Monte Carlo methods for computing the capacitance of the unit cube

Hwang, Chi‐Ok; Mascagni, Michael; Won, Taeyoung

doi:10.1016/j.matcom.2008.03.003

Cited by 14 publications

(12 citation statements)

References 17 publications

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“…2. For N = 3, we find good agreement between simulation and the independently derived estimate for C 3 from [19]. From physical arguments detailed at the end of this letter, we have determined an expansion of the Newtonian capacitance for large N given by…”

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confidence: 66%

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First-Passage Time to Clear the Way for Receptor-Ligand Binding in a Crowded Environment

Newby¹,

Allard²

2016

Phys. Rev. Lett.

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Certain biological reactions, such as receptor-ligand binding at cellcell interfaces and macromolecules binding to biopolymers, require many smaller molecules crowding a reaction site to be cleared. Examples include the T cell interface, a key player in immunological information processing. Diffusion sets a limit for such cavitation to occur spontaneously, thereby defining a timescale below which active mechanisms must take over. We consider N independent diffusing particles in a closed domain, containing a sub-region with N0 particles, on average. We investigate the time until the sub-region is empty, allowing a subsequent reaction to proceed. The first passage time is computed using an efficient exact simulation algorithm and an asymptotic approximation in the limit that cavitation is rare. In this limit, we find that the mean first passage time is subexponential, T ∝ e N 0 /N 2 0 . For the case of T cell receptors, we find that stochastic cavitation is exceedingly slow, 10 9 seconds at physiological densities, however can be accelerated to occur within 5 second with only a four-fold dilution.Diffusion drives many biological processes, both positively, by delivering cargo to a target, and negatively, by removal of cargo from a region of interest (ROI). While the temporal dynamics of diffusional delivery have been extensively studied [5,4,24,12], diffusion-driven removal has been less characterized experimentally or theoretically [3]. Removal is of particular interest in the crowded environment of cells, where large biomolecules and cellular structures require the displacement of smaller molecules, a phenomenon we term stochastic cavitation.A specific example arises in the study of cell-cell interfaces including the T-cell/antigen-presenting-cell interface [22,2,29,8] (see Fig. 1). A fundamental question for all cell-cell interfaces is how receptors and ligands come into

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confidence: 66%

“…Using the exact simulation algorithm, we obtain the numerical estimate, α 2 ≈ −1.67. Our MFPT calculation thus provides an approximation for the capacitance C N , which otherwise remains challenging to compute [19]. For fixed 0 < < 1, an asymptotic expansion for N 1 is given bȳ…”

mentioning

confidence: 99%

First-Passage Time to Clear the Way for Receptor-Ligand Binding in a Crowded Environment

Newby¹,

Allard²

2016

Phys. Rev. Lett.

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“…However, it should be noted that the surface charge method with extrapolation to an infinite number of subdivisions gives a quite reasonable value for the capacitance of the unit cube. [8] Milovanovic et al describes the calculations of the capacitance per unit length of one or multilayer dielectric lines are presented. Special attention is given to the calculations of the capacitance per unit length of lines with rectangular cross sections, whose electrodes may be in different or the same layers of a two layer dielectric line.…”

Section: General Analysismentioning

confidence: 96%

Efficient capacitance computation for computational electromagnetics

Dhamodaran¹,

Dhanasekaran²

2014

2014 International Conference on Communication and Signal Processing

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The capacitance evaluation of conducting bodies is an importance step for prediction of electrostatic discharge problem. In this paper an attempt has been made for the evaluation of charge distribution and the capacitance of conducting surface. There are different methods such as method of moment (MOM), Finite element method (FEM), Finite difference method (FDM), Charge Simulation method (CSM), point matching method and Surface charge method. In this paper the MOM based on the pulse basis function and point matching is used. The integrand is divided into a regular and a singular part. The MOM is based upon the transformation of an integral equation, into a matrix equation by employing expansion of the unknown in terms of known basis functions with unknown coefficients such as charge distribution and hence the capacitance is to be determined. This paper reviews the results of computing the capacitance-per-unit length of square plates. Index Terms-Capacitance, electrostatic discharge, point matching, rectangular subdomain, method of moments, finite element method.

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“…Neither total capacitance nor charge distribution on a conducting cube is not known analytically and only numerical capacitance is known. [ 14,18 ] In this section, we compute charge distribution over a finite region of a unit cube held at unit potential (see Figure and compare with the results of the first‐passage algorithm.…”

Section: Illustrating Applicationsmentioning

confidence: 99%

Last‐Passage Algorithm for Charge Distribution Over a Finite Region

Jang

Given

et al. 2021

Advcd Theory and Sims

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First‐passage and last‐passage Monte Carlo algorithms have been used for computing charge distribution on a conducting object. First‐passage algorithms are used for an overall charge distribution on a conducting object and Given–Hwang's last‐passage algorithms are used for a charge density at a specific point on a flat or spherical surface of a conductor. In this paper, a last‐passage algorithm for computing charge distribution over a finite region of a conducting object is presented.

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Monte Carlo methods for computing the capacitance of the unit cube

Cited by 14 publications

References 17 publications

First-Passage Time to Clear the Way for Receptor-Ligand Binding in a Crowded Environment

First-Passage Time to Clear the Way for Receptor-Ligand Binding in a Crowded Environment

Efficient capacitance computation for computational electromagnetics

Last‐Passage Algorithm for Charge Distribution Over a Finite Region

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