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These improvements are obtained by following action of the limiter at edges, more detailed linear numerical analysis of the difference scheme, and considering the velocity gradient in the diffusion and antidiffusion coefficients.
In several instances, the improvements involved the creation of more detailed linear pathways connecting biological components.
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A more detailed non-linear contact spring formulation with lower stiffness at small indentations results in a reduced high-frequency content in the contact forces and the simulated noise.
Accounting for these features in a dynamic way requires using more detailed, non-linear, mathematical models [ 17, 18].
OK well, as I've indicated, in the next lecture we'll return to a much more detailed discussion of linear constant-coefficient differential and difference equations.
More detailed study of the non-linear f ( R ) effects on the power spectrum are presented in a companion paper.
To get a more detailed insight into a possible non-linear course of non-adherence over time, we also fit a generalized additive model including a spline-smoothed function of exposure time (SAS 'gam' procedure) [ 23].
Higher resolution linear probes can reveal more detailed anatomy of the worm.
See the Supplementary Methods for a more detailed description of the mathematical modeling process, including splines, linear mixed-effects models and the LASSO multivariate regression.
A higher frequency (7 12 MHz) linear probe is useful in providing more detailed views of superficial structures.
To get more detailed structural information during the progressive collapse, a non-linear numerical analysis was conducted using the LS-DYNA finite element software (Hallquist 2007).
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