18th IEEE Workshop on Nonlinear Dynamics of Electronic Systems: Proceedings

Proceedings of the 18th IEEE Workshop on Nonlinear Dynamics of Electronic Systems, which took place in Dresden, Germany, 26 – 28 May 2010.:Welcome Address ........................ Page I Table of Contents ........................ Page III Symposium Committees .............. Page IV Special Thanks ............................. Page V Conference program (incl. page numbers of papers) ................... Page VI Conference papers Invited talks ................................ Page 1 Regular Papers ........................... Page 14 Wednesday, May 26th, 2010 ......... Page 15 Thursday, May 27th, 2010 .......... Page 110 Friday, May 28th, 2010 ............... Page 210 Author index ............................... Page XII

Rate-induced critical transitions

This thesis focuses on rate-induced critical transitions or tipping points (R-tipping points), where the system undergoes a critical transition if the time-varying external conditions vary faster than some critical rate. Such a critical transition is usually a sudden and unexpected change of the system state. The change can be either irreversible: a permanent tipping point with no return to the original state, or reversible: a temporary tipping point with self-recovery back to the original state, both of which may cause significant consequences in applications. Indeed, R-tipping is an ubiquitous nonlinear phenomenon in nature that remains largely unexplored by the scientists. From a mathematical viewpoint, it is a genuine nonautonomous instability that cannot be explained by the classical (autonomous) bifurcation theory and requires an alternative approach. The first part of the thesis focuses on a mathematical framework for R-tipping in systems of nonautonomous differential equations, where the nonautonomous terms representing time-varying external conditions decay asymptotically. In particular, special compactification techniques for asymptotically autonomous systems are developed to simplify analysis of R-tipping. In the second part of the thesis, the main concepts of edge states and thresholds are introduced to define the R-tipping phenomenon. Then, simple testable criteria for the occurrence of reversible and irreversible R-tipping in arbitrary dimension are given. This part extends the previous results on irreversible R-tipping in one dimension. The third part of the thesis identifies canonical examples of R-tipping based on the system dimension, timescales and the threshold type. These examples are relatively simple low-dimensional nonlinear systems that capture different R-tipping mechanisms. R-tipping analysis of canonical examples, which is underpinned by the compactification framework developed in the second part, reveals intricate R-tipping diagrams with multiple critical rates and transitions between different types of R-tipping

Hydrodynamics

The phenomena related to the flow of fluids are generally complex, and difficult to quantify. New approaches - considering points of view still not explored - may introduce useful tools in the study of Hydrodynamics and the related transport phenomena. The details of the flows and the properties of the fluids must be considered on a very small scale perspective. Consequently, new concepts and tools are generated to better describe the fluids and their properties. This volume presents conclusions about advanced topics of calculated and observed flows. It contains eighteen chapters, organized in five sections: 1) Mathematical Models in Fluid Mechanics, 2) Biological Applications and Biohydrodynamics, 3) Detailed Experimental Analyses of Fluids and Flows, 4) Radiation-, Electro-, Magnetohydrodynamics, and Magnetorheology, 5) Special Topics on Simulations and Experimental Data. These chapters present new points of view about methods and tools used in Hydrodynamics

Dynamics of free-running, pump-modulated and coupled semiconductor and solid-state lasers

