Discrete kink dynamics in hydrogen-bonded chains I: The one-component model

We study topological solitary waves (kinks and antikinks) in a nonlinear one-dimensional Klein-Gordon chain with the on-site potential of a double-Morse type. This chain is used to describe the collective proton dynamics in quasi-one-dimensional networks of hydrogen bonds, where the on-site potential plays role of the proton potential in the hydrogen bond. The system supports a rich variety of stationary kink solutions with different symmetry properties. We study the stability and bifurcation structure of all these stationary kink states. An exactly solvable model with a piecewise ``parabola-constant'' approximation of the double-Morse potential is suggested and studied analytically. The dependence of the Peierls-Nabarro potential on the system parameters is studied. Discrete travelling-wave solutions of a narrow permanent profile are shown to exist, depending on the anharmonicity of the Morse potential and the cooperativity of the hydrogen bond (the coupling constant of the interaction between nearest-neighbor protons).Comment: 12 pages, 20 figure

Mechanical Models of Microtubules

Microtubules are the major part of the cytoskeleton. They are involved in nuclear and cell division and serve as a network for motor proteins. The first model that describes nonlinear dynamics of microtubules was introduced in 1993. Three nonlinear models are described in this chapter. They are longitudinal U-model, representing an improved version of the first model, radial φ -model and new general model. Also, two mathematical procedures are explained. These are continuum and semi-discrete approximations. Continuum approximation yields to either kink-type or bell-type solitons, while semi-discrete one predicts localized modulated waves moving along microtubules. Some possible improvements and suggestions for future research are discussed

Nonlinear waves in a model for silicate layers

Some layered silicates are composed of positive ions, surrounded by layers of ions with opposite sign. Mica muscovite is a particularly interesting material, because there exist fossil and experimental evidence for nonlinear excitations transporting localized energy and charge along the cation rows within the potassium layers. This evidence suggest that there are different kinds of excitations with different energies and properties. Some of the authors proposed recently a one-dimensional model based in physical principles and the silicate structure. The main characteristic of the model is that it has a hard substrate potential and two different repulsion terms, between ions and nuclei. In a previous work with this model, it was found the propagation of crowdions, i.e., lattice kinks in a lattice with substrate potential that transport mass and charge. They have a single specific velocity and energy coherent with the experimental data. In the present work we perform a much more thorough search for nonlinear excitations in the same model using the pseudospectral method to obtain exact nanopteron solutions, which are single kinks with tails, crowdions and bi-crowdions. We analyze their velocities, energies and stability or instability and the possible reasons for the latter. We relate the different excitations with their possible origin from recoils from different beta decays and with the fossil tracks. We explore the consequences of some variation of the physical parameters because their values are not perfectly known. Through a different method, we also have found stationary and moving breathers, that is, localized nonlinear excitations with an internal vibration. Moving breathers have small amplitude and energy, which is also coherent with the fossil evidence.MINECO (Spain) FIS2015-65998-C2-2-PJunta de Andalucía 2017/FQM-280Universidad de Sevilla (España) grants VI PPIT-US-201

Complexity, Emergent Systems and Complex Biological Systems:\ud Complex Systems Theory and Biodynamics. [Edited book by I.C. Baianu, with listed contributors (2011)]

An overview is presented of System dynamics, the study of the behaviour of complex systems, Dynamical system in mathematics Dynamic programming in computer science and control theory, Complex systems biology, Neurodynamics and Psychodynamics.\u

