This analysis allows an elegant formulation of the evolution equations that avoids the otherwise necessary continuous checking for morphological changes during the integration of the differential equations.
The hybrid distribution is then evolved by Monte Carlo using the implicit formulation for the time evolution.
Finally, based on the test results of stiffness degradation, an analytical formulation for the damage evolution law of SFRC is developed and the prediction yields a close estimation of SFRC damage progression.
The DNA gene sequence informatics represented by Shannon entropy and fractal dimension have been used to form 2D maps, and coordinate changes have been used in a displacement vector formulation for the studying of evolution with directionality.
Detailed phylogenetic analysis allows formulation of a hypothesis for the evolution of the TAM: Although TamB was already present from the earliest-branching Phyla, TamA is the result of a gene duplication of BamA followed by drastic adaptation or partial sequence exchange of two POTRA domains, resulting in the TAM complex exemplified today in E. coli.
The model reduces to a finite-volume formulation for the balance equations expressing the evolution in time and space of the interface measure, where its local growth rate within chaotic regions is controlled by the average 〈D x,t):eu x,t eu x,t)〉, D x,t) being the deformation tensor and eu x,t) the unit vector spanning the unstable invariant subspace at the point x.
With this formulation, the evolution of allelic frequencies, and thus the evolution of alternative splicing, in (infinitely) large populations can be studied by classical equations of deterministic selection.
Equation B1 shows a matrix formulation for the differential equations that govern the time evolution of the detected signal.
It is then shown how the method may be modified to allow for the evolution of overhanging waves, using a novel time-dependent arclength formulation.
