Synchronization framework for modeling transition to thermoacoustic instability in laminar combustors

We, herein, present a new model based on the framework of synchronization to describe a thermoacoustic system and capture the multiple bifurcations that such a system undergoes. Instead of applying flame describing function to depict the unsteady heat release rate as the flame's response to acoustic perturbation, the new model considers the acoustic field and the unsteady heat release rate as a pair of nonlinearly coupled damped oscillators. By varying the coupling strength, multiple dynamical behaviors, including limit cycle oscillation, quasi-periodic oscillation, strange nonchaos, and chaos can be captured. Furthermore, the model was able to qualitatively replicate the different behaviors of a laminar thermoacoustic system observed in experiments by Kabiraj et al.~[Chaos 22, 023129 (2012)]. By analyzing the temporal variation of the phase difference between heat release rate oscillations and pressure oscillations under different dynamical states, we show that the characteristics of the dynamical states depend on the nature of synchronization between the two signals, which is consistent with previous experimental findings.Comment: 18 pages, 7 figure

Incommensurate dynamics of resonant breathers in Josephson junction ladders

We present theoretical and experimental studies of resonant localized resistive states in a Josephson junction ladder. These complex breather states are obtained by tuning the breather frequency into the upper band of linear electromagnetic oscillations of the ladder. Their prominent feature is the appearance of resonant steps in the current-voltage (I-V) characteristics. We have found the resonant breather-like states displaying incommensurate dynamics. Numerical simulations show that these incommensurate resonant breathers persist for very low values of damping. Qualitatively similar incommensurate breather states are observed in experiments performed with Nb-based Josephson ladders. We explain the appearance of these states with the help of resonance-induced hysteresis features in the I-V dependence.Comment: 5 pages, 6 figure

Boolean Delay Equations: A simple way of looking at complex systems

Boolean Delay Equations (BDEs) are semi-discrete dynamical models with Boolean-valued variables that evolve in continuous time. Systems of BDEs can be classified into conservative or dissipative, in a manner that parallels the classification of ordinary or partial differential equations. Solutions to certain conservative BDEs exhibit growth of complexity in time. They represent therewith metaphors for biological evolution or human history. Dissipative BDEs are structurally stable and exhibit multiple equilibria and limit cycles, as well as more complex, fractal solution sets, such as Devil's staircases and ``fractal sunbursts``. All known solutions of dissipative BDEs have stationary variance. BDE systems of this type, both free and forced, have been used as highly idealized models of climate change on interannual, interdecadal and paleoclimatic time scales. BDEs are also being used as flexible, highly efficient models of colliding cascades in earthquake modeling and prediction, as well as in genetics. In this paper we review the theory of systems of BDEs and illustrate their applications to climatic and solid earth problems. The former have used small systems of BDEs, while the latter have used large networks of BDEs. We moreover introduce BDEs with an infinite number of variables distributed in space (``partial BDEs``) and discuss connections with other types of dynamical systems, including cellular automata and Boolean networks. This research-and-review paper concludes with a set of open questions.Comment: Latex, 67 pages with 15 eps figures. Revised version, in particular the discussion on partial BDEs is updated and enlarge

CONTROL OF SERIES IMPEDANCE OF POWER LINES USING POWER FLOW CONTROLLER

In this paper, the possibility of unified power flow controller (UPFC) to modulate both series resistance R and series reactance X of an overhead power line is discussed. The classical power flow control system of the UFPC is modified in the manner that standard input references signals (active and reactive powers) are replaced by reference signals of series resistance and reactance. Using the procedure described in this work, the reference signals for active and reactive powers are generated indirectly. The operation of UPFC in proposed operation mode is analyzed using computer simulation, based on a model of single machine infinite bus (SMIB) with constant impedance loads and two parallel lines. The goal is to show that UPFC is capable to control both series line parameters (R and X) directly and independently by means of a simple control system without additional decoupling controllers. An additional task is to show that power flows can be indirectly controlled this way. The step response of series line resistance and reactance is used to validate the operation of the proposed control system. The obtained results clearly show that all goals are fulfilled

MPPT oscillations minimization in PV system by controlling non-linear dynamics in SEPIC DC-DC converter

Solar PV power generation has achieved rapid growth in developing countries which has many merits such as absence of noise, longer life, no pollution, less time for installation, and ease of grid interface. A maximum power point tracking circuit (MPPT) consists of DC-DC power electronics converters that are used to improve the energy attainment from solar PV array. This paper presents a detailed analysis to control of chaos, a non-linear dynamic in SEPIC DC-DC converter interfaced solar PV system, to minimize the oscillations near to MPP. In SEPIC DC-DC converter, the input inductor current is continuous and capable of sweeping the whole I-V curve of a PV module from open circuit voltage (Voc) to short circuit current (Isc) operating points. To trace the true maximum power point and to nullify the oscillations near to MPP, the yield output voltage needs to ensure period-1 operation