The output of a laser is a high frequency propagating electromagnetic field with superior coherence and brightness compared to that emitted by thermal sources. A multitude of different types of lasers exist, which also translates into large differences in the properties of their output. Moreover, the characteristics of the electromagnetic field emitted by a laser can be influenced from the outside, e.g., by injecting an external optical field or by optical feedback. In the case of free-running solitary class-B lasers, such as semiconductor and Nd:YVO4 solid-state lasers, the phase space is two-dimensional, the dynamical variables being the population inversion and the amplitude of the electromagnetic field. The two-dimensional structure of the phase space means that no complex dynamics can be found. If a class-B laser is perturbed from its steady state, then the steady state is restored after a short transient. However, as discussed in part (i) of this Thesis, the static properties of class-B lasers, as well as their artificially or noise induced dynamics around the steady state, can be experimentally studied in order to gain insight on laser behaviour, and to determine model parameters that are not known ab initio. In this Thesis particular attention is given to the linewidth enhancement factor, which describes the coupling between the gain and the refractive index in the active material. A highly desirable attribute of an oscillator is stability, both in frequency and amplitude. Nowadays, however, instabilities in coupled lasers have become an active area of research motivated not only by the interesting complex nonlinear dynamics but also by potential applications. In part (ii) of this Thesis the complex dynamics of unidirectionally coupled, i.e., optically injected, class-B lasers is investigated. An injected optical field increases the dimensionality of the phase space to three by turning the phase of the electromagnetic field into an important variable. This has a radical effect on laser behaviour, since very complex dynamics, including chaos, can be found in a nonlinear system with three degrees of freedom. The output of the injected laser can be controlled in experiments by varying the injection rate and the frequency of the injected light. In this Thesis the dynamics of unidirectionally coupled semiconductor and Nd:YVO4 solid-state lasers is studied numerically and experimentally.Det finns många olika typer av lasrar, vilket också betyder att egenskaperna hos det ljus som lasrar emitterar varierar mycket. Därtill kan egenskaperna hos laserljus ändras genom till exempel optisk injektion. Vid optisk injektion injiceras ljus in i en laser från en extern ljuskälla, som oftast är en annan liknande laser. I den här avhandlingen har dynamiken hos frigående, modulerade och optiskt injicerade halvledar- och fasta tillståndets lasrar undersökts experimentellt och numeriskt. Frigående halvledar- och fasta tillståndets lasrar har två frihetsgrader: amplituden på det elektromagnetiska fältet (uteffekt) och populationsinversionen i det aktiva området (mängden exciterade atomer). Om en sådan laser störs från sitt jämviktsläge återgår den snabbt tillbaka till jämviktsläget via ett fåtal oscillationer. Frigående lasrar av ovannämnda typer uppvisar med andra ord inte komplicerad (och intressant) dynamik. Däremot kan man undersöka artificiellt eller brus inducerad dynamik runt jämviktsläget i syfte att mäta olika parametrar som beskriver egenskaper hos dessa lasrar. I avhandlingens första del har stor vikt satts på att experimentellt mäta den så kallade alfa-faktorn, som beskriver kopplingen mellan förstärkningen och brytningsindexet i laserns aktiva del. Med andra ord kvantifierar alfa-faktorn kopplingen mellan det emitterade ljusets amplitud och fas. I avhandlingens andra del har dynamiken under optisk injektion undersökts. Injektion av ljus från en annan laser ändrar radikalt på lasrarnas beteende. Det beror på att det injicerade ljuset omvandlar fasen på det elektromagnetiska fältet till en viktig variabel och ökar således antalet frihetsgrader från två till tre. Beroende på det injicerade ljusets effekt och frekvens, kan den icke-linjära växelverkan ge upphov till bland annat stabila, periodiska och kaotiska tillstånd i lasern. Optiskt injicerade halvledarlasrar har en del nutida tillämpningar och även några potentiella framtida tillämpningar. I dagsläget används optisk injektion till att förstärka svagt ljus av god kvalitet och till karakterisering av lasrar. I framtiden kan optisk injektion även finna tillämpningar inom telekommunikationsindustrin och radarteknologin. Optiskt injicerade lasrar och andra typer av kopplade lasersystem är dock inte endast intressanta tack vare tillämpningarna. Dessa lättkontrollerade system ger också goda möjligheter att experimentellt studera egenskaper hos icke-linjära dynamiska system

Laser Systems for Applications

This book addresses topics related to various laser systems intended for the applications in science and various industries. Some of them are very recent achievements in laser physics (e.g. laser pulse cleaning), while others face their renaissance in industrial applications (e.g. CO2 lasers). This book has been divided into four different sections: (1) Laser and terahertz sources, (2) Laser beam manipulation, (3) Intense pulse propagation phenomena, and (4) Metrology. The book addresses such topics like: Q-switching, mode-locking, various laser systems, terahertz source driven by lasers, micro-lasers, fiber lasers, pulse and beam shaping techniques, pulse contrast metrology, and improvement techniques. This book is a great starting point for newcomers to laser physics

