East Asian mathematical journal

The Youngnam Mathematical Society (영남수학회)
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A NOTE ON NUMERICAL APPROACHES FOR HEAT-DIFFUSION EQUATION WITH HETEROGENEOUS MEDIA AND ITS APPLICATIONS

  • Seo, Sat byul (Department of Mathematics Education, Kyungnam University)
  • Received : 2018.12.04
  • Accepted : 2019.01.27
  • Published : 2019.01.31
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Abstract

In this paper, we introduce a numerical approach to solve heat-diffusion equation with discontinuous diffusion coefficients in the three dimensional rectangular domain. First, we study the support operator method and suggest a new method, the continuous velocity method. Further, we apply both methods to a diffusion process for neurotransmitter release in an individual synapse and compare their results.

Keywords

E1BGBB_2019_v35n1_99_f0001.png 이미지

FIGURE 2. Total concentration of glutamate molecules as time spends.

E1BGBB_2019_v35n1_99_f0002.png 이미지

FIGURE 4. NMDA receptor opening probability

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FIGURE 1. (A) The synaptic cleft is divided into two zones. Diffusion coeffcients were taken different values in two re-gions(inside and outside), which represent slow and fast motion of neurotransmitters released due to different compositions in the synaptic cleft. (B) Top view of synaptic cleft dividing into two parts.

E1BGBB_2019_v35n1_99_f0004.png 이미지

FIGURE 3. (A) 16 NMDA receptors are evenly distributed on the postsynaptic terminal surface (B) Relative discrepancy be-tween Support-Operator and Continuous Velocity models of glutamate concentration over 16 NMDA receptors.

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