Sentence examples for macroscopic quantities for from inspiring English sources

Synthesis methods have improved over the years to produce economically viable, size-controlled CNTs in macroscopic quantities for commercial applications.

The approximation error can be analyzed quantitatively for the comparison of simulation results for macroscopic quantities of the conventional subsystem with those of a corresponding layer-based model.

In 1990 physicists Donald R. Huffman of the United States and Wolfgang Krätschmer of Germany announced a simple technique for producing macroscopic quantities of fullerenes, using an electric arc between two graphite rods in a helium atmosphere to vaporize carbon.

Macroscopic quantities of interest such as the Piola Kirchhoff stress tensor can be approximated for any value of the strain gradient by numerically solving a nonlinear PDE.

The overall macroscopic quantities of whole composite structure are obtained by assembling those of each coarse element.

A novel and inexpensive chemical route leading to obtain macroscopic quantities of room temperature magnetic carbon is reported.

It has been demonstrated that regional anesthesia needles can carry macroscopic quantities of ultrasound gel into tissues [ 1].

The resulting numerical differences in the macroscopic quantities are irrelevant for the presented data.

The generalized Hook law for macroscopic quantities can be written as {sigma}_{ij}={C}_{ijmn}{varepsilon}_{mn} (47 where C ijmn is the tensor of the effective elasticity moduli.

Boltzmann introduced the hypothesis in developing classical statistical mechanics; it was used to provide a suitable basis for identifying macroscopic quantities with statistical averages of microscopic quantities, such as the identification of gas temperature with the mean kinetic energy of the gas molecules.

In fact, from the numerical point of view, a system of PDEs for a set of macroscopic quantities is much more desirable than a single equation for a density in phase-space, where also the components of momentum are independent variables.