Traveling interface modulations in the NH 3 + O 2 reaction on a Rh(110) surface

A new type of traveling interface modulation has been observed in the NH 3 + O 2 reaction on a Rh(110) surface. A model is set up which reproduces the effect, which is attributed to diffusional mixing of two spatially separated adsorbates causing an excitability which is strictly localized to the vicinity of the interface of the adsorbate domains. © 2012 the Owner Societies

Capture of fixation by rotational flow; a deterministic hypothesis regarding scaling and stochasticity in fixational eye movements.

Visual scan paths exhibit complex, stochastic dynamics. Even during visual fixation, the eye is in constant motion. Fixational drift and tremor are thought to reflect fluctuations in the persistent neural activity of neural integrators in the oculomotor brainstem, which integrate sequences of transient saccadic velocity signals into a short term memory of eye position. Despite intensive research and much progress, the precise mechanisms by which oculomotor posture is maintained remain elusive. Drift exhibits a stochastic statistical profile which has been modeled using random walk formalisms. Tremor is widely dismissed as noise. Here we focus on the dynamical profile of fixational tremor, and argue that tremor may be a signal which usefully reflects the workings of oculomotor postural control. We identify signatures reminiscent of a certain flavor of transient neurodynamics; toric traveling waves which rotate around a central phase singularity. Spiral waves play an organizational role in dynamical systems at many scales throughout nature, though their potential functional role in brain activity remains a matter of educated speculation. Spiral waves have a repertoire of functionally interesting dynamical properties, including persistence, which suggest that they could in theory contribute to persistent neural activity in the oculomotor postural control system. Whilst speculative, the singularity hypothesis of oculomotor postural control implies testable predictions, and could provide the beginnings of an integrated dynamical framework for eye movements across scales

Optogenetic Control of Cardiac Arrhythmias

The regular, coordinated contraction of the heart muscle is orchestrated by periodic waves generated by the heart’s natural pacemaker and transmitted through the heart’s electrical conduction system. Abnormalities occurring anywhere within the cardiac electrical conduction system can disrupt the propagation of these waves. Such dis- ruptions often lead to the development of high frequency spiral waves that override normal pacemaker activity and compromise cardiac function. The occurrence of high frequency spiral waves in the heart is associated with cardiac rhythm disorders such as tachycardia and fibrillation. While tachycardia may be terminated by rapid periodic stimulation known as anti-tachycardia pacing (ATP), life-threatening ventricular fibril- lation requires a single high-voltage electric shock that resets all the activity and restore the normal heart function. However, despite the high success rate of defibrillation, it is associated with significant side effects including tissue damage, intense pain and trauma. Thus, extensive research is conducted for developing low-energy alternatives to conventional defibrillation. An example of such an alternative is the low-energy anti-fibrillation pacing (LEAP). However, the clinical application of this technique, and other evolving techniques requires a detailed understanding of the dynamics of spiral waves that occur during arrhythmias. Optogenetics is a tool, that has recently gained popularity in the cardiac research, which serves as a probe to study biological processes. It involves genetically modifying cardiac muscle cells such that they become light sensitive, and then using light of specific wavelengths to control the electrical activity of these cells. Cardiac optogenetics opens up new ways of investigating the mechanisms underlying the onset, maintenance and control of cardiac arrhythmias. In this thesis, I employ optogenetics as a tool to control the dynamics of a spiral wave, in both computer simulations and in experiments.In the first study, I use optogenetics to investigate the mechanisms underlying de- fibrillation. Analogous to the conventional single electric-shock, I apply a single globally-illuminating light pulse to a two-dimensional cardiac tissue to study how wave termination occurs during defibrillation. My studies show a characteristic transient dynamics leading to the termination of the spiral wave at low light intensities, while at high intensities, the spiral waves terminate immediately. Next, I move on to explore the use of optogenetics to study spiral wave termina- tion via drift, theoretically well-known mechanism of arrhythmia termination in the context of electrical stimulation (e.g. ATP). I show that spiral wave drift can be induced by structured illumination patterns using lights of low intensity, that result in a spatial modulation of cardiac excitability. I observe that drift occurs in the positive direction of light intensity gradient, where the spiral also rotates with a longer period. I further show how modulation of the excitability in space can be used to control the dynamics of a spiral wave, resulting in the termination of the wave by collision with the domain boundary. Based on these observations, I propose a possible mechanism of optogenetic defibrillation. In the next chapter, I use optogenetics to demonstrate control over the dynamics of the spiral waves by periodic stimulation with light of different intensities and pacing frequencies resulting in a temporal modulation of cardiac excitability. I demonstrate how the temporal modulation of excitability leads to efficient termination of arrhythmia. In addition, I use computer simulations to identify mechanisms responsible for arrhyth- mia termination for sub- and supra-threshold light intensities. My numerical results are supported by experimental studies on intact hearts, extracted from transgenic mice. Finally, I demonstrate that cardiac optogenetics not only allows control of excita- tion waves, but also by generating new waves through the induction of wave breaks. We demonstrate the effects of high sub-threshold illumination on the morphology of the propagating wave, leading to the creation of new excitation windows in space that can serve as potential sites for re-entry initiation. In summary, this thesis investigates several approaches to control arrhythmia dy- namics using optogenetics. The experimental and numerical results demonstrate the potential of feedback-induced resonant pacing as a low-energy method to control arrhythmia.2022-01-1

