• 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.

• 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.

• 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.

• 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.

• 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 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.

• JSTS:Journal of Semiconductor Technology and Science
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• v.14 no.4
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• pp.451-456
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• 2014

A compact model of a depletion-mode silicon-nanowire (Si-NW) pH sensor is proposed. This drain current model is obtained from the Pao-Sah integral and the continuous charge-based model, which is derived by applying the parabolic potential approximation to the Poisson's equation in the cylindrical coordinate system. The threshold-voltage shift in the drain-current model is obtained by solving the nonlinear Poisson-Boltzmann equation for the electrolyte. The simulation results obtained from the proposed drain-current model for the Si-NW field-effect transistor (SiNWFET) agree well with those of the three-dimensional (3D) device simulation, and those from the Si-NW pH sensor model also agree with the experimental data.

• 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.

• 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.

• Proceeding of EDISON Challenge
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• 2014.03a
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• pp.75-88
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• 2014

본 연구에서는 비선형 Poisson-Boltzmann 식의 해를 구할 수 있는 웹 기반 EPBS를 이용하여 이온채널의 전하 분포와 유전률이 이온채널의 이온선택성에 미치는 영향에 대해 알아본다. 모델로 사용한 이온채널은 이온채널과 유사한 구조를 갖는 합성 단백질인 고리형 펩타이드 나노튜브와 자연계에 존재하는 Gramicidin A 이다. 계산 결과로부터 용매인 물과 단백질의 유전율 차이에 의해 이온이 이온채널을 통과할 때 반응장이 생성되며, 이는 이온과 상호작용을 통해 이온 종류에 관계없이 이온 통과를 방해하는 에너지 장벽을 형성함을 알 수 있다. 한편, 두 이온채널 부분 전하, 특히 골격에 존재하는 카르보닐기의 쌍극자 모멘트에 의해 이온채널 내부에는 0 보다 작은 정전기 퍼텐셜이 형성된다. 이온채널 내부의 총 정전기 퍼텐셜은 이온채널의 부분 전하에 의한 정전기 퍼텐셜과 유전률 차이에 의한 반응장의 합으로 나타나며, 계산 결과 0 보다 작은 값을 갖는다. 이로부터 본 연구에서 사용된 두 종류의 이온채널이 양이온에 선택성이 있음을 알 수 있다.