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In particular, we first applied the regular perturbation method to give an analytical solution for the nonlinear elastostatic equation given a force profile assuming weak nonlinearity.
In the models assuming weak faults, average ground surface uplifts are 0.4 1.8 cm for the injection rates of 1 5 million tonnes per year, over an area of approximately 2.5 km radius around the hypothetical injection site.
By assuming weak deformation and high enough cross-sectional symmetry it was found that 1D models yield a sufficiently good approximation and could be used in the calculation of thermal conductance for long nanofibers.
Since direct coupling between thermal and structural fields would result in prohibitive computational costs, the problem is solved by assuming weak coupling between both fields and the nonlinear coupled thermal and structural analyses are performed in a sequential iterative scheme, implemented in ANSYS™ finite element software.
The log-normal fading model is usually used to model the FSO links assuming weak atmospheric turbulence conditions, whereas the Gamma-Gamma fading model is more accurate and can be used to model the FSO links under both weak and strong turbulence conditions.
Assuming weak separability and applying a two-stage budgeting model could lead to problems with respect to the endogeneity of the expenditure variable in the budget share equation, because the expenditure variable could be correlated with the equation errors (Attfield [1985]).
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Material depletion and multiple intergranular crack paths are modelled by assuming weaker grain boundaries having realistically a reduced critical damage index of a factor of 2 less than that of the grains.
In a recent analysis, economists at Goldman Sachs assumed weak revenues and a return to the spending patterns that held before the 1990s (when spending grew 1% faster than GDP).
Most of these derivations assume weak scattering, although schemes that exploit multiple scattering are also possible.
The reason we assume weak TP will be described in a later section.
Both approaches assume weak noise, though [286] makes no assumptions about relative time scales, and is thus a slightly more general approach than that of [287].
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