Sentence examples for formulations with two from inspiring English sources
Mixed weak formulations, with two or three main (tensor) variables, are stated and theoretically analyzed for general multi-dimensional dipolar Gradient Elasticity (biharmonic) boundary value problems.
Five formulations with four factors (residues) and constraints were used according a mixture design.
A 32 factorial design was used to assess the effect of SS formulations with three blends of different grade coarse lactose supplemented with different levels of fine lactose.
The suite of problems encompasses a range of challenging problem properties including (1) many-objective formulations with four or more objectives, (2) multi-modality (or false optima), (3) nonlinearity, (4) discreteness, (5) severe constraints, (6) stochastic objectives, and (7) non-separability (also called epistasis).
We demonstrate the application of the finite element formulation with two cases: ambipolar diffusion and kinetic demixing.
The formulation with two active slip planes was implemented into a finite element code and used to simulate biaxial shear tests on dry sand.
We propose a constitutive model for shape memory alloys, based on a micromechanical formulation with two macroscopic internal variables; a scalar one (the global volume fraction of martensite) and a tensorial one (the mean transformation strain).
The numerical implementation is based on an operator-split formulation, with two straightforward steps: a perpendicular transport step (including sources), and a Lagrangian (field-line integral) parallel transport step.
Finally, the proposed MaOP is reduced to be a bi-objective formulation with two conflicting groups of objectives.
To handle topological changes, the energy ϵ(C, f 1, f 2) is incorporated into a variational level set formulation with two extra internal energy functionals.
We also addressed the problem of neo-epitopes and non-junction cleavage sites arising from spacer sequences and the order of the epitopes within the string-of-beads by extending the formulation with two additional objective functions.