Computer modeling and analysis of biological rhythms

Biological rhythms are an important phenomenon and feature of physiologic systems. Indirect means have to be employed for their description and exploration due to the unclear internal nature of the system. This study analyzed and developed several possible mathematical models using single or multidimensional nonlinear differential equations to approach the experimental circadian data. The numerical solutions of the models were obtained by computer simulation and the simulated and experimental acquired circadian data were analyzed in both the time and frequency domains. Phase plane plots, phase response curves and power spectrum analysis were employed to determine the nonlinearity of the system and its relation to the harmonic structure while bispectrum analysis showed the relation between the harmonics. Dynamic spectrum and frequency demodulation techniques were used to explore the dynamic transient process of the circadian rhythms when a stimulus is applied. The coherence function was examined to explore the frequency correlation between two different circadian rhythms: temperature and activity of the same subject. The study showed that a two dimensional coupled nonlinear oscillator model can be used to describe the circadian rhythm better and a model with relatively large nonlinearity closely approximated the experimental data. The research revealed the harmonic structure of circadian rhythms. This structure related to the nonlinearity of the system with the 2nd harmonic of experimental data representing bimodality in the time series. All the models developed in this research reflected this important feature. The effects of a nonperiodic stimulus to the circadian system were simulated in the model and an overshoot phenomenon was found during the frequency transient process. High values of coherence were found at the fundamental and third harmonics while no phase relation was found between harmonics of the experimental data using the bispectrum method

Phase Noise Analyses and Measurements in the Hybrid Memristor-CMOS Phase-Locked Loop Design and Devices Beyond Bulk CMOS

Phase-locked loop (PLLs) has been widely used in analog or mixed-signal integrated circuits. Since there is an increasing market for low noise and high speed devices, PLLs are being employed in communications. In this dissertation, we investigated phase noise, tuning range, jitter, and power performances in different architectures of PLL designs. More energy efficient devices such as memristor, graphene, transition metal di-chalcogenide (TMDC) materials and their respective transistors are introduced in the design phase-locked loop. Subsequently, we modeled phase noise of a CMOS phase-locked loop from the superposition of noises from its building blocks which comprises of a voltage-controlled oscillator, loop filter, frequency divider, phase-frequency detector, and the auxiliary input reference clock. Similarly, a linear time-invariant model that has additive noise sources in frequency domain is used to analyze the phase noise. The modeled phase noise results are further compared with the corresponding phase-locked loop designs in different n-well CMOS processes. With the scaling of CMOS technology and the increase of the electrical field, the problem of short channel effects (SCE) has become dominant, which causes decay in subthreshold slope (SS) and positive and negative shifts in the threshold voltages of nMOS and pMOS transistors, respectively. Various devices are proposed to continue extending Moore\u27s law and the roadmap in semiconductor industry. We employed tunnel field effect transistor owing to its better performance in terms of SS, leakage current, power consumption etc. Applying an appropriate bias voltage to the gate-source region of TFET causes the valence band to align with the conduction band and injecting the charge carriers. Similarly, under reverse bias, the two bands are misaligned and there is no injection of carriers. We implemented graphene TFET and MoS2 in PLL design and the results show improvements in phase noise, jitter, tuning range, and frequency of operation. In addition, the power consumption is greatly reduced due to the low supply voltage of tunnel field effect transistor

