Sentence examples for three dimensional problem from inspiring English sources

We conclude with results including the formation of hexagonal patterns for the three dimensional problem.

A three dimensional problem is presented for an interaction problem between a spherical particle and Taylor Green vortices, and the result is verified by comparing with the independently-conducted numerical results.

With this in mind, the fully three dimensional problem of determining the thermal field in a conducting sphere with an asymmetric split ring current carrying heating source is resolved in an analytical or almost analytical form, implying either a closed form solution or utmost expressions involving a simple numerical integration.

To achieve this purpose, a new concept of "forbidden circle", which is the projection of the three dimensional "singular cone" associated with tool orientations in a two dimensional space named P-plane, is established for the first time to transform the complicated three dimensional problem into a two dimensional problem.

Although this approach is extremely powerful in solving two- and three-dimensional problem, it has some limitations such as incorporating the influence of storage and skin effects.

To design these barriers whilst taking into account their inherent acoustic complexity, we present an overlapping numerical model here that enables us to split the real three-dimensional problem into two two-dimensional ones, allowing both the reduction of the computational cost and the separate analysis of each one of the noise control mechanisms involved.

Those companies that approach this three-dimensional problem with only two dimensions — by cutting corners or finding "shortcuts" — have found themselves lost.

First, the interaction between a penny-shaped crack and two spherical inclusions is analyzed by considering the three-dimensional problem of an infinite solid, composed of an elastic matrix, a penny-shaped crack and two spherical inclusions, under tension.

Taking into account that typically, in actual self-assembled QDs, the height is much smaller than the lateral dimensions; one can take an advantage of the adiabatic approximation, which allows us to exclude temporarily the rapid particle motions along z-axis from consideration and, in this way, to reduce the dimensionality of the initial three-dimensional problem.

An overall speed-up factor of about eight and a saving in storage requirements about one order of magnitude for a typical three-dimensional problem in comparison with the unstructured grid method are demonstrated.

A key feature of our solution procedure is the reduction of a three-dimensional problem to a two-dimensional problem through a coordinate transform designed to combine the two time derivatives into one.