Nonlinear Instabilities in Chemical and Electrochemical Systems

This dissertation focuses on designing and manipulating nonlinear chemical and electrochemical reactions, with the aim of discovering new behaviors as well as gaining insights into their underlying mechanisms. In Chapter 2 the nonlinear behavior of the 4-aminophenol – bromate photoreaction was investigated from two directions. First, a second autocatalytic cycle was introduced through the incorporation of the metal catalyst cerium (IV). It was found that once the autocatalytic cycles were effectively balanced, complexity in the form of mixed mode oscillations was observed in a closed reactor. This dynamic behavior was successfully simulated using a modified model, which qualitatively reproduced the experimental results. It was also found that the precipitate which forms at the onset of the reaction of 4-aminophenol with bromate, N-bromo-1,4-benzoquinone-4-imine, could form a new bromate-based photochemical oscillator. In Chapter 3, the autocatalytic oxidation of 2-methyl-1,4-hydroquinone by acidic bromate lead to the discovery of a new photochemical oscillator. The system was found to be very sensitive to the intensity of illumination supplied, and complexity in the form of sequential oscillations was discovered using either ferroin or cerium (IV) as catalysts. Interestingly, cerium (IV) had a much more profound effect on the dynamical behavior, substantially lengthening the oscillatory period as well as being capable of inducing mixed-mode oscillations. Chapter 4 reports findings on the photosensitive 4-nitrophenol - bromate reaction. Extreme photo-inhibition was found to occur when illumination was supplied to the system whether in a stirred reactor or when being studied in a spatially extended system. Reaction diffusion experiments showed that under certain conditions long lasting complexity in the form of propagation failures took place. In Chapter 5, oscillations in both current density and potential were observed during the electro-oxidation of bromide ions. Interestingly, mechanistic findings suggest that the oscillations occurring during the oxidation of bromide ions on a platinum electrode belong to the type of oscillator referred to as Capacitance Mediated Positive Differential Resistance oscillator, and is the first solution based system to fit this class. In Chapter 6, the electro-oxidation of two sulfur compounds was seen to display nonlinear behavior. First, the oxidation of hydroxymethanesulfinate leads to oscillations in both current and potential on platinum or gold electrodes. The formation of an inhibiting layer was seen to have a substantial influence on the systems’ ability to support sustained oscillatory behavior. Electrochemical Impedance Spectroscopy showed that the oxidation of hydroxymethanesulfinate fits the class of an HN-NDR type oscillator. The oxidation of methionine only displayed nonlinear behavior on a gold surface, and only when operated under potentiostatic conditions. The oscillations were accompanied by gold dissolution and it was found that the electro-oxidation of methionine belongs to the N-NDR class. Two novel examples of utilizing nonlinear reactions towards application-based research is shown in Chapter 7. Here, the 4-nitrophenol – bromate oscillator is used to fabricate platinum nanoparticles, exploiting the dynamic bromide ion concentration to guide the growth of the noble metal nanocrystals. As an example of using an electrochemical nonlinear reaction, the gold dissolution occurring during the oxidation of methionine was found to lead to the fabrication of a Au nanoparticle modified electrode. This modified electrode was found to be capable of simultaneously detecting both hydroquinone and pyrocatechol in solutions containing both isomers, which is a significant improvement over regular Au electrodes

Marshall Space Flight Center Research and Technology Report 2019

Today, our calling to explore is greater than ever before, and here at Marshall Space Flight Centerwe make human deep space exploration possible. A key goal for Artemis is demonstrating and perfecting capabilities on the Moon for technologies needed for humans to get to Mars. This years report features 10 of the Agencys 16 Technology Areas, and I am proud of Marshalls role in creating solutions for so many of these daunting technical challenges. Many of these projects will lead to sustainable in-space architecture for human space exploration that will allow us to travel to the Moon, on to Mars, and beyond. Others are developing new scientific instruments capable of providing an unprecedented glimpse into our universe. NASA has led the charge in space exploration for more than six decades, and through the Artemis program we will help build on our work in low Earth orbit and pave the way to the Moon and Mars. At Marshall, we leverage the skills and interest of the international community to conduct scientific research, develop and demonstrate technology, and train international crews to operate further from Earth for longer periods of time than ever before first at the lunar surface, then on to our next giant leap, human exploration of Mars. While each project in this report seeks to advance new technology and challenge conventions, it is important to recognize the diversity of activities and people supporting our mission. This report not only showcases the Centers capabilities and our partnerships, it also highlights the progress our people have achieved in the past year. These scientists, researchers and innovators are why Marshall and NASA will continue to be a leader in innovation, exploration, and discovery for years to come

Dynamics and mechanism studies of nonlinear chemical systems

The kinetics and mechanisms of oxidation of selected thiocarbamides (tetra-methylthiourea, trimethylthiourea, phenylthiourea, and 2-aminoethanethiolsulfuric acid) by chlorite in aqueous acidic media are investigated using UV/Vis, NMR, Stopped-flow techniques, and qualitative analysis. The reactions were extremely complex, with reaction dynamics strongly influenced by the pH of the reaction medium and formation of stable intermediates (sulfonic acids). Results revealed that oxidations of substituted thioureas do not always proceed via a stepwise oxidation of the sulfur center. Instead, reactions occurred in two stages: S-oxygenation of the sulfur center to yield the sulfinic acid, which then reacts in the second phase predominantly through an initial hydrolysis to produce a urea-type residue and the sulfoxylate anion. The sulfoxylate anion, a highly reducing species, is then rapidly oxidized to sulfate.;Experimental and numerical studies of local periodic forcing on an excitable Belousov-Zhabotinsky (BZ) medium in a thin gel layer are reported. Rather than the traditional suprathreshold perturbations giving rise to a local oscillatory state, waves were initiated in an excitable system via localized small amplitude variations in light intensity, without crossing into the oscillatory regime of the autonomous system. Initiation of waves in the initially quiescent medium was possible when the frequency of the sinusoidal perturbation was suitably tuned to that of the autonomous system. The region in phase space where wave initiation was possible depended on the parameter values of the perturbation, namely forcing frequency and forcing amplitude, and on the inherent properties of the autonomous system. Resonance patterns are found by relating the period between two waves to the period of the sinusoidal perturbation.;Experimental and theoretical studies of the peroxidase-oxidase (PO) reaction are reviewed. Numerical investigations into the initiation of trigger waves in an oscillatory one-dimensional PO reaction-diffusion system are presented. Trigger waves are initiated in the oscillatory system via localized perturbations in the concentration of one of the variables using the extended BFSO model. The chemical waves traveled with a sharp front and were not able to penetrate barriers to diffusion, which are properties characteristic of trigger waves