Sentence examples for smallest principal from inspiring English sources

A hydraulic fracture may be initiated by natural, geological processes in the earth whereby the fluid pressure increases and/or the smallest principal stress decreases.

Hydraulic fracturing in rocks takes place when the fluid pressure within the rock exceeds the smallest principal stress plus the tensile strength of the rock.

If S hmin is the smallest principal stress magnitude, a strike-slip faulting regime is supposed to reactivate vertical structures at two conjugated 30° angles around S Hmax.

Artificial or man-made hydraulic fractures in petroleum activities are normally initiated by increasing the fluid pressure in the borehole to the point where the smallest principal stress at the borehole becomes tensile.

The principal effective stresses in the local borehole coordinate system in which shear stress is zero are given by σ t max = 1 2 ( σ zz + σ θ θ + ( σ zz - σ θ θ ) 2 + 4 σ θ z 2 ), (4) σ t min = 1 2 σ zz + σ θ θ - ( σ zz - σ θ θ ) 2 + 4 σ θ z 2. (5)where σtmax is the largest and σtmin is the smallest principal stress (Zoback 2007).

Mass spectra corresponding to rare cells may not strongly influence the largest principal vectors but may be identified by projecting the data onto the smallest principal vectors.

Here, we assume that energy eigenvalues are well approximated by those of the hydrogen atom for smaller principal quantum numbers.

As the CPI fell, interest payments on the bonds would decline because the fixed-coupon rate would be applied to a smaller principal amount.

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Third, to minimize the loss of information in the original marker matrix, while keeping the dimension small, principal component scores (U D) of X were used as inputs as well.

This could be a better deal in the long run than a smaller principal with a higher interest rate.