Stochastic and complex dynamics in mesoscopic brain networks

The aim of this thesis is to deepen into the understanding of the mechanisms responsible for the generation of complex and stochastic dynamics, as well as emerging phenomena, in the human brain. We study typical features from the mesoscopic scale, i.e., the scale in which the dynamics is given by the activity of thousands or even millions of neurons. At this scale the synchronous activity of large neuronal populations gives rise to collective oscillations of the average voltage potential. These oscillations can easily be recorded using electroencephalography devices (EEG) or measuring the Local Field Potentials (LFPs). In Chapter 5 we show how the communication between two cortical columns (mesoscopic structures) can be mediated efficiently by a microscopic neural network. We use the synchronization of both cortical columns as a probe to ensure that an effective communication is established between the three neural structures. Our results indicate that there are certain dynamical regimes from the microscopic neural network that favor the correct communication between the cortical columns: therefore, if the LFP frequency of the neural network is of around 40Hz, the synchronization between the cortical columns is more robust compared to the situation in which the neural network oscillates at a lower frequency (10Hz). However, microscopic topological characteristics of the network also influence communication, being a small-world structure the one that best promotes the synchronization of the cortical columns. Finally, this Chapter shows how the mediation exerted by the neural network cannot be substituted by the average of its activity, that is, the dynamic properties of the microscopic neural network are essential for the proper transmission of information between all neural structures. The oscillatory brain electrical activity is largely dependent on the interplay between excitation and inhibition. In Chapter 6 we study how groups of cortical columns show complex patterns of cortical excitation and inhibition taking into account their topological features and the strength of their couplings. These cortical columns segregate between those dominated by excitation and those dominated by inhibition, affecting the synchronization properties of networks of cortical columns. In Chapter 7 we study a dynamic regime by which complex patterns of synchronization between chaotic oscillators appear spontaneously in a network. We show what conditions must a set of coupled dynamical systems fulfill in order to display heterogeneity in synchronization. Therefore, our results are related to the complex phenomenon of synchronization in the brain, which is a focus of study nowadays. Finally, in Chapter 8 we study the ability of the brain to compute and process information. The novelty here is our use of complex synchronization in the brain in order to implement basic elements of Boolean computation. In this way, we show that the partial synchronization of the oscillations in the brain establishes a code in terms of synchronization / non-synchronization (1/0, respectively), and thus all simple Boolean functions can be implemented (AND, OR, XOR, etc.). We also show that complex Boolean functions, such as a flip-flop memory, can be constructed in terms of states of dynamic synchronization of brain oscillations.L'objectiu d'aquesta Tesi és aprofundir en la comprensió dels mecanismes responsables de la generació de dinàmica complexa i estocàstica, així com de fenòmens emergents, en el cervell humà. Estudiem la fenomenologia característica de l'escala mesoscòpica, és a dir, aquella en la que la dinàmica característica ve donada per l'activitat de milers de neurones. En aquesta escala l'activitat síncrona de grans poblacions neuronals dóna lloc a un fenomen col·lectiu pel qual es produeixen oscil·lacions del seu potencial mitjà. Aquestes oscil·lacions poden ser fàcilment enregistrades mitjançant aparells d'electroencefalograma (EEG) o enregistradors de Potencials de Camp Local (LFP). En el Capítol 5 mostrem com la comunicació entre dos columnes corticals (estructures mesoscòpiques) pot ser conduïda de forma eficient per una xarxa neuronal microscòpica. De fet, emprem la sincronització de les dues columnes corticals per comprovar que s'ha establert una comunicació efectiva entre les tres estructures neuronals. Els resultats indiquen que hi ha règims dinàmics de la xarxa neuronal microscòpica que afavoreixen la correcta comunicació entre les columnes corticals: si la freqüència típica de LFP a la xarxa neuronal està al voltant dels 40Hz la sincronització entre les columnes corticals és més robusta que a una menor freqüència (10Hz). La topologia de la xarxa microscòpica també influeix en la comunicació, essent una estructura de tipus món petit (small-world) la que més afavoreix la sincronització. Finalment, la mediació de xarxa neuronal no pot ser substituïda per la mitjana de la seva activitat, és a dir, les propietats dinàmiques microscòpiques són imprescindibles per a la correcta transmissió d'informació entre totes les escales cerebrals. L'activitat elèctrica oscil·latòria cerebral ve donada en gran mesura per la interacció entre excitació i inhibició neuronal. En el Capítol 6 estudiem com grups de columnes corticals mostren patrons complexos d'excitació i inhibició segons quina sigui la seva topologia i d'acoblament. D'aquesta manera les columnes corticals se segreguen entre aquelles dominades per l'excitació i aquelles dominades per la inhibició, influint en les capacitats de sincronització de xarxes de columnes corticals. En el Capítol 7 estudiem un règim dinàmic segons el qual patrons complexos de sincronització apareixen espontàniament en xarxes d'oscil·ladors caòtics. Mostrem quines condicions s'han de donar en un conjunt de sistemes dinàmics acoblats per tal de mostrar heterogeneïtat en la sincronització, és a dir, coexistència de sincronitzacions. D'aquesta manera relacionem els nostres resultats amb el fenomen de sincronització complexa en el cervell. Finalment, en el Capítol 8 estudiem com el cervell computa i processa informació. La novetat aquí és l'ús que fem de la sincronització complexa de columnes corticals per tal d'implementar elements bàsics de computació Booleana. Mostrem com la sincronització parcial de les oscil·lacions cerebrals estableix un codi neuronal en termes de sincronització/no sincronització (1/0, respectivament) amb el qual totes les funcions Booleanes simples poden ésser implementades (AND, OR, XOR, etc). Mostrem, també, com emprant xarxes mesoscòpiques extenses les capacitats de computació creixen proporcionalment. Així funcions Booleanes complexes, com una memòria del tipus flip-flop, pot ésser construïda en termes d'estats de sincronització dinàmica d'oscil·lacions cerebrals.Postprint (published version