On the estimation of nonlinear time series models

In the present paper, a framework for parametric estimation in nonlinear time series is developed. Strong consistency and asymptotic normality of minimum Hellinger distance estimates for a determined class of nonlinear models are investigated. The main Interest for these estimates is motivated by their robustness under perturbations as it has been emphazized in Beran [2]. The first part of the paper is devoted to the study of some probabilistic properties which ensure the existence and the optimal properties of the estimates     

Time-delay effects on dynamics of a two-actor conflict model

We present a study of time-delay effects on a two-actor conflict model based on nonlinear differential equations. The state of each actor depends on its own state in isolation, its previous state, its inertia to change, the positive or negative feedback and a time delay in the state of the other actor. We use both theoretical and numerical approaches to characterize the evolution of the system for several values of time delays. We find that, under particular conditions, a time delay leads to the appearance of oscillations in the states of the actors. Besides, phase portraits for the trajectories are presented to illustrate the evolution of the system for different time delays. Finally, we discuss our results in the context of social conflict models.     

Time optimality and the maximum principle in infinite dimension

We present three counterexamples related to the maximum principle for the time optimal problem. The system is linear, infinite dimensional, with point target and “full” control     

Optimal feedback gains of a delayed proportional-derivative (PD) control for balancing an inverted pendulum

In the dynamics analysis and synthesis of a con-trolled system, it is important to know for what feedback gains can the controlled system decay to the demanded steady state as fast as possible. This article presents a sys-tematic method for finding the optimal feedback gains by taking the stability of an inverted pendulum system with a delayed proportional-derivative controller as an example. First, the condition for the existence and uniqueness of the stable region in the gain plane is obtained by using the D-subdivision method and the method of stability switch. Then the same procedure is used repeatedly to shrink the stable region by decreasing the real part of the rightmost charac-teristic root. Finally, the optimal feedback gains within the stable region that minimizes the real part of the rightmost root are expressed by an explicit formula. With the optimal feedback gains, the controlled inverted pendulum decays to its trivial equilibrium at the fastest speed when the initial val-ues around the origin are fixed. The main results are checked by numerical simulation.     

On the moments of the time to ruin in dependent Sparre Andersen models with emphasis on Coxian interclaim times

The structural properties of the moments of the time to ruin are studied in dependent Sparre Andersen models. The moments of the time to ruin may be viewed as generalized versions of the Gerber–Shiu function. It is shown that structural properties of the Gerber–Shiu function hold also for the moments of the time to ruin. In particular, the moments continue to satisfy defective renewal equations. These properties are discussed in detail in the model of Willmot and Woo (2012), which has Coxian interclaim times and arbitrary time-dependent claim sizes. Structural quantities needed to determine the moments of the time to ruin are specified under this model. Numerical examples illustrating the methodology are presented.     

Direct calculation of time varying Aharonov-Bohm effect

The Aharonov-Bohm effect (ABE) for steady magnetic fields is a well known phenomenon. However, if the current in the infinite solenoid that creates the magnetic field is time-dependent, that is in the presence of both magnetic and electric fields, there is no agreement whether the effect would be present. In this note, we try to investigate time varying ABE by a direct calculation in a set-up with a weak time dependent magnetic field. We find that the electric field arising out of the time-varying magnetic field in the path of the electrons does not enter the action integral but only changes the path of the electron from the source to the slits and then on to the detector. We find a frequency dependent AB phase shift. At low frequencies the result smoothly approaches the one for a constant field as the frequency tends towards zero. On the other hand, for high frequencies such that the AB-phase induced in the path of the wave packet oscillates rapidly, the net effect will be very small which is borne out by our results.     

Time reversal acoustic communication receivers: DSP implementation and fast channel estimation

A communication system is implemented on digital signal processors (DSPs) for the underwater acoustic environment. The implemented receiver uses time reversal multi-channel combining followed by a single-channel decision feedback equalizer. Periodic channel estimation is employed to track the channel fluctuations. These techniques are used to mitigate time-varying inter-symbol interference, which is the main challenge in the underwater acoustic channel at operating frequencies greater than 10 kHz. Various optimization tasks are performed to reduce the receiver computational complexity. A fast implementation of the matching pursuit algorithm is tested on the DSP platform. Its performance, in terms of accuracy and run-time, is compared with that of the basic matching pursuit algorithm. Experimental results of the transmission and demodulation of binary phase-shift keying signals at three different symbol rates were obtained in the local Delaware Bay. The low bit error rates demonstrate the effectiveness of our implementation.     

Concentration Dependence of NMR T1 in Agar Solutions

In this study, in order to explain solvent proton relaxation mechanism, the spin-lattice relaxation time (T1) of agar solutions was measured as a function of agar concentration. Relaxation measurements were carried out by a FT-NMR spectrometer operating at 60 MHz and inversion recovery pulse squence was used. Relaxation rate(1/T1a) was linearly proportional to concentration of agar solution (C), and the T1 mechanism of solvent water protons in agar solutions should be caused by the chemical exchange of water protons between free and bound water.     

Super-resolution in time-reversal focusing on a moving source

This paper presents a detailed analysis of time-reversal experiments involving a moving point source that emits a pulse. Different configurations are addressed with full-aperture or partial-aperture time-reversal mirrors and with subsonic or supersonic sources. Doppler effects and lack of source-receiver reciprocity significantly affect the time-reversal refocusing when the velocity of the source becomes comparable as or larger than the speed of propagation. The main result is that refocusing can be enhanced when the velocity of the source becomes close to the speed of propagation compared to the classical diffraction-limited refocusing properties when the source does not move, and this super-resolution effect can be quantified by simple and explicit formulas.     

Time domain simulation of vortex-induced vibrations in stationary and oscillating flows

This paper focuses on the further development of a previously published semi-empirical method for time domain simulation of vortex-induced vibrations (VIV). A new hydrodynamic damping formulation is given, and the necessary coefficients are found from experimental data. It is shown that the new model predicts the observed hydrodynamic damping in still water and for cross-flow oscillations in stationary incoming flow with high accuracy. Next, the excitation force model, which is one component of the total hydrodynamic force model, is optimized by simulating the VIV response of an elastic cylinder in a series of experiments with stationary flow. The optimization is performed by repeating the simulations until the best possible agreement with the experiments is found. The optimized model is then applied to simulate the cross-flow VIV of an elastic cylinder in oscillating flow, without introducing any changes to the hydrodynamic force modeling. By comparison with experiment, it is shown that the model predicts the frequency content, mode and amplitude of vibration with a high level of realism, and the amplitude modulations occurring at high Keulegan–Carpenter numbers are well captured. The model is also utilized to investigate the effect of increasing the maximum reduced velocity and the mass ratio of the elastic cylinder in oscillating flow. Simulations show that complex response patterns with multiple modes and frequencies appear when the maximum reduced velocity is increased. If, however, the mass ratio is increased by a factor of 5, a single mode dominates. This illustrates that, in oscillating flows, the mass ratio is important in determining the mode participation at high maximum reduced velocities.