Theory and New Amplification Regime in Periodic Multi Modal Slow Wave Structures with Degeneracy Interacting with an Electron Beam

We present the theory of a new amplification regime in Travelling Wave Tubes (TWTs) composed of a slow-wave periodic structure that supports multiple electromagnetic modes that can all be synchronized with the electron beam. The interaction between the multimodal slow-wave structure and the electron beam is quantified using a Multi Transmission Line approach (MTL) based on a generalized Pierce model and transfer matrix analysis leading to the identification of modes with complex Bloch wavenumber. In particular, we address a new possible operation condition for TWTs based on the super synchronism between an electron beam and four modes exhibiting a degeneracy condition near a band edge of the periodic slowwave MTL. We show a phenomenological change in the band structure of periodic MTL where we observe at least two growing modal cooperating solutions as opposed to a uniform MTL interacting with an electron beam where there is rigorously only one growing modal solution. We discuss the advantage of using such a degeneracy condition in TWTs that leads to larger gain conditions in amplifier regimes and also to very lowstarting beam current in high power oscillators.Comment: Version 2. 33 pages, 16 figure

Nonlinear physics of electrical wave propagation in the heart: a review

The beating of the heart is a synchronized contraction of muscle cells (myocytes) that are triggered by a periodic sequence of electrical waves (action potentials) originating in the sino-atrial node and propagating over the atria and the ventricles. Cardiac arrhythmias like atrial and ventricular fibrillation (AF,VF) or ventricular tachycardia (VT) are caused by disruptions and instabilities of these electrical excitations, that lead to the emergence of rotating waves (VT) and turbulent wave patterns (AF,VF). Numerous simulation and experimental studies during the last 20 years have addressed these topics. In this review we focus on the nonlinear dynamics of wave propagation in the heart with an emphasis on the theory of pulses, spirals and scroll waves and their instabilities in excitable media and their application to cardiac modeling. After an introduction into electrophysiological models for action potential propagation, the modeling and analysis of spatiotemporal alternans, spiral and scroll meandering, spiral breakup and scroll wave instabilities like negative line tension and sproing are reviewed in depth and discussed with emphasis on their impact in cardiac arrhythmias.Peer ReviewedPreprin

Synchronization of spatiotemporal patterns and modeling disease spreading using excitable media

Studies of the photosensitive Belousov-Zhabotinsky (BZ) reaction are reviewed and the essential features of excitable media are described. The synchronization of two distributed Belousov-Zhabotinsky systems is experimentally and theoretically investigated. Symmetric local coupling of the systems is made possible with the use of a video camera-projector scheme. The spatial disorder of the coupled systems, with random initial configurations of spirals, gradually decreases until a final state is attained, which corresponds to a synchronized state with a single spiral in each system. The experimental observations are compared with numerical simulations of two identical Oregonator models with symmetric local coupling, and a systematic study reveals generalized synchronization of spiral waves. Modeling studies on disease spreading have been reviewed. The excitable medium of the photosensitive BZ reaction is used to model disease spreading, with static networks, dynamic networks, and a domain model. The spatiotemporal dynamics of disease spreading in these complex networks with diffusive and non-diffusive connections is characterized. The experimental and numerical studies reveal that disease spreading in these model systems is highly dependent on the non-diffusive connections

Key Bifurcations of Bursting Polyrhythms in 3-Cell Central Pattern Generators

We identify and describe the key qualitative rhythmic states in various 3-cell network motifs of a multifunctional central pattern generator (CPG). Such CPGs are neural microcircuits of cells whose synergetic interactions produce multiple states with distinct phase-locked patterns of bursting activity. To study biologically plausible CPG models, we develop a suite of computational tools that reduce the problem of stability and existence of rhythmic patterns in networks to the bifurcation analysis of fixed points and invariant curves of a Poincare´ return maps for phase lags between cells. We explore different functional possibilities for motifs involving symmetry breaking and heterogeneity. This is achieved by varying coupling properties of the synapses between the cells and studying the qualitative changes in the structure of the corresponding return maps. Our findings provide a systematic basis for understanding plausible biophysical mechanisms for the regulation of rhythmic patterns generated by various CPGs in the context of motor control such as gait-switching in locomotion. Our analysis does not require knowledge of the equations modeling the system and provides a powerful qualitative approach to studying detailed models of rhythmic behavior. Thus, our approach is applicable to a wide range of biological phenomena beyond motor control