Traveling interface modulations in the NH₃ + O₂ reaction on a Rh(110) surface

A new type of traveling interface modulation has been observed in the NH₃ + O₂ reaction on a Rh(110) surface. A model is set up which reproduces the effect, which is attributed to diffusional mixing of two spatially separated adsorbates causing an excitability which is strictly localized to the vicinity of the interface of the adsorbate domains.Facultad de Ciencias ExactasInstituto de Investigaciones Fisicoquímicas Teóricas y Aplicada

A versatile cortical pattern-forming circuit based on Rho, F-actin, Ect2 and RGA-3/4

Many cells can generate complementary traveling waves of actin filaments (F-actin) and cytoskeletal regulators. This phenomenon, termed cortical excitability, results from coupled positive and negative feedback loops of cytoskeletal regulators. The nature of these feedback loops, however, remains poorly understood. We assessed the role of the Rho GAP RGA-3/4 in the cortical excitability that accompanies cytokinesis in both frog and starfish. RGA-3/4 localizes to the cytokinetic apparatus, “chases” Rho waves in an F-actin–dependent manner, and when coexpressed with the Rho GEF Ect2, is sufficient to convert the normally quiescent, immature Xenopus oocyte cortex into a dramatically excited state. Experiments and modeling show that changing the ratio of RGA-3/4 to Ect2 produces cortical behaviors ranging from pulses to complex waves of Rho activity. We conclude that RGA-3/4, Ect2, Rho, and F-actin form the core of a versatile circuit that drives a diverse range of cortical behaviors, and we demonstrate that the immature oocyte is a powerful model for characterizing these dynamics

