Sentence examples for formulation rigorously from inspiring English sources

The mathematical model formulation rigorously accounts for energy and momentum conservation, while faithfully representing the interfacial phenomena affecting solidification phase change and particle motion.

The mathematical model formulation rigorously accounts for mass, energy, and momentum conservation while simultaneously representing capillary physics of the menisci, tracking of the solidification front, and self-consistent determination of ribbon thickness.

All three formulations can be formulated rigorously from a unified treatment of the inverse integral transforms.

The topology optimization formulation uses rigorously computed sensitivities.

Furthermore, the semi-discrete form for the problem is given and, the stability and convergence of the semi-discrete variational formulation are rigorously proved in L2 norm and fractional norm respectively.

The completeness of the potential formulation is demonstrated rigorously.

Based on this new mathematical formulation, we prove rigorously existence and uniqueness as well as nonexistence of the ground states, and discuss the existence of global weak solution and finite time blow-up of the dynamics in different parameter regimes of dipolar BECs.

Here, a robust MILP formulation is used to rigorously optimize the structure, sizing and operation of DESS.

The second-order formulation has further been rigorously shown to be unconditionally stable for linear hyperbolic and parabolic equations in two-dimensional space.

This formulation allows us to rigorously deal both with noise in the experimental data and uncertainty associated with the structure-building process.

However, the proposed methodologies produce the optimum results because of the rigorously proved linear formulation.