The implementation of stable, accurate, and wideband second-order microwave integrators (SOMIs) is presented in this paper. These designs of SOMIs are obtained by using different combinations of transmission line sections and shunt stubs in cascading. Particle swarm optimization (PSO), cuckoo search algorithm (CSA), and gravitational search algorithm (GSA) are applied to obtain the optimal values of the characteristic impedances of these line elements to approximate the magnitude response of ideal second-order integrator (SOI). The performance measure criteria for the proposed SOMIs are carried out based on magnitude response, absolute magnitude error, phase response, convergence rate, pole-zero plot, and improvement graph. The simulation results and statistical analysis demonstrate that GSA surpasses the PSO and CSA to approximate the ideal SOI in all state-of-the-art, that is eligible for wide-band microwave integrator. The designed SOMI is compact in size and suitable to cover microwave applications. The magnitude errors for the proposed SOMIs GSA based are as low as 4.9954 and 3.6573, respectively. The structure of the designed SOMI is implemented in the form of microstrip line on RT/Duroid substrate with dielectric constant 2.2 and having height 0.762 mm. The simulated and measured magnitude result agrees well with the ideal one in the frequency range of 3–15 GHz.

We analyze in this paper the pressure splitting scheme of a partitioned semi-implicit coupling algorithm for fluid-structure interaction (FSI) simulation. The semi-implicit coupling algorithm is developed on the ground of the artificial compressibility characteristic-based split (AC-CBS) scheme that serves not only for the fluid subsystem but also for the global FSI system. As the dual-time stepping procedure recommended for quasi-incompressible flows is incorporated into the implicit coupling stage, the fluctuating pressure may be unusually susceptible to the AC coefficient. Moreover, it is not trivial to devise an optimal AC formulation for pressure estimation. Instead, we consider a stabilized second-order pressure splitting scheme in the AC-CBS-based partitioned semi-implicit coupling algorithm. Computer simulation of a benchmark FSI experiment demonstrates that good agreement is exposed between the available and present data.

We study the existence of multiple solutions for a two-point boundary-value problem associated with a planar system of second-order ordinary differential equations by using a shooting technique. We consider asymptotically linear nonlinearities satisfying suitable sign conditions. Multiplicity is ensured by assumptions involving the Morse indices of the linearizations at zero and at infinity.

Consider the second order nonlinear differential equation

y" + a(t)f(y) = 0

where a(t) ∈ C[0,∞),f(y) GC1 (-∞, ∞),ƒ'(y) ≥ 0 and yf(y) > 0 for y ≠ 0. Furthermore, f(y) also satisfies either a superlinear or a sublinear condition, which covers the prototype nonlinear function f(y) = |γ|γ sgny with γ > 1 and 0 < γ < 1 known as the Emden-Fowler case. The coefficient a(t) is allowed to be negative for arbitrarily large values of t. Oscillation criteria involving integral averages of a(t) due to Wintner, Hartman, and recently Butler, Erbe and Mingarelli for the linear equation are shown to remain valid for the general equation, subject to certain nonlinear conditions on f(y). In particular, these results are therefore valid for the Emden-Fowler equation.