A State Space Odyssey — The Multiplex Dynamics of Cardiac Arrhythmias

With three million people worldwide (three hundred thousand people in the United States alone) experiencing sudden cardiac arrest per year, it is one of the most common causes of death in developed countries. Ventricular fibrillation, a dysfunction of the heart characterized by a highly chaotic spatio-temporal wave dynamics, is the main cause for sudden cardiac arrest. The application of a high-energy defibrillation shock, as the current medical treatment to restore the sinus rhythm, comes along with severe side-effects, among others additional damage of the heart. Furthermore, patients with an ICD (implantable cardioverter-defibrillator) in particular suffer from posttraumatic stress symptoms. The goal of this thesis is to investigate the dynamics of the heart (and in particular the nature of cardiac arrhythmias (specifically ventricular fibrillation)) using concepts and perceptions from the dynamical systems theory. On the basis of the interdisciplinary interplay between mathematical approaches and interaction with experimental and clinical knowledge and results, two general scientific objectives are addressed: Derive an enhanced understanding of the dynamics during episodes of ventricular fibrillation, including the development of concepts for the improvement of current defibrillation techniques and suggestions for completely new strategies which may find their way into the clinical application. Obtain novel insights into the fundamental dynamics of complex, nonlinear systems (thus excitable systems and beyond). These objectives are addressed using numerical simulations, which constitute the main tool to investigate specific research questions. The results of this thesis are organized in four chapters, each focusing on one specific question: The first results chapter is dealing with the mechanism of spontaneous termination of ventricular fibrillation. We investigate the transient behavior of spiral and scroll wave dynamics using different cell models. The observed transients can be classified into the group of so called type-II supertransients. We find, that in 3D simulations, a critical thickness of the medium plays an essential role. Basic features of the simulations agree with general observations of clinicians, e.g. that larger heart muscle volumes increase the risk of cardiac arrhythmias. In the second results chapter, we address the question whether a self-termination of a chaotic episode can be predicted. By applying small but finite perturbations to specific trajectories of chaotic spiral wave dynamics we find that the state space structure close to the “exits” of the chaotic regime changes significantly. We could verify this effect also in low-dimensional maps. This analysis shows, that although the upcoming self-termination is not visible in conventional variables, it should in principle be possible to derive such a quantity. In the third results chapter, we investigate complexity fluctuations of the chaotic spatio-temporal dynamics in simulations using realistic heart geometries. We show, that the level of organization of the spatio-temporal dynamics can be estimated by analyzing the time series of a multi-electrode setup. In the last results chapter, we discuss whether a successful termination of chaotic spiral wave dynamics is possible using a minimal interaction with the system. We show, that since the underlying topological object which determines the chaotic dynamics is a chaotic saddle, one can terminate the dynamics (as a proof of concept) by the application of a specific but very small perturbation. We hope that the insights provided by this thesis contribute to the general understanding of cardiac arrhythmias and the nonlinear dynamics of complex systems. The results suggest that an improved medical treatment of cardiac arrhythmias can benefit from: A more detailed state analysis of the dynamics during spatio-temporal chaos, incorporating diverse measure techniques (e.g. multiple-ECG measurements, CT scans, MRI scans). An intervention strategy which should adapt to individual patients and the respective dynamical state of the heart. A variety of new experimental approaches will be available which may help to achieve these goals and to improve the understanding of the phenomena investigated in this thesis: Filament identification in the bulk tissue during experiments using sophisticated ultra sound techniques, inverse ECG measurements for the reconstruction of spatio-temporal wave dynamics or using techniques from optogenetics for the stimulation of cardiac tissue via light pulses are promising candidates which can have a significant impact on the field of cardiac dynamics. This technological progress in combination with novel data analysis techniques from the fields of machine learning or data assimilation and sophisticated simulations of the complex dynamics has great potential to develop advanced and efficient strategies for a patient specific medical treatment

