Sentence examples for a circular solution from inspiring English sources

For a circular solution of radius R ψ is conveniently written as ψ ( r ) = ∫ 0 2 π ∫ 0 R w ( | r − r ′ | ) r ′ d r ′ d θ, r = ( r, θ ).

Dashed branches indicate azimuthal instabilities of different modes m which deform the circular solution.

However, the resulting integrals of the nonuniform circular solution for displacements and stresses cannot be given in closed form; hence, numerical integrations are required.

For the specific type of semi-circular tunnel the distribution of stresses and displacements around the tunnel periphery predicted by the analytical model are compared with those of the FLAC2D numerical model, as well as, with Kirsch's "circular" solution.

Furthermore, the circular solution in the membrane module could flush away the adsorbed metaborate on the Pt NPs, preventing passivation of the Pt NPs and increasing the accessibility of the active sites.

This year called for a massive expansion of our international sales force to answer a growing demand for circular solutions at all levels of consumption, making for our most profitable yet.

Thus, within the family of circular solutions, there is a one-to-one correspondence between the noise entropy and the average spike probability.

The zeros of the first derivative of E L i a p. with respect to R give the stationary circular solutions, including the trivial case R = 0, as expected.

In order to obtain circular solutions we use the standard parametrization of a circle for the contour and write r = R [ sin θ 1 − cos θ ], n = [ sin θ − cos θ ], θ ∈ [ 0, 2 π ). (36). Hence the right hand side of (33) can be calculated using ∮ ∂ B d s ′ n ( s ′ ) ⋅ R i ( s, s ′ ) = 1 α i ∫ 0 2 π d θ K 1 [ α i R ] R R 2 ( 1 − cos θ ), (37).

For radially symmetric kernels we expect stationary circular solutions.

The dotted branches are circular solutions unstable to uniform changes of size.