Sentence examples for modes solutions to from inspiring English sources
To eliminate the numerical stiffness caused by the interaction of slow and fast dynamic modes, solutions to the problem are presented in terms of LMIs which are independent of the singular perturbation ε.
To alleviate the numerical stiffness resulting from the interaction of slow and fast dynamic modes, solutions to the problem are given in terms of linear matrix inequalities which are independent of the singular perturbation ε.
To eliminate the ill-conditioning caused by the interaction of slow and fast dynamic modes, solutions to the problem are presented in terms of LMIs which are independent of the singular perturbation ɛ.
A suboptimal dual-mode solution to constrained nonlinear quadratic regulator (CNLQR) problem is studied.
The specified non-uniform velocity of the vibrator is expressed as a time-dependent modal expansion where the modes are solutions to the homogeneous problem.
In modal analysis, the exact normal mode solutions corresponding to the eigenfrequencies for each position of the moving mass and the ratios of the weight of the beam mass cart system are used.
The resulting normal mode solutions are compared to those obtained by the finite element analysis for several examples of transmission containing flexible gears.
The ESWs in space are regarded to as electron phase-space potential holes (electron holes, EHs) that are the Bernstein-Greene-Kruskal (BGK) modes, i.e., 1D equilibrium solutions to the time-independent Vlasov-Poisson equations [Bernstein et al. [1957]; Chen and Parks [2002].
The phononic field (Pi t,x)) is then quantized by associating creation and annihilation operators (a^{dagger}_{k}) and (a_{k}) to the mode solutions of the Klein-Gordon equation in the effective metric [5, 20], and can be expanded as (Pi t,x)= sum_{k} [ phi_{k} t,x) a_{k} + phi^_{k} t,x) a^{dagger}_{k}]).
A normal-mode solution is applied to a set of non-dimensional coupled partial differential equations.
Explicit mode solution forms leading to a pair of simultaneous equations which determine the characteristic frequencies are found when a certain linear cross-densities relationship is satisfied.