The dynamics of circumbinary discs and embedded planets

Since the first detection of a circumbinary planet with the Kepler space telescope in 2011 nine more circumbinary planets have been discovered. All these circumbinary Kepler systems have two things in common: First they are very flat, meaning that the orbit of the binary and the planet are in one plane, suggesting that they formed in an accretion disc surrounding both binary components. Second, the orbits of the planets are very close to the calculated stability limit. To explain the formation of these planets two scenarios are possible: An in situ formation at the observed location or a formation further outside in the disc followed by radial migration to the current observed position. Simulations have shown that an in situ formation is unlikely, due to destructive collisions of planetesimals on orbits close to the binary. The second scenario leads to the question of how the migrating planets can be stopped at the observed location. In this thesis the second scenario is examined through numerical simulations. The gravitational interaction between the binary and the disc leads to the formation of an eccentric inner gap, which precesses slowly in a prograde manner around the binary. This inner gap constitutes a barrier for a migrating planet. Therefore, the first part of this thesis investigates how binary parameters (eccentricity, mass ratio) as well as disc parameters (pressure, viscosity) influence the size, eccentricity, and precession period of the gap. The binary eccentricity (ebin) is identified as an important parameter. In the precession period – gap-size diagram a bifurcation occurs for varying ebin. Increasing the binary eccentricity from zero, precession period and gap-size decrease until a critical eccentricity of ebin = 0.18 is reached. From this point onward, precession period and gap-size increase again for increasing binary eccentricities. The binary mass ratio changes only the precession period, which decreases with increasing mass ratios, while the gap-size remains constant. For increasing viscosity and pressure in the disc the expected behaviour is observed: precession period and gap-size decrease. The second part of this thesis investigates the migration of planets in circumbinary discs. For five Kepler systems (Kepler-16, -34, -35, -38, -413) the dependence of the final orbital parameters on the planet-to-disc mass ratio is examined as well as the change in the disc structure due to the presence of the planet. The planets migrate in all cases to the edge of the gap, as expected. Depending on the planet mass, two migration scenarios are observed. Massive planets dominate the disc by shrinking and circularising the inner gap, whereas light planets are influenced by the disc. They align their orbits to the precessing disc and their eccentricity is excited. In general the final simulated orbital parameters are too large compared to the observations. Circumbinary planets around systems which create large, eccentric gaps (Kepler-34 and -413) also have the highest simulated eccentricities in agreement with the observations.Seit der ersten Entdeckung eines zirkumbinären Planeten mit dem Kepler Weltraumteleskop im Jahr 2011 wurden neun weitere Planeten entdeckt, die um einen Binärstern kreisen. All diese zirkumbinären Kepler Systeme haben folgende Gemeinsamkeiten: Sie sind planar, das heißt die Umlaufbahn des Planeten liegt in derselben Ebene wie die Umlaufbahn des Binärsterns, was auf eine Entstehung der Planeten in einer Akkretionsscheibe, die beide Komponenten des Binärsterns umgab, hindeutet. Des Weiteren liegt die Umlaufbahn all dieser Planeten sehr nahe am berechneten Stabilitätslimit. Für die Entstehung von zirkumbinären Planeten gibt es grundsätzlich zwei Erklärungsmöglichkeiten: Eine Entstehung direkt am Ort der heutigen Beobachtung oder eine Entstehung in den äußeren Bereichen der Scheibe, gefolgt von einer Migration zur beobachteten Position. Wie Simulationen gezeigt haben, ist eine Entstehung am Ort der Beobachtung unwahrscheinlich, da Planetesimale auf Umlaufbahnen in der Nähe des Binärsterns destruktiv kollidieren. Das zweite Szenario führt direkt zur Frage, wie die Migration der Planeten an der beobachteten Stelle gestoppt werden kann. In dieser Arbeit wird das zweite Szenario mit Hilfe von numerischen Simulationen untersucht. Die gravitative Interaktion zwischen Binärstern und Akkretionsscheibe führt zur Bildung einer zentralen, exzentrischen Lücke, die langsam prograd um den Binärstern präzediert. Diese innere Lücke formt eine Barriere für den migrierenden Planeten. Daher untersucht der erste Teil dieser Arbeit wie Parameter des Binärsterns (Exzentrizität, Massenverhältnis) und Parameter der Scheibe (Druck, Viskosität) die Größe, Exzentrizität und Präzessionsperiode der Lücke beeinflussen. Dabei stellt sich die Exzentrizität des Binärsterns (ebin) als ein wichtiger Parameter heraus. So zeigt sich, wenn man die Präzession der Lücke gegen ihre Größe darstellt, eine Bifurkation bei Variation von ebin. Erhöht man, von null ausgehend, die Exzentrizität des Binärsterns, so sinken zunächst die Präzessionsperiode und die Größe der Lücke. Dieses Verhalten ändert sich mit Erreichen einer kritischen Exzentrizität von ebin = 0.18, ab der Präzessionsperiode und Größe der Lücke wieder zunehmen. Das Massenverhältnis des Binärsterns hat lediglich Auswirkung auf die Präzessionsperiode, die mit steigendem Massenverhältnis sinkt, die Größe der Lücke bleibt konstant. Bei der Variation des Druckes und der Viskosität erhält man das erwartete Ergebnis, dass sich mit steigendem Druck und Viskosität die Größe der Lücke verringert. Im zweiten Teil dieser Arbeit wird der Migrationsprozess von Planeten in zirkumbinären Scheiben untersucht. Dazu wurde anhand von fünf Kepler Systemen (Kepler-16, -34, -35, -38 und -413) simuliert wie die finalen Bahnparameter vom Verhältnis der Planeten- und Scheiben- masse abhängen, und wie die Planeten die Struktur der Scheibe verändern. Wie erwartet migrieren die Planeten in allen Fällen bis zur Lücke. In Abhängigkeit der Planetenmasse zeigen sich zwei verschiedene Migrationsszenarien: Schwere Planeten dominieren die Scheibe, verringern die Größe der inneren Lücke und formen sie kreisförmiger. Leichte Planeten werden hingegen von der Scheibe dominiert. Sie richten ihren Orbit an der präzedierenden Lücke in der Scheibe aus und ihre Exzentrizität wird angeregt. Im Allgemeinen sind die simulierten finalen Bahnparameter, im Vergleich zu den Beobachtungen, zu groß. Zirkumbinäre Planeten um Systeme, welche sehr exzentrische Lücke erzeugen (Kepler-34 und -413) haben auch die höchsten simulierten Exzentrizitäten im Einklang mit den Beobachtungen