Nonlinear dynamics of semiconductor lasers with active optical feedback

An in-depth theoretical as well as experimental analysis of the nonlinear dynamics in semiconductor lasers with active optical feedback is presented. Use of a monolithically integrated multi-section device of sub-mm total length provides access to the short-cavity regime. By introducing an amplifier section as novel feature, phase and strength of the feedback can be separately tuned. In this way, the number of modes involved in the laser action can be adjusted. We predict and observe specific dynamical scenarios. Bifurcations mediate various transitions in the device output, from single-mode steady-state to self-pulsation and between different kinds of self-pulsations, reaching eventually chaotic behavior in the multi-mode limit

Network Dynamics, Synchronization, and Self-Propelled Particles in Chemical Systems

Neural networks are a class of biological networks of great importance. They are a key component of the central nervous system that coordinates body functions. The exploration of the detailed mechanism of biological neural networks remains extremely active. Inspired by the structure of biological neural networks, artificial neural networks have been designed to solve a variety of problems in pattern recognition, prediction, optimization and control. However, few studies have been reported that explore the dynamics of biological neural networks using chemical systems. As part of this thesis, an experimentally trainable network based on the photosensitive Belousov-Zhabotinsky reaction is developed, where the individual node is a catalyst loaded micro-particle. The interactions between nodes in the network are created by arranging links with different weights, similar to the excitable and inhibitory synapses in biological neural networks. The distribution of the weights of the excitable links has been studied. The results indicate that a stable distribution of the weights is exhibited.;Synchronization in coupled nonlinear oscillators is a remarkable and ubiquitous phenomenon in nature. Application of periodic global feedback to oscillators allows the creation of new kinds of wave patterns with the coexistence of stable phase states. In experiments with the photosensitive BZ reaction, periodic global feedback is implemented by varying the illumination intensity. In a 1:1 frequency-locked entrainment, 2pi phase fronts called phase kinks have been observed in the photosensitive BZ reaction. Generally, a phase kink represents the existence of stable phase differences, propagating as an analog of traveling waves in 2D excitable media. By modifying the conditions of local forcing, the experiments show that a phase kink can be trapped to form a closed pattern.;Self-propulsion is an essential feature of many living systems. There are numerous realizations of self-propelled particles in biological systems, such as the bacteria Listeria monocytogenes in cells. Such biological phenomena inspire the creation of artificial self-propelled particles. Recently, nonbiological micro- to nanoscale particles, that convert chemical energy into translational motion, have been investigated. Studies show that Pt-coated polystyrene particles, coated on one hemisphere with Pt, exhibit self-propulsion in dilute H2O2 solutions. Here, we experimentally study the dynamical behavior of silica particles that are asymmetrically coated with Pt in H2O2 solutions, similar to Pt-coated polystyrene particles. The focus of our study is on the particle orientation with respect to the direction of motion. This is investigated using velocity autocorrelation and propulsion direction analyses

A Multi-cell, Multi-scale Model of Vertebrate Segmentation and Somite Formation

Somitogenesis, the formation of the body's primary segmental structure common to all vertebrate development, requires coordination between biological mechanisms at several scales. Explaining how these mechanisms interact across scales and how events are coordinated in space and time is necessary for a complete understanding of somitogenesis and its evolutionary flexibility. So far, mechanisms of somitogenesis have been studied independently. To test the consistency, integrability and combined explanatory power of current prevailing hypotheses, we built an integrated clock-and-wavefront model including submodels of the intracellular segmentation clock, intercellular segmentation-clock coupling via Delta/Notch signaling, an FGF8 determination front, delayed differentiation, clock-wavefront readout, and differential-cell-cell-adhesion-driven cell sorting. We identify inconsistencies between existing submodels and gaps in the current understanding of somitogenesis mechanisms, and propose novel submodels and extensions of existing submodels where necessary. For reasonable initial conditions, 2D simulations of our model robustly generate spatially and temporally regular somites, realistic dynamic morphologies and spontaneous emergence of anterior-traveling stripes of Lfng. We show that these traveling stripes are pseudo-waves rather than true propagating waves. Our model is flexible enough to generate interspecies-like variation in somite size in response to changes in the PSM growth rate and segmentation-clock period, and in the number and width of Lfng stripes in response to changes in the PSM growth rate, segmentation-clock period and PSM length