Dynamics of Simple Balancing Models with State Dependent Switching Control

Time-delayed control in a balancing problem may be a nonsmooth function for a variety of reasons. In this paper we study a simple model of the control of an inverted pendulum by either a connected movable cart or an applied torque for which the control is turned off when the pendulum is located within certain regions of phase space. Without applying a small angle approximation for deviations about the vertical position, we see structurally stable periodic orbits which may be attracting or repelling. Due to the nonsmooth nature of the control, these periodic orbits are born in various discontinuity-induced bifurcations. Also we show that a coincidence of switching events can produce complicated periodic and aperiodic solutions.Comment: 36 pages, 12 figure

"Assessing how electroporation affects the effective conductivity tensor of biological tissues"

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Comparison of single-shot rapid acquisition with relaxation enhancement and echo planar current density MRI sequences for monitoring of electric pulse delivery in irreversible electroporation

Success of electroporation treatment critically depends on coverage of the target tissue with electric field. The electric field during delivery of the electroporation pulses can be reconstructed by the magnetic resonance electric impedance tomography, a method that uses current density distribution data and electric potentials at the electrodes for reconstruction of electric field in the sample. In this study, two complementary MRI methods for current density imaging during delivery of irreversible electroporation pulses are presented. One of the methods is based on the single-shot rapid acquisition with relaxation enhancement while the other is based on the echo planar imaging MRI method. The methods were compared in terms of their sensitivity and susceptibility to image artifacts by experiments on a liver test sample that were performed on a 2.35 T small bore MRI scanner. In the experiments, a standard protocol for irreversible electroporation where 90 electric pulses of 100 μs, 3000 V are delivered at 1 Hz was performed. Results of the study confirmed that both methods have comparable sensitivity. The RARE-based method was found less susceptible to artifacts while the EPI-based method has lower SAR value and may therefore be a better candidate for use in clinics