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In mammals, there are four Ago proteins that possibly assemble small RNAs into RISC with different rate constants (Scheme 1).
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Different alkyl and aryl carboxylic acids were tested under the developed reaction conditions using aniline, the amine component, as a constant (Scheme 1).
In the piece-wise constant scheme, this formula works well.
Also, as shown in Table 1, the piece-wise constant scheme was about 30% faster than the linear Lagrange scheme.
Another way is a hybrid method that combines the piece-wise constant scheme with the linear Lagrange scheme.
The results show that the piece-wise constant scheme is sufficiently accurate even with a coarse mesh.
We then implemented the linear Lagrange scheme in our TIM-OS framework and compared the linear Lagrange scheme with the piece-wise constant scheme (the original TIM-OS).
Since the utility of the linear Lagrange scheme is rather limited, we believe that the piece-wise constant scheme is generally effective and efficient.
In the piece-wise constant scheme, the optical parameters for a tetrahedron were determined by the center position of the tetrahedron.
Let Φ = { ϕ 1,..., ϕ n } represent the fluence values, and Φ s l the surface fluence values from the linear Lagrange scheme, Φ v l the volumetric fluence from the linear Lagrange scheme, Φ s p the surface fluence values from the piece-wise constant scheme, Φ v p the volumetric fluence values from the piece-wise constant scheme.
Since the scheme used in MCML [ 1] can be applied to piece-wise constant scheme directly [ 7], in the following sections, we will only describe the MC simulation in the linear Lagrange scheme.
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