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A Taylor series analysis of the upwind scheme discussed above will show that it is first-order accurate in space and time. Modified wavenumber analysis shows that the first-order upwind scheme introduces severe numerical diffusion /dissipation in the solution where large gradients exist due to necessity of high wavenumbers to represent sharp ...
However, for large Peclet numbers (generally > 2) this approximation gave inaccurate results. It was recognized independently by several investigators [1] [2] that the less expensive but only first order accurate upwind scheme can be employed but that this scheme produces results with false diffusion for multidimensional cases. Many new schemes ...
Unlike first-order upwind scheme, the MacCormack does not introduce diffusive errors in the solution. However, it is known to introduce dispersive errors ( Gibbs phenomenon ) in the region where the gradient is high.
Wobble base pairs for inosine and guanine. A wobble base pair is a pairing between two nucleotides in RNA molecules that does not follow Watson-Crick base pair rules. [1] The four main wobble base pairs are guanine-uracil (G-U), hypoxanthine-uracil (I-U), hypoxanthine-adenine (I-A), and hypoxanthine-cytosine (I-C).
Following the classical finite volume method framework, we seek to track a finite set of discrete unknowns, = / + / (,) where the / = + (/) and = form a discrete set of points for the hyperbolic problem: + (()) =, where the indices and indicate the derivatives in time and space, respectively.
Let (,) and (,) be ordered pairs. Then the characteristic (or defining) property of the ordered pair is: (,) = (,) = =.. The set of all ordered pairs whose first entry is in some set A and whose second entry is in some set B is called the Cartesian product of A and B, and written A × B.
Solution in the central difference scheme fails to converge for Peclet number greater than 2 which can be overcome by using an upwind scheme to give a reasonable result. [1]: Fig. 5.5, 5.13 Therefore the upwind differencing scheme is applicable for Pe > 2 for positive flow and Pe < −2 for negative flow. For other values of Pe, this scheme ...
Chemical structures for Watson–Crick and Hoogsteen A•T and G•C+ base pairs. The Hoogsteen geometry can be achieved by purine rotation around the glycosidic bond (χ) and base-flipping (θ), affecting simultaneously C8 and C1 ′ (yellow). [1] A Hoogsteen base pair is a variation of base-pairing in nucleic acids such as the A