Rotating Thin Films: the Vortex Fluidic Device

The motivation of this thesis, is the understanding of the role of fluid mechanics in the performance of the Vortex Fluidic Device (VFD), developed by the Raston laboratory at Flinders University, Australia. The VFD is a novel technology in the synthesis of organic chemicals and in material processing, and is considered a green technology device, achieving enhanced chemical reactivity without temperature variations or the use of additional catalysts. This is the first research project focused in the fluid mechanics of the VFD, thus relevant literature is limited to the performance of the device with respect to chemical reactivity. The methodology employed to pursue this understanding is based on the two processing methods, i.e. confined mode (CM) and continuous flow (CF). In CM, a fixed volume of liquid is placed at the base of the VFD before rotation is initiated, with the characteristics of the film at steady state describing the fluid mechanics environment for most of the processing time. In CF, droplets fall periodically in a rotating tube which sustains a liquid thin film developed along the walls. To explore the dynamics of droplet landing and spreading, experiments were conducted using flat and hemispherical disks. In every spinning disk experiment the radial evolution of single droplets and the onset of instabilities, at the contact line and along the free surface of the film, were explored for a range of parameters. The parameters under investigation were the rotation rate, the height of release, the droplet volume, the smoothness and the geometry of the disk. During the spreading, the droplet was divided in two different areas, the film and the ring, with the ring volume being an important component for the onset of instabilities. The fluid motion related to ring volume variations (initially growing and later decreasing in volume, leaving liquid behind), described in this thesis, has not been found in existing literature. Perturbations at the contact line lead to fingering instability, with the fingers unfolding retrograde to the rotating disk. In parallel, spiral waves appear at the free surface of the film, unfolding prograde to the rotating disk. In the VFD, experiments were conducted under CM, exploring the film development over time, the film thickness and the reaction rate at a steady state of rotation. In CF, the entrainment of droplets in an already rotating film was explored. The film thickness tends to be the most critical parameter for the performance of the device as it defines whether the reaction occurs under turbulent or laminar conditions. Neutron imaging experiments, conducted at the Australian Nuclear Science and Technology Organisation (ANSTO), gave an insight to the film thickness at steady state in CM. The technique is more appropriate for stationary objects, thus a new methodology was developed in this thesis for rotating objects. Knowing the film thickness, pressure gradients along the film were determined. Keeping all the non-fluid related parameters the same, increased rotation rate leads to decreased thickness, which works in favour of homogeneous distribution of the reactants and increased pressure differences, directly related to variations in diffusion and advection. Overall, mathematical approximations were developed to describe the experimental observations both in the rotating disks and in the VFD. A new spreading pattern, was observed in the rotating disks, while mechanisms for enhanced diffusion and advection were observed in the VFD.John S. Latsis Foundation Tima Foundation Minas Kulukundis Trust Muscular Dystrophy Association Hellas Department of Applied Mathematics and Theoretical Physics Queens' college, Cambridge Disability Resource Centre, Cambridge Engineering and Physical Sciences Research Council (EPSRC