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Using Multiple Dirac Delta Points to Describe Inhomogeneous Flux Density over a Cell Boundary in a Single-Cell Diffusion Model

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Using Multiple Dirac Delta Points to Describe Inhomogeneous Flux Density over a Cell Boundary in a Single-Cell Diffusion Model. / Peng, Qiyao; Hille, Sander C.
Numerical Mathematics and Advanced Applications ENUMATH 2023, Volume 2 - European Conference, 2023. ed. / Adélia Sequeira; Ana Silvestre; Svilen S. Valtchev; João Janela. Vol. 2 Cham: Springer, 2025. p. 243-251 (Lecture Notes in Computational Science and Engineering; Vol. 154).

Research output: Contribution in Book/Report/Proceedings - With ISBN/ISSN › Conference contribution/Paper › peer-review

Harvard

Peng, Q & Hille, SC 2025, Using Multiple Dirac Delta Points to Describe Inhomogeneous Flux Density over a Cell Boundary in a Single-Cell Diffusion Model. in A Sequeira, A Silvestre, SS Valtchev & J Janela (eds), Numerical Mathematics and Advanced Applications ENUMATH 2023, Volume 2 - European Conference, 2023. vol. 2, Lecture Notes in Computational Science and Engineering, vol. 154, Springer, Cham, pp. 243-251. https://doi.org/10.1007/978-3-031-86169-7_25

APA

Peng, Q., & Hille, S. C. (2025). Using Multiple Dirac Delta Points to Describe Inhomogeneous Flux Density over a Cell Boundary in a Single-Cell Diffusion Model. In A. Sequeira, A. Silvestre, S. S. Valtchev, & J. Janela (Eds.), Numerical Mathematics and Advanced Applications ENUMATH 2023, Volume 2 - European Conference, 2023 (Vol. 2, pp. 243-251). (Lecture Notes in Computational Science and Engineering; Vol. 154). Springer. https://doi.org/10.1007/978-3-031-86169-7_25

Vancouver

Peng Q, Hille SC. Using Multiple Dirac Delta Points to Describe Inhomogeneous Flux Density over a Cell Boundary in a Single-Cell Diffusion Model. In Sequeira A, Silvestre A, Valtchev SS, Janela J, editors, Numerical Mathematics and Advanced Applications ENUMATH 2023, Volume 2 - European Conference, 2023. Vol. 2. Cham: Springer. 2025. p. 243-251. (Lecture Notes in Computational Science and Engineering). doi: 10.1007/978-3-031-86169-7_25

Author

Peng, Qiyao ; Hille, Sander C. / Using Multiple Dirac Delta Points to Describe Inhomogeneous Flux Density over a Cell Boundary in a Single-Cell Diffusion Model. Numerical Mathematics and Advanced Applications ENUMATH 2023, Volume 2 - European Conference, 2023. editor / Adélia Sequeira ; Ana Silvestre ; Svilen S. Valtchev ; João Janela. Vol. 2 Cham : Springer, 2025. pp. 243-251 (Lecture Notes in Computational Science and Engineering).

Bibtex

@inproceedings{110d9be740b44bf883af45805d3b2e39,
title = "Using Multiple Dirac Delta Points to Describe Inhomogeneous Flux Density over a Cell Boundary in a Single-Cell Diffusion Model",
abstract = "Biological cells can release compounds into their direct environment, generally inhomogeneously over their cell membrane, after which the compounds spread by diffusion. In mathematical modelling and simulation of a collective of such cells, it is theoretically and numerically advantageous to replace spatial extended cells with point sources, in particular when cell numbers are large, but still so small that a continuum density description cannot be justified, or when cells are moving. We show that inhomogeneous flux density over the cell boundary may be realized in a point source approach, thus maintaining computational efficiency, by utilizing multiple, clustered point sources (and sinks). In this report, we limit ourselves to a sinusoidal function as flux density in the spatial exclusion model, and we show how to determine the amplitudes of the Dirac delta points in the point source model, such that the deviation between the point source model and the spatial exclusion model is small.",
author = "Qiyao Peng and Hille, {Sander C.}",
year = "2025",
month = apr,
day = "28",
doi = "10.1007/978-3-031-86169-7_25",
language = "English",
isbn = "9783031861680",
volume = "2",
series = "Lecture Notes in Computational Science and Engineering",
publisher = "Springer",
pages = "243--251",
editor = "Ad{\'e}lia Sequeira and Ana Silvestre and Valtchev, {Svilen S.} and Jo{\~a}o Janela",
booktitle = "Numerical Mathematics and Advanced Applications ENUMATH 2023, Volume 2 - European Conference, 2023",

}

RIS

TY - GEN

T1 - Using Multiple Dirac Delta Points to Describe Inhomogeneous Flux Density over a Cell Boundary in a Single-Cell Diffusion Model

AU - Peng, Qiyao

AU - Hille, Sander C.

PY - 2025/4/28

Y1 - 2025/4/28

N2 - Biological cells can release compounds into their direct environment, generally inhomogeneously over their cell membrane, after which the compounds spread by diffusion. In mathematical modelling and simulation of a collective of such cells, it is theoretically and numerically advantageous to replace spatial extended cells with point sources, in particular when cell numbers are large, but still so small that a continuum density description cannot be justified, or when cells are moving. We show that inhomogeneous flux density over the cell boundary may be realized in a point source approach, thus maintaining computational efficiency, by utilizing multiple, clustered point sources (and sinks). In this report, we limit ourselves to a sinusoidal function as flux density in the spatial exclusion model, and we show how to determine the amplitudes of the Dirac delta points in the point source model, such that the deviation between the point source model and the spatial exclusion model is small.

AB - Biological cells can release compounds into their direct environment, generally inhomogeneously over their cell membrane, after which the compounds spread by diffusion. In mathematical modelling and simulation of a collective of such cells, it is theoretically and numerically advantageous to replace spatial extended cells with point sources, in particular when cell numbers are large, but still so small that a continuum density description cannot be justified, or when cells are moving. We show that inhomogeneous flux density over the cell boundary may be realized in a point source approach, thus maintaining computational efficiency, by utilizing multiple, clustered point sources (and sinks). In this report, we limit ourselves to a sinusoidal function as flux density in the spatial exclusion model, and we show how to determine the amplitudes of the Dirac delta points in the point source model, such that the deviation between the point source model and the spatial exclusion model is small.

U2 - 10.1007/978-3-031-86169-7_25

DO - 10.1007/978-3-031-86169-7_25

M3 - Conference contribution/Paper

SN - 9783031861680

VL - 2

T3 - Lecture Notes in Computational Science and Engineering

SP - 243

EP - 251

BT - Numerical Mathematics and Advanced Applications ENUMATH 2023, Volume 2 - European Conference, 2023

A2 - Sequeira, Adélia

A2 - Silvestre, Ana

A2 - Valtchev, Svilen S.

A2 - Janela, João

PB - Springer

CY - Cham

ER -