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The one-dimensional pressure drop equation is also modified to give a shear factor for use with the volume averaged Navier Stokes equation and it is given as where F is the shear factor and Rev is the local modified Reynolds number.
It allows us to overcome the computational difficulties according to the properties of the local modified Swift-Hohenberg equation.
In this paper, we investigate a global random attractor for a stochastic local modified Swift-Hohenberg equation with multiplicative noise in Stratonovich sense.
In this section, we mainly show uniform a priori estimates of a solution for the stochastic local modified Swift-Hohenberg equation.
Until now, there are few results on the dynamics behaviors of the stochastic local modified Swift-Hohenberg equation with multiplicative noise in Stratonovich sense.
Through the Ornstein-Uhlenbeck (O-U) transformation, we obtain the random dynamical system associated with the stochastic local modified Swift-Hohenberg equation.
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International and national guidelines can be locally modified, and local guidelines can be developed.
Semi-local, Hubbard modified semi-local, and hybrid electronic exchange-correlation functionals are used to capture the energetics and phase transitions.
Why these two sets of results are so different is still not understood, but one can invoke possibly different types of resident cells in the two models that have differential requirements for activation, or perhaps local modifying factors (such as proteins).
The CLI-UK included similar international dates, with the national and local landmarks modified to reflect UK, rather than Australian events, see Figure 1B.
Local psychiatrists modified the scenarios following the pre-pilot session, altering details and demographic data to make the scenarios more realistic and culturally appropriate.
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