We propose a novel floating memristor chaotic circuit with serial connection between a charge-controlled memristor and an inductor.Basic dynamic properties of the system are investigated with conventional dynamic analysis method. It shows that the system produces a pair of "heart" type attractors about origin symmetry. Simulation results indicate that strange attractors like bow tie type are observed as voltage and electricity signal in observing chaotic attractors are generalized to power and energy signal. Hopf bifurcation behavior is analyzed and verified by numerical simulation. It shows that the system can produce two bifurcation behaviors by adjusting parameters. They are Hopf bifurcation and anti-period doubling bifurcation. Remarkable feature of the citcuit is that it adopts a floating memristor, and with different initial state it generates nonlinear phenomena including coexisting chaotic and coexisting chaotic-periodic attractors.

Taking 3D acoustic analysis as an example, a semi-analytic algorithm is proposed which can be used to compute nearly singular integrals with high order element exactly. With analysis of geometry features of high order elements, approximate geometric parameters are constructed. Then, a kernel function of nearly singular integral is decomposed into two parts using subtraction method. One is regular part and the other is singular part. Integral of regular part is computed accurately using conventional Gauss quadrature. For integral of the singular part, semi-analytic algorithm gives exact result. Classical examples are given including 3D acoustic internal and external problems. Sound pressures at points near boundary are calculated with different methods. Comparisons of results demonstrate accuracy and effectiveness of the algorithm.