2002
DOI: 10.1002/jnm.446
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Distribution in TLM models for diffusion (Part I: one‐dimensional treatment)

Abstract: SUMMARYThe signal obtained at each time step of a TLM simulation for one-dimensional diffusion is analysed for single shot injections. A combinatorial formula is provided to predict the signal value at any given spatial positions. Formulas for expectation and variance are obtained using a technique based on generating functions. We briefly compare the resulting variance and that of the underlying diffusion process. Copyright #

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Cited by 4 publications
(6 citation statements)
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“…Note that if 0 x = 0 and 0 s 2 Vn = 0, this is equivalent to the equation for cell variance derived by Chardaire and de Cogan [9,10,13]. Equation (46) applies to the LR TLM formulation and gives the cell variance at any time step, no matter what the initial conditions are.…”
Section: Distribution Variancementioning
confidence: 97%
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“…Note that if 0 x = 0 and 0 s 2 Vn = 0, this is equivalent to the equation for cell variance derived by Chardaire and de Cogan [9,10,13]. Equation (46) applies to the LR TLM formulation and gives the cell variance at any time step, no matter what the initial conditions are.…”
Section: Distribution Variancementioning
confidence: 97%
“…While equations for the variance at any time step have been established previously for a number of lossy TLM networks [9,10,13], the relationship between the variance and the mean positions of the initial incident voltage distributions has not. It will be shown that the equations derived above can be used to improve the accuracy of the LR lossy TLM algorithm under some circumstances by reducing the long-term variance error to zero for models initialized using the standard method.…”
Section: Distribution Variancementioning
confidence: 99%
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“…100-107]) as a means of developing a phenomenological expression for the variance as a function of n; r and t: In our previous paper [2] we have supported this with a rigorous analysis and have proven that the variance, at time step n; for a one-dimensional TLM model of diffusion is…”
Section: Introductionmentioning
confidence: 84%
“…We will use the same methodology as in the one-dimensional case [2] to determine the first and second moment of X n and Y n : Let…”
Section: Expectation and Variancementioning
confidence: 99%