Browsing by Subject "Nonlinear dynamics"

Now showing 1 - 4 of 4

Open Access
Dynamical effects of noise on nonlinear systems
(2014) Duman, Özer
Randomness and nonlinear dynamics consitute the most essential part of many events in nature. Therefore, a better and comprehensive understanding of them is a crucial step in describing natural phenomena as well as the prospect of predicting their future outcome. Besides the interest from a fundamental point of view, it is also useful in a wide variety of applications requiring delicate and careful use of energy. Especially recent advances in micro- and nano-scale technology requires harnessing the underlying noise itself as it is relatively hard to exert forces without damaging the system at that scale. The main aim of this work is to study the effects of noise on nonlinear dynamics. We show that the interplay between noise, nonlinearity and nonequilibrium conditions leads to a finite drift with the potential to change the dynamics of the system completely in a predictable and tunable fashion. We report that the noise-induced drift disrupts the phase space of a 2-D nonlinear system by shifting the fixed point by a finite amount which may result in dramatic alterations over the temporal behavior of the system. We track such alterations to several multi-dimensional model systems from ecology, soft matter and statistical physics. In a 2-D ecological model describing two species competing for the same resource, it is found that the system switches between coexistence and extinction states depending on the shift due to the noise-induced drift whereas for an aggregate of Brownian particles, it is shown that noise-induced drift selectively shifts the probability distribution in certain geometries which can be used in the realization of a microparticle sorter in the mould of Feynman ratchets. In the case of the aggregate consisting of microswimmers, tunable anomalous diffusion depending on the confinement length is reported.
Open Access
Herarchically slaved multi-pulsing mode-lock dynamics
(2021-09) Choura, Aladin
Passive mode-locking is the self-assembly of optical energy in a laser cavity to-wards narrow pulses. Often, the energy available in the cavity goes into multiple coexisting pulses with little control on their number, their energies, or their tem-poral positions. This phenomenon is vaguely known as pulse energy quantization and has been anecdotally linked to pulse splitting induced by optical nonlinear-ity. Research has focussed mainly on avoiding pulse energy quantization and any complex behavior associated with it while driving the pulses to higher and higher energies. The complex multi-pulsing behavior is often regarded as an output of a black box ﬁlled with complex nonlinear dynamics with little hope to control it. There’s a want for a clear and workable understanding of these dynamics. The central point of this thesis is that standard, few-dimensional, nearly de-terministic nonlinear dynamics oﬀers this understanding; while mode-locking is indeed the result of noisy interactions of thousands of optical modes shaping the optical pulses, due to fast pulse-shaping processes involved in mode-locking, the pulse shapes tend to be slaved to one or few order parameters, mainly the pulse energy. Then, the complex behavior is understood as the result of a much simpler nonlinear dynamical system. This understanding is supported by our experiments on a multi-pulsing Mamyshev oscillator, and in return, it guides us towards re-liably controlling it. With this control, multiple pulsation, which has been little more than a scientiﬁc curiosity, becomes technologically valuable for applications such as ablation-cooled material removal and frequency metrology. First, we address the issue of multiple pulsation. We deﬁne an energy map which describes the evolution of each pulse. Using the energy map, we show that stable coexistence of multiple pulses is permitted despite their competition on the gain if the growth of a pulse is self-limiting, i.e., if the energy map features a stable ﬁxed point even at a constant gain. The energy map similarly explains the intimately related phenomena of period-doubling, non-identical pulses, and response to perturbations. The physical processes leading to these phenomena in our laser and others are discussed in parallel, and analogies to other systems are drawn. Many attractors are permitted by the energy map, highlighting the eﬀect of bifurcations, hysteresis, and kinetics of pulse formation. Accordingly, we present guidelines for the control of multi-pulsing lasers and a procedure to control the number of pulses in a Mamyshev oscillator. Having controlled the number of pulses, we turn our attention to the temporal organization they take. Pulses coexisting in a laser cavity tend to evolve towards stable patterns due to long-range interactions between them. Several interaction mechanisms have been proposed in the literature, but the pulse interactions are still poorly understood. This is due partially to the multitude of possible inter-action mechanisms and partially to the focus of their discussion on the physical processes that allow the pulses to interact without analyzing the dynamics that result from these interactions. We argue that the temporal organization dynamics is slaved and present the form of the dynamical system for all long-ranged inter-action mechanisms and use it to derive for the ﬁrst time the stability criterion for harmonic mode-locking. A comparison between the interaction mechanisms sug-gests the dominance of acoustically mediated interactions in our oscillator. We show theoretically that the acoustic eﬀect is coupled to the single-pulse evolution dynamics and inﬂuences the individual pulse energies, which in turn, slave their speeds. This is a distinguishing feature of pulse interactions in our oscillator. We show experimentally that these interactions permit multiple stable ﬁxed points for a given number of pulses and demonstrate noise-induced transitions as well as bifurcation based on parameters of single-pulse mode-lock dynamics, conﬁrm-ing our interaction theory. Lastly, we demonstrate drastic manipulation of the acoustic interactions using a novel secondary loop, allowing richer pulse patterns, and further supporting our interactions theory.
Open Access
Numerical study on a polymer-shelled microbubble submerged in soft tissue
(IOP Publishing, 2020) Ghalichi, F.; Behnia, S.; Mottaghi, F.; Yahyavi, Mohammad
Ultrasound contrast agents have been recently utilized in therapeutical implementations for targeted delivery of pharmaceutical substances. Radial pulsations of the encapsulated microbubbles under the action of an ultrasound field are complex and high nonlinear, particularly for drug and gene delivery applications with high acoustic pressure amplitudes. The dynamics of a polymer-shelled agent are studied through applying the method of chaos physics whereas the effects of the outer medium compressibility and the shell were considered. The stability of the ultrasound contrast agent is examined by plotting the bifurcation diagrams, Lyapunov exponent, and time series over a wide range of variations of influential parameters. The findings of the study indicate that by tuning the shear modulus of surrounding medium and shell viscosity, the radial oscillations of microbubble cluster undergoes a chaotic unstable region as the amplitude and frequency of ultrasonic pulse are increased mainly due to the period doubling phenomenon. Furthermore, influences of various parameters which present a comprehensive view of the radial oscillations of the microbubble are quantitatively discussed with clear descriptions of the stable and unstable regions of the microbubble oscillations for typical therapeutic ultrasound pulses.
Open Access
Reservoir computing model using a single nonlinear nanoelectromechanical resonator at atmospheric conditions
(2024-07) Kartal, Enise
Reservoir computing is an alternative method to conventional systems using computationally expensive recurrent neural networks (RNNs). In this method, the training is performed only at the final layer of a nonlinear physical system functioning as a black box substituted instead of the hidden layers in RNNs requiring intensive training. This study suggests using a small nanoelectromechanical systems (NEMS) resonator with intrinsic nonlinearities for reservoir computing instead of relying on complicated feedback loops or spatially extended reservoirs as used in the earlier works. The linear classification is made possible by trans-forming the input data into a higher dimensional space, which is accomplished by utilizing the combination of the nonlinearity of the NEMS resonator and its fading memory behavior stemming from its transient response. Compared to reservoir computing using micromechanical resonators, the use of nanoelectromechanical resonators results in faster information processing, enabled by their rapid decay times arising from their small dimensions. Moreover, the implementation of the proposed NEMS reservoir computing architecture is more practical since it can operate at atmospheric conditions and occupies less space than its MEMS counterparts. This study emphasizes the efficient and feasible information processing potential of the suggested approach for a range of applications by the evaluation of its performance with the MNIST handwritten digit recognition task.