The concept is based on a mesoscale approach in which the non-slip boundary conditions in the vicinity of the packed beds are explicitly imposed by utilizing the immersed boundary (IB) method.
By utilizing the synergy of boundary and probabilistic power flow algorithms, development of efficient line outage simulation and use of constant Jacobian approach, the computational burden has been kept to a manageable level.
By utilizing the anti-periodic boundary condition (x(1) = - x(T)), it follows that c_{1} = -frac{1}{2} biggl[ I^{alpha}biggl( frac{1}{p}I^{beta}g_{x} biggr) (T) - I^{alpha}biggl( frac{r}{p}x biggr) (T) + c_{0} I^{alpha}biggl( frac{1}{p} biggr) (T) biggr].
The authors have successfully derived these functions by utilizing the Papkovich Neuber potentials and appropriate boundary conditions.
For example, in [23], He and Zhang analyzed the existence for the extremal solutions to first order impulsive difference equations with periodic boundary conditions by utilizing the monotone iterative technique under these two cases.
6– 8, 10, 12, 13 We applied TSA by utilizing the Lan-DeMets alpha-spending approach with monitoring boundaries corresponding to the O'Brien-Fleming boundaries to assess the reliability of pooled inferences from our meta-analysis on TB. 10, 22 Three systematic reviews on the topic have previously been published in year 1998, 1999, and 2004.
The governing equations, initial conditions and boundary conditions are derived by utilizing the Hamilton's principle.
Based on the theory of surface piezoelectricity and nonlocal piezoelectricity, a novel two-dimensional theory of piezoelectric nanoplates and boundary conditions are derived by utilizing the Hamilton's principle.
They dealt with many boundary conditions given in the literature in a unified way by utilizing the fixed point index theory in cones.
The variational consistent equilibrium equations and boundary conditions in terms of both displacements and stress resultants are derived by utilizing the variational principle.
