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

Relaxation of a dewetting contact line Part 1: A full-scale hydrodynamic calculation

The relaxation of a dewetting contact line is investigated theoretically in the so-called "Landau-Levich" geometry in which a vertical solid plate is withdrawn from a bath of partially wetting liquid. The study is performed in the framework of lubrication theory, in which the hydrodynamics is resolved at all length scales (from molecular to macroscopic). We investigate the bifurcation diagram for unperturbed contact lines, which turns out to be more complex than expected from simplified 'quasi-static' theories based upon an apparent contact angle. Linear stability analysis reveals that below the critical capillary number of entrainment, Ca_c, the contact line is linearly stable at all wavenumbers. Away from the critical point the dispersion relation has an asymptotic behaviour sigma~|q| and compares well to a quasi-static approach. Approaching Ca_c, however, a different mechanism takes over and the dispersion evolves from |q| to the more common q^2. These findings imply that contact lines can not be treated as universal objects governed by some effective law for the macroscopic contact angle, but viscous effects have to be treated explicitly.Comment: 21 pages, 9 figure

Nonlinear Systems

Open Mathematics is a challenging notion for theoretical modeling, technical analysis, and numerical simulation in physics and mathematics, as well as in many other fields, as highly correlated nonlinear phenomena, evolving over a large range of time scales and length scales, control the underlying systems and processes in their spatiotemporal evolution. Indeed, available data, be they physical, biological, or financial, and technologically complex systems and stochastic systems, such as mechanical or electronic devices, can be managed from the same conceptual approach, both analytically and through computer simulation, using effective nonlinear dynamics methods. The aim of this Special Issue is to highlight papers that show the dynamics, control, optimization and applications of nonlinear systems. This has recently become an increasingly popular subject, with impressive growth concerning applications in engineering, economics, biology, and medicine, and can be considered a veritable contribution to the literature. Original papers relating to the objective presented above are especially welcome subjects. Potential topics include, but are not limited to: Stability analysis of discrete and continuous dynamical systems; Nonlinear dynamics in biological complex systems; Stability and stabilization of stochastic systems; Mathematical models in statistics and probability; Synchronization of oscillators and chaotic systems; Optimization methods of complex systems; Reliability modeling and system optimization; Computation and control over networked systems

Stochastic models of intracellular transport

The interior of a living cell is a crowded, heterogenuous, fluctuating environment. Hence, a major challenge in modeling intracellular transport is to analyze stochastic processes within complex environments. Broadly speaking, there are two basic mechanisms for intracellular transport: passive diffusion and motor-driven active transport. Diffusive transport can be formulated in terms of the motion of an over-damped Brownian particle. On the other hand, active transport requires chemical energy, usually in the form of ATP hydrolysis, and can be direction specific, allowing biomolecules to be transported long distances; this is particularly important in neurons due to their complex geometry. In this review we present a wide range of analytical methods and models of intracellular transport. In the case of diffusive transport, we consider narrow escape problems, diffusion to a small target, confined and single-file diffusion, homogenization theory, and fractional diffusion. In the case of active transport, we consider Brownian ratchets, random walk models, exclusion processes, random intermittent search processes, quasi-steady-state reduction methods, and mean field approximations. Applications include receptor trafficking, axonal transport, membrane diffusion, nuclear transport, protein-DNA interactions, virus trafficking, and the self–organization of subcellular structures

Introduction to State Estimation of High-Rate System Dynamics

Engineering systems experiencing high-rate dynamic events, including airbags, debris detection, and active blast protection systems, could benefit from real-time observability for enhanced performance. However, the task of high-rate state estimation is challenging, in particular for real-time applications where the rate of the observer’s convergence needs to be in the microsecond range. This paper identifies the challenges of state estimation of high-rate systems and discusses the fundamental characteristics of high-rate systems. A survey of applications and methods for estimators that have the potential to produce accurate estimations for a complex system experiencing highly dynamic events is presented. It is argued that adaptive observers are important to this research. In particular, adaptive data-driven observers are advantageous due to their adaptability and lack of dependence on the system model

Task-space dynamic control of underwater robots

This thesis is concerned with the control aspects for underwater tasks performed by marine robots. The mathematical models of an underwater vehicle and an underwater vehicle with an onboard manipulator are discussed together with their associated properties. The task-space regulation problem for an underwater vehicle is addressed where the desired target is commonly specified as a point. A new control technique is proposed where the multiple targets are defined as sub-regions. A fuzzy technique is used to handle these multiple sub-region criteria effectively. Due to the unknown gravitational and buoyancy forces, an adaptive term is adopted in the proposed controller. An extension to a region boundary-based control law is then proposed for an underwater vehicle to illustrate the flexibility of the region reaching concept. In this novel controller, a desired target is defined as a boundary instead of a point or region. For a mapping of the uncertain restoring forces, a least-squares estimation algorithm and the inverse Jacobian matrix are utilised in the adaptive control law. To realise a new tracking control concept for a kinematically redundant robot, subregion tracking control schemes with a sub-tasks objective are developed for a UVMS. In this concept, the desired objective is specified as a moving sub-region instead of a trajectory. In addition, due to the system being kinematically redundant, the controller also enables the use of self-motion of the system to perform sub-tasks (drag minimisation, obstacle avoidance, manipulability and avoidance of mechanical joint limits)

Instantons revisited: dynamical tunnelling and resonant tunnelling

Starting from trace formulae for the tunnelling splittings (or decay rates) analytically continued in the complex time domain, we obtain explicit semiclassical expansions in terms of complex trajectories that are selected with appropriate complex-time paths. We show how this instanton-like approach, which takes advantage of an incomplete Wick rotation, accurately reproduces tunnelling effects not only in the usual double-well potential but also in situations where a pure Wick rotation is insufficient, for instance dynamical tunnelling or resonant tunnelling. Even though only one-dimensional autonomous Hamiltonian systems are quantitatively studied, we discuss the relevance of our method for multidimensional and/or chaotic tunnelling