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Generally speaking, one must determine this minimizer numerically with an iterative optimization procedure.
It is found that perturbation theory can be used to determine the numerically induced shift.
A further task is to determine numerically the width of the reinforcement and the number of layers needed for reinforcement or repair.
A genetic algorithm procedure coupled with an analytical model of shell buckling has been developed to determine numerically optimized stacking sequences.
For problems not amenable for analytical solutions, an algorithm is developed to determine these parameters numerically.
For a given Δ > 0, we determine numerically the number N Δ of input pulses that are needed to generate an action potential in the target.
Another possibility is to determine the eigenquantities numerically, and then Eqs.
To go farther, we use an interpolation of the friction force in terms of cos(2α) and determine numerically (Wolfram, Mathematica 9.0), taking into account the simple condition that P M×F=0, the resulting trajectory.
This numerically determined minimal action S λ * (0 ) together with the approximation Equation 32 describes the rate of the ratchet, as determined in simulations, extremely well.
This value is the single mode cut-off diameter and is determined by numerically calculating the solutions to Eq. 2 while iteratively increasing d until a second solution emerges.
The values of Kc and Kη were determined using numerically and experimentally calculated convergence times.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com