Abstract: The problem of nonlinear oscillations of a two-layer liquid completely filling a limited volume is considered. Using two basic asymmetric harmonics excited in two mutually perpendicular planes, ordinary differential equations of nonlinear oscillations of the interface of a two-layer liquid are investigated. In this paper, hydrodynamic coefficients of linear and nonlinear problems in integral relations were determined. As a result, the instability regions of forced oscillations of a two-layered liquid in a cylindrical tank occurring in the plane of action of the disturbing force are constructed, as well as the dynamic instability regions of the parametric resonance for different ratios of densities of the upper and lower liquids depending on the amplitudes of liquids from the excitations frequencies. Steady-state regimes of fluid motion were found in the regions of dynamic instability of the initial oscillation form. The Bubnov-Galerkin method is used to construct instability regions for approximate solution of nonlinear differential equations.
Abstract: We have previously introduced an ultrasonic imaging
approach that combines harmonic-sensitive pulse sequences with a
post-beamforming quadratic kernel derived from a second-order
Volterra filter (SOVF). This approach is designed to produce images
with high sensitivity to nonlinear oscillations from microbubble
ultrasound contrast agents (UCA) while maintaining high levels of
noise rejection. In this paper, a two-step algorithm for computing the
coefficients of the quadratic kernel leading to reduction of tissue
component introduced by motion, maximizing the noise rejection and
increases the specificity while optimizing the sensitivity to the UCA
is presented. In the first step, quadratic kernels from individual
singular modes of the PI data matrix are compared in terms of their
ability of maximize the contrast to tissue ratio (CTR). In the second
step, quadratic kernels resulting in the highest CTR values are
convolved. The imaging results indicate that a signal processing
approach to this clinical challenge is feasible.