each integral transform technique are discussed.

• Water for future
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• v.29 no.4
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• pp.199-208
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• 1996

The multiple flow direction algorithm to calculate the spatial variation of the saturation tendency, i.e. topographic index, is integrated into the Geogrphic Information System, GRASS. A procedure is suggested to consider the effect of a tile system on calculating the topographic index. A small agricultural subwatershed (3.4$\textrm{km}^2$) is used for this study. The impact of a tile system on the groundwater table can be effectively considered by the Laplace's equation to the DEM. The analysis shows that a tile system has a high degree of saturation compared to the case without tile drainage, and the predicted riparian area is well fitted to the actual watershed condition. A procedure is suggested to consider the effect of tile system on calculating the topographic index.

• Structural Engineering and Mechanics
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• v.27 no.5
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• pp.609-623
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• 2007

The problem of a semi-infinite magneto-electro-elastically impermeable mode-III crack in a magneto-electro-elastic material is considered under the action of impact loads. For the case when a pair of concentrated anti-plane shear impacts, electric displacement and magnetic induction impacts are exerted symmetrically on the upper and lower surfaces of the crack, the magneto-electro-elastic field ahead of the crack tip is determined in explicit form. The dynamic intensity factors and dynamic energy density factor are obtained. The method adopted is to reduce the mixed initial-boundary value problem, by using the Laplace and Fourier transforms, into three simultaneous dual integral equations, one of which is converted into an Abel's integral equation and the others into a singular integral equation with Cauchy kernel. Based on the obtained fundamental solutions of point impact loads, the solutions of two kinds of different loading cases are evaluated by integration. For some particular cases, the present results reduce to the previous results.

• Journal of the Korean institute of surface engineering
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• v.27 no.4
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• pp.223-233
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• 1994

It is well known that compositionally modulated Cu-Ni alloy can be produced by an electrochemical method in Ni sulfate solution containing trace amount of Cu. a mathematical model is presented to describe the current distribution and weight percent of Cu in Ni layer on the rotating disk electrode. The model includes convective-diffusion equation, the Laplace's equation and various overpotentials, and is solved numerically. The thickness of Cu layer is almost uniform whereas the thickness of Ni layer as well as the Ni/Cu weight ratio are increased approaching to the edge of the disk. These results agree well with the experimental values. The ohmic potential drop is suggested as a major cause of a nonuniformity in Ni layer. The optimum plating condition for the fabrication of susperlattice is proposed based on the results of this study.

• Bulletin of the Korean Chemical Society
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• v.33 no.11
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• pp.3805-3809
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• 2012

Results for molecular dynamics simulation method of small liquid drops of argon (N = 1200-14400 molecules) at 94.4 K through a Lennard-Jones intermolecular potential are presented in this paper as a preliminary study of drop systems. We have calculated the density profiles ${\rho}(r)$, and from which the liquid and gas densities ${\rho}_l$ and ${\rho}_g$, the position of the Gibbs' dividing surface $R_o$, the thickness of the interface d, and the radius of equimolar surface $R_e$ can be obtained. Next we have calculated the normal and transverse pressure tensor ${\rho}_N(r)$ and ${\rho}_T(r)$ using Irving-Kirkwood method, and from which the liquid and gas pressures ${\rho}_l$ and ${\rho}_g$, the surface tension ${\gamma}_s$, the surface of tension $R_s$, and Tolman's length ${\delta}$ can be obtained. The variation of these properties with N is applied for the validity of Laplace's equation for the pressure change and Tolman's equation for the effect of curvature on surface tension through two routes, thermodynamic and mechanical.

• International journal of advanced smart convergence
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• v.6 no.4
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• pp.33-40
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• 2017

In this paper, complex quadruplet zeros of microwave filter systems are investigated. For the cascaded systems the chain matrices are most conveniently used to derive the voltage transfer function of Laplace transform with cascaded two-port subsystems. The convenient relations of transfer function and chain matrix are used in order to find the transmission zeros. Starting from a ladder network, we introduced a crossed-coupled lumped element, in order to show the improved response of bandpass filter. By solving the transmission zero characteristic equation derived from the cascaded subsystems, we found the zeros of filter system with externally cross-coupled lumped elements. With the cross-coupled elements of capacitors, the numerator polynomial of system transfer function is used to locate the quadruplet zeros in complex plane. When the two pairs of double are on the zeros -axis, with the perturbed values of element, we learned that the transition band of lowpass filter is improved. By solving the characteristic equation of cascaded transfer function, we can obtain the zeros of the cross-coupled filter system, as a result of perturbed values on lumped element.

• Steel and Composite Structures
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• v.43 no.2
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• pp.185-200
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• 2022

A Closed-form solution for dynamic response of a functionally graded (FG) nonlocal nanobeam due to action of moving harmonic load is presented in this paper. Due to analyzing in small scale, a nonlocal elasticity theory is utilized. The governing equation and boundary conditions are derived based on the Euler-Bernoulli beam theory and Hamilton's principle. The material properties vary through the thickness direction. The harmonic moving load is modeled by Delta function and the FG nanobeam is simply supported. Using the Laplace transform the dynamic response is obtained. The effect of important parameters such as excitation frequency, the velocity of the moving load, the power index law of FG material and the nonlocal parameter is analyzed. To validate, the results were compared with previous literature, which showed an excellent agreement.