Despite advances in design and fabrication, backlash remains a fundamental problem in precision mechanical applications. Deadzone and "play" in mechanical couplings cause hysteretic behavior as can structural components with memory. This behavior can degrade the performance of mechanical systems. When the system involves servo control, backlash can cause undesirable limit cycle oscillations. Ou...

Understanding biomolecular systems is important both for the analysis of naturally occurring systems as well as for the design of new ones. However, mathematical tools for analysis of such complex systems are generally lacking. Here, we present an application of the method of sinusoidal-input describing function for the analysis of such a system. Using this technique, we approximate the input-o...

An analysis is presented for the transfer functions of a particular pulse-width modulator and power switch subsystem that has been widely used in practical switching-mode d-c regulator systems. The switch and filter are in a "buck" configuration, and the switch is driven by a con­ stant-frequency variable duty-ratio push-pull magnetic modulator employing square-loop cores. The two transfer func...

Most of the DNA in a eucaryotic cell nucleus is accurately described as an extremely long thin fiber which is smoothly folded by histones into a thicker fiber called the 30 nm fiber. For the DNA to remain biologically functional, the 30 nm fiber must be only marginally stable. Therefore, we assume that the 30 nm fiber has fluidlike properties under physiologic conditions. It does not possess a ...

Abstract. We propose a many-body wave function that exhibits both diagonal and off-diagonal long-range order. Incorporating short-range correlations due to interatomic repulsion, this wave function is shown to allow condensation of zero-point lattice vibrations and phase rigidity. In the presence of an external velocity field, such a perfect crystal will develop non-classical rotational inertia...

We consider comparator-based nonlinear feedback systems, and use Tsypkin’s method to develop a strategy with which to find systems with low-pass linear part for which the describing function technique erroneously predicts limit cycles. We produce an infinite set of examples of systems with very low-pass linear parts for which the describing function technique predicts spurious limit cycles, and...

The robust control problem for nonlinear systems is discussed from the standpoint of the amplitude sensitivity of the nonlinear plant and final control system. Failure to recognize and accommodate this factor may give rise to nonlinear control systems that behave differently for small versus large input excitation, or perhaps exhibit limit cycles or instability. Sinusoidal-input describing func...

In this paper, we are going to estimate the domain of attraction of tumor-free equilibrium points in a perturbed cancer tumor model describing the tumor-immune system competition dynamics. The proposed method is based on an optimization problem solution for a chosen Lyapunov function that can be casted in terms of Linear Matrix Inequalities constraint and Taylor expansion of nonlinear terms. We...