• Proceedings of the Korean Institute of Information and Commucation Sciences Conference
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• 2021.10a
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• pp.138-139
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• 2021

This work introduces neural network based simulation for Poisson Boltzmann equation. First, samples are generated via a finite element method, whose pairs are used to train neural network. We report the performance of the neural network.

• Journal of the Institute of Electronics Engineers of Korea SD
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• v.39 no.2
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• pp.27-38
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• 2002

A new self-consistent mathematical model for semiconductor quantum well device was developed. The model was based on the direct solution of the Boltzmann transport equation, coupled to the Schrodinger and Poisson equations. The solution yielded the distribution function for a two-dimensional electron gas(2DEG) in quantum well devices. To solve the Boltzmann equation, it was transformed into a tractable form using a Legendre polynomial expansion. The Legendre expansion facilitated analytical evaluation of the collision integral, and allowed for a reduction of the dimensionality of the problem. The transformed Boltzmann equation was then discretized and solved using sparce matrix algebra. The overall system was solved by iteration between Poisson, Schrodinger and Boltzmann equations until convergence was attained.

• Proceedings of the Korean Institute of Information and Commucation Sciences Conference
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• 2022.05a
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• pp.216-217
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• 2022

Poisson-Boltzmann equation (PBD), which describes the effects of charges inside cells, plays important roles in various disciplinaries including biology. In this presentation, we introduce a ResNet based method to predict solution of PBE. First, we generate solutions of PBE based on FEM. Next, we train networks whose input shape includes location of charge and shape of cell and while output shape includes the electronic potential.

• Membrane Journal
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• v.13 no.1
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• pp.37-46
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• 2003

The electrokinetic effect can be found in cases of the fluid flowing across the charged membrane micropores. The externally applied body force originated from the electrostatic interaction between the nonlinear Poisson-Boltzmann field and the flow-induced electrical field is taken into the equation of motion. The electrostatic potential profile is computed a priori by applying the finite difference scheme, and an analytical solution to the Navier-Stokes equation of motion for slit-like pore is obtained via the Green's function. An explicit analytical expression for the flow-induced streaming potential is derived as functions of relevant physicochemical parameters. The influences of the electric double layer, the surface potential of the wall, and the charge condition of the pore wall upon the velocity profile as well as the streaming potential are examined. With increasing of either the electric double layer thickness or the surface potential, the average fluid velocity is entirely reduced, while the streaming potential increases.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.26 no.2
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• pp.181-186
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• 2022

Poisson-Boltzmann equation (PBE) is used to model problems arising from various disciplinary including bio-pysics and colloid chemistry. Therefore, to predict a numerical solution of PBE is an important issue. The authors proposed deep learning based methods to solve PBE while the computational time to generate finite element method (FEM) solutions were bottlenecks of the algorithms. In this work, we shorten the generation time of FEM solutions in two directions. First, we experimentally find certain penalty parameter in a bilinear form. Second, we applied algebraic multigrids methods to the algebraic system so that condition number is bounded regardless of the meshsize. In conclusion, we have reduced computation times to solve algebraic systems for PBE. We expect that algebraic multigrids methods can be further employed in various disciplinary to generate deep learning samples.

• Korea-Australia Rheology Journal
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• v.15 no.2
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• pp.83-90
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• 2003

In cases of the microfluidic channel, the electrokinetic influence on the transport behavior can be found. The externally applied body force originated from the electrostatic interaction between the nonlinear Poisson-Boltzmann field and the flow-induced electrical field is applied in the equation of motion. The electrostatic potential profile is computed a priori by applying the finite difference scheme, and an analytical solution to the Navier-Stokes equation of motion for slit-like microchannel is obtained via the Green's function. An explicit analytical expression for the induced electrokinetic potential is derived as functions of relevant physicochemical parameters. The effects of the electric double layer, the zeta potential of the solid surface, and the charge condition of the channel wall on the velocity profile as well as the electroviscous behavior are examined. With increases in either electric double layer or zeta potential, the average fluid velocity in the channel of same charge is entirely reduced, whereas the electroviscous effect becomes stronger. We observed an opposite behavior in the channel of opposite charge, where the attractive electrostatic interactions are presented.

• Journal of the Institute of Electronics Engineers of Korea SD
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• v.39 no.2
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• pp.14-26
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• 2002

A new model for degenerate semiconductor quantum well devices was developed. In this model, the multi-subband Boltzmann transport equation was formulated by applying the Pauli exclusion principle and coupled to the Schrodinger and Poisson equations. For the solution of the resulted nonlinear system, the finite difference method and the Newton-Raphson method was used and carrier energy distribution function was obtained for each subband. The model was applied to a Si MOSFET inversion layer. The results of the simulation showed the changes of the distribution function from Boltzmann like to Fermi-Dirac like depending on the electron density in the quantum well, which presents the appropriateness of this modeling, the effectiveness of the solution method, and the importance of the Pauli -exclusion principle according to the reduced size of semiconductor devices.

• Bulletin of the Korean Chemical Society
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• v.26 no.4
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• pp.585-588
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• 2005

Bipyridine and its derivatives have been widely used as the ligands in transition metal complexes. The proton affinities of pyridine derivatives were calculated using an ab initio quantum mechanical method (B3LYP with various double zeta and triple zeta basis sets) in combination with the Poisson-Boltzmann continuum solvation model. Van der Waals radii of the atoms in the heterocyclic rings for the solvation energy calculation were set to values determined to reproduce the $pK_a$ values of guanine and oxoguanine derivatives and that of chlorine was optimized to reproduce the experimental values of relating compounds. The $pK_a$ values for the heterocyclic ring compounds were in agreement with the experimental values with a mean unsigned error of 0.45 $pK_a$ units.

• Bulletin of the Korean Chemical Society
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• v.31 no.9
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• pp.2553-2556
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• 2010

On the basis of a simple modified Poisson-Boltzmann (SMPB) theory, taking into account the finite ionic size, the analytic expression for the effect of ionic size on the diffuse layer potential drop at negative charge densities has been given for the simple 1:1 electrolyte. It is shown that the potential drop across the diffuse layer depends on the size of the ions in the electrolyte. For a given electrolyte concentration and electrode charge density, the diffuse layer potential drop in a small ion system is smaller than that in a large ion system. It is also displayed that the diffuse layer potential drop is always less than the value of the Gouy-Chapman (GC) theory, and the deviation increases as the electrode charge density increases for a given electrolyte concentration. These theoretical results are consistent with the results of the Monte-Carlo simulation [Fawcett and Smagala, Electrochimica Acta 53, 5136 (2008)], which indicates the importance of including steric effects in modeling diffuse layer properties.

• Interaction and multiscale mechanics
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• v.3 no.2
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• pp.157-171
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• 2010

In this paper, a theoretical method has been developed for the electric double layer interaction under condition of the variable dielectric permittivity of water. Using Poisson-Boltzmann equation (PBE), for one plate and two plates having similar or dissimilar constant charge or constant potential, we have investigated the electric double layer potential, its gradient and the disjoining pressure as well as the effect of variation of dielectric permittivity on these parameters. It has been assumed that plates are separated by a specific distance and contain a liquid solution in between. It is shown that reduction of the dielectric permittivity near the interfaces results in compression of electric double layers and affects the potential and its gradient which leads to a decreased electrostatic repulsion. In addition, it is shown that variation of dielectric permittivity in the case of higher electrolyte concentration, leads to a greater change in potential distribution between two plates.