Sentence examples for useful approximation for the from inspiring English sources

This expression provides what we think is a potentially useful approximation for the group velocity times wave energy (the solid black lines) for all types of equatorial waves, as we show in the "Methods/Experimental" section.

The initial rate of development of constitutional undercooling is shown to be equivalent to the growth restriction factor and is a useful approximation for the effect of solute on grain size when potent nucleant substrates are present.

Nevertheless, using the Rayleigh functional (38) with appropriate test functions one can obtain useful approximations for the eigenvalues.

Note that we do not expect (16) to hold exactly in any parameter regime because the time to fixation is actually a random variable (and furthermore, both τ f and λ are altered when interference is frequent), but we find that pinter is a useful approximation for describing the interference in simulations during the rescaling process.

These models rendered a useful approximation for binding requirements in the BBB-choline transporter and, until such time as the cloned transporter becomes available, may have significant utility in developing a predictive model for the rational design of drugs targeted to the brain.

Although this exact cancellation of the radial and angular dispersion effects provides a useful approximation for many types of proton pairs, the 3-fold rotational jumps of methyl protons deviates strongly from spherical isotropy.

The method appears to be a useful approximation for a wide variety of problems.

These assumptions are not too restrictive and the solution appears to be a useful approximation for a broad range of material-mill combinations.

The main focus is on thin shell theory, which provides a useful approximation for many deformation scenarios.

In materials science, this is a useful approximation for semi-conductors and a very good approximation for metals at room temperature.

For example, a transfer of a single electron between atoms is a useful approximation for bonds that form between atoms with one-electron more than a filled shell, and others that are one-electron short of a full shell, such as occurs in the compound sodium chloride and other chemical ionic salts.