Igor A. Khovanov

The role of excitations statistic and nonlinearity in energy harvesting from random impulsive excitations

Design of an efficient energy harvester is now feasible as technology develops and a viable approach to solve this need is to exploit the concept and application of a nonlinear design. In this letter, we conducted a comparative analysis of linear and nonlinear piezoelectric energy harvesting from random impulsive excitations modelled by white Poisson noise. It is shown that the harvester performance depends on both nonlinearity and properties of ambient energy, and nonlinearity should be optimized for a given type of ambient vibration in order to achieve efficient harvesting.

OPTIMAL FLUCTUATIONS AND THE CONTROL OF CHAOS

The energy-optimal migration of a chaotic oscillator from one attractor to another coexisting attractor is investigated via an analogy between the Hamiltonian theory of fluctuations and Hamiltonian formulation of the control problem. We demonstrate both on physical grounds and rigorously that the Wentzel-Freidlin Hamiltonian arising in the analysis of fluctuations is equivalent to Pontryagins Hamiltonian in the control problem with an additive linear unrestricted control. The deterministic optimal control function is identied with the optimal fluctuational force. Numerical and analogue experiments undertaken to verify these ideas demonstrate that, in the limit of small noise intensity, fluctuational escape from the chaotic attractor occurs via a unique (optimal) path corresponding to a unique (optimal) fluctuational force. Initial conditions on the chaotic attractor are identified. The solution of the boundary value control problem for the Pontryagin Hamiltonian is found numerically. It is shown that this solution is approximated very accurately by the optimal fluctuational force found using statistical analysis of the escape trajectories. A second series of numerical experiments on the deterministic system (i.e. in the absence of noise) show that a control function of precisely the same shape and magnitude is indeed able to instigate escape. It is demonstrated that this control function minimizes the cost functional and the corresponding energy is found to be smaller than that obtained with some earlier adaptive control algorithms.

Intrinsic dynamics of heart regulatory systems on short timescales : from experiment to modelling

We discuss open problems related to the stochastic modeling of cardiac function. The work is based on an experimental investigation of the dynamics of heart rate variability (HRV) in the absence of respiratory perturbations. We consider first the cardiac control system on short time scales via an analysis of HRV within the framework of a random walk approach. Our experiments show that HRV on timescales of less than a minute takes the form of free diffusion, close to Brownian motion, which can be described as a non-stationary process with stationary increments. Secondly, we consider the inverse problem of modeling the state of the control system so as to reproduce the experimentally observed HRV statistics of. We discuss some simple toy models and identify open problems for the modelling of heart dynamics.

Sodium binding sites and permeation mechanism in the NaChBac channel : a molecular dynamics study

NaChBac was the first discovered bacterial sodium voltage-dependent channel, yet computational studies are still limited due to the lack of a crystal structure. In this work, a pore-only construct built using the NavMs template was investigated using unbiased molecular dynamics and metadynamics. The potential of mean force (PMF) from the unbiased run features four minima, three of which correspond to sites IN, CEN, and HFS discovered in NavAb. During the run, the selectivity filter (SF) is spontaneously occupied by two ions, and frequent access of a third one is often observed. In the innermost sites IN and CEN, Na+ is fully hydrated by six water molecules and occupies an on-axis position. In site HFS sodium interacts with a glutamate and a serine from the same subunit and is forced to adopt an off-axis placement. Metadynamics simulations biasing one and two ions show an energy barrier in the SF that prevents single-ion permeation. An analysis of the permeation mechanism was performed both computing minimum energy paths in the axial-axial PMF and through a combination of Markov state modeling and transition path theory. Both approaches reveal a knock-on mechanism involving at least two but possibly three ions. The currents predicted from the unbiased simulation using linear response theory are in excellent agreement with single-channel patch-clamp recordings.

Stochastic webs and quantum transport in superlattices: an introductory review

Stochastic webs were discovered, first by Arnold for multi-dimensional Hamiltonian systems, and later by Chernikov et al. for the low-dimensional case. Generated by weak perturbations, they consist of thread-like regions of chaotic dynamics in phase space. Their importance is that, in principle, they enable transport from small energies to high energies. In this introductory review, we concentrate on low-dimensional stochastic webs and on their applications to quantum transport in semiconductor superlattices subject to electric and magnetic fields. We also describe a recently-suggested modification of the stochastic web to enhance chaotic transport through it and we discuss its possible applications to superlattices.

A New Approach to the Treatment of Separatrix Chaos and Its Applications

We consider time-periodically perturbed 1D Hamiltonian systems possessing one or more separatrices. If the perturbation is weak, then the separatrix chaos is most developed when the perturbation frequency lies in the logarithmically small or moderate ranges: this corresponds to the involvement of resonance dynamics into the separatrix chaos. We develop a method matching the discrete chaotic dynamics of the separatrix map and the continuous regular dynamics of the resonance Hamiltonian. The method has allowed us to solve the long-standing problem of an accurate description of the maximum of the separatrix chaotic layer width as a function of the perturbation frequency. It has also allowed us to predict and describe new phenomena including, in particular: (i) a drastic facilitation of the onset of global chaos between neighbouring separatrices, and (ii) a huge increase in the size of the low-dimensional stochastic web.

Nonlinear Energy Harvesting from Random Narrow-Band Excitations

The efficiency of linear and nonlinear harvesters with different types of nonlinearity is compared. Narrow band ambient vibrations are modeled by harmonic Gaussian noise. We show that the performance of nonlinear harvesters strongly depends on both the form of nonlinearity and the properties of the noise. Particular forms of nonlinearities which can produce a better than linear response are identified, and these depend on the spectral width of the harmonic noise.

Dynamics of ions in the selectivity filter of the KcsA channel

The statistical and dynamical properties of ions in the selectivity filter of the KcsA ion channel are considered on the basis of molecular dynamics (MD) simulations of the KcsA protein embedded in a lipid membrane surrounded by an ionic solution. A new approach to the derivation of a Brownian dynamics (BD) model of ion permeation through the filter is discussed, based on unbiased MD simulations. It is shown that depending on additional assumptions, ion’s dynamics can be described either by under-damped Langevin equation with constant damping and white noise or by Langevin equation with a fractional memory kernel. A comparison of the potential of the mean force derived from unbiased MD simulations with the potential produced by the umbrella sampling method demonstrates significant differences in these potentials. The origin of these differences is an open question that requires further clarifications.

A NEW APPROACH TO THE TREATMENT OF SEPARATRIX CHAOS

We review an approach to separatrix chaos that has allowed us to solve some significant problems by: (i) finding analytically the maximum width of the chaotic layer, a problem that lay unsolved for 40 years, and showing that the maximum may be much larger than had previously been assumed; (ii) describing the drastic facilitation of the onset of global chaos between neighboring separatrices, a phenomenon discovered eight years ago.

Numerical simulations versus theoretical predictions for a non-Gaussian noise induced escape problem in application to full counting statistics

A theoretical approach for characterizing the influence of asymmetry of noise distribution on the escape rate of a multistable system is presented. This was carried out via the estimation of an action, which is defined as an exponential factor in the escape rate, and discussed in the context of full counting statistics paradigm. The approach takes into account all cumulants of the noise distribution and demonstrates an excellent agreement with the results of numerical simulations. An approximation of the third-order cumulant was shown to have limitations on the range of dynamic stochastic system parameters. The applicability of the theoretical approaches developed so far is discussed for an adequate characterization of the escape rate measured in experiments.