A Van der Pol-Mathieu equation for the dynamics of dust grain charge in dusty plasmas

The chaotic profile of dust grain dynamics associated with dust-acoustic oscillations in a dusty plasma is considered. The collective behaviour of the dust plasma component is described via a multi-fluid model, comprising Boltzmann distributed electrons and ions, as well as an equation of continuity possessing a source term for the dust grains, the dust momentum and Poisson's equations. A Van der Pol–Mathieu-type nonlinear ordinary differential equation for the dust grain density dynamics is derived. The dynamical system is cast into an autonomous form by employing an averaging method. Critical stability boundaries for a particular trivial solution of the governing equation with varying parameters are specified. The equation is analysed to determine the resonance region, and finally numerically solved by using a fourth-order Runge–Kutta method. The presence of chaotic limit cycles is pointed out.

On velocity-based local model networks for nonlinear identification

This paper exposes the strengths and weaknesses of the recently proposed velocity-based local model (LM) network. The global dynamics of the velocity-based blended representation are directly related to the dynamics of the underlying local models, an important property in the design of local controller networks. Furthermore, the sub-models are continuous-time and linear providing continuity with established linear theory and methods. This is not true for the conventional LM framework, where the global dynamics are only weakly related to the affine sub-models. In this paper, a velocity-based multiple model network is identified for a highly nonlinear dynamical system. The results show excellent dynamical modelling performances, highlighting the value of the velocity-based approach for the design and analysis of LM based control. Three important practical issues are also addressed. These relate to the blending of the velocity-based local models, the use of normalised Gaussian basis functions and the requirement of an input derivative.

Comparison of two construction algorithms for local model networks

The divide-and-conquer approach of local model (LM) networks is a common engineering approach to the identification of a complex nonlinear dynamical system. The global representation is obtained from the weighted sum of locally valid, simpler sub-models defined over small regions of the operating space. Constructing such networks requires the determination of appropriate partitioning and the parameters of the LMs. This paper focuses on the structural aspect of LM networks. It compares the computational requirements and performances of the Johansen and Foss (J&F) and LOLIMOT tree-construction algorithms. Several useful and important modifications to each algorithm are proposed. The modelling performances are evaluated using real data from a pilot plant of a pH neutralization process. Results show that while J&F achieves a more accurate nonlinear representation of the pH process, LOLIMOT requires significantly less computational effort.

Oblique electrostatic excitations in a magnetized plasma in the presence of excess superthermal electrons

The nonlinear propagation of ion-acoustic waves is considered in a magnetized plasma, composed of kappa distributed electrons and an inertial ion fluid. The fluid-dynamical system of equations governing the dynamics of ion-acoustic waves is reduced to a pseudoenergy-balance equation. The properties of arbitrary amplitude, obliquely propagating ion-acoustic solitary waves are thus investigated via a mechanical-motion analog (Sagdeev potential) approach. The presence of excess superthermal electrons is shown to influence the nature of magnetized ion-acoustic solitons. The influence on the soliton characteristics of relevant physical parameters such as obliqueness (the angle between soliton propagation direction and magnetic field), the electron deviation from a Maxwellian ("superthermality") and the soliton speed is investigated.

Lichen-induced biomodification of calcareous surfaces: Bioprotection versus biodeterioration

Studies demonstrate the active and passive capability of lichens to inhibit or retard the weathering of calcareous surfaces. Lichen coverage may actively protect a surface through shielding by the thallus and the binding and waterproofing of the rock surface and subsurface by fungal hyphae. Passive protection of rock surfaces may be induced by the formation of an insoluble encrustation, such as calcium oxalate, at the lichen-rock interface. Recent research suggests that the decay of hyphae, induced by changes in microenvironmental conditions, necrosis, parasitism or the natural physiological traits of particular lichen species, may expose a chemically and physically weakened substrate to dissolution triggering relatively rapid weathering-related surface lowering. Consequently, certain epilithic crustose and endolithic lichens may induce a period of surface stability throughout the course of their lifespan, followed by a phase of instability and rapid episodic microtopographical evolution after death and decay. A series of conceptual models is proposed to illustrate this idea over short (single lichen lifespan) and long (multiple lichen lifespans) timescales. The models suggest that the microscale biogeomorphological system of lichen-rock interaction is underpinned by nonlinear dynamical system theory as it exhibits dynamical instability and is consequently difficult to predict over a long timescale. Dominance by biodeterioration or bioprotection may be altered by changes in lichen species or in environmental conditions over time.

Direct, positive feedbacks produce instability in models of interrelationships among soil structure, plants and arbuscular mycorrhizal fungi

Current conceptual models of reciprocal interactions linking soil structure, plants and arbuscular mycorrhizal fungi emphasise positive feedbacks among the components of the system. However, dynamical systems with high dimensionality and several positive feedbacks (i.e. mutualism) are prone to instability. Further, organisms such as arbuscular mycorrhizal fungi (AMF) are obligate biotrophs of plants and are considered major biological agents in soil aggregate stabilization. With these considerations in mind, we developed dynamical models of soil ecosystems that reflect the main features of current conceptual models and empirical data, especially positive feedbacks and linear interactions among plants, AMF and the component of soil structure dependent on aggregates. We found that systems become increasingly unstable the more positive effects with Type I functional response (i.e., the growth rate of a mutualist is modified by the density of its partner through linear proportionality) are added to the model, to the point that increasing the realism of models by adding linear effects produces the most unstable systems. The present theoretical analysis thus offers a framework for modelling and suggests new directions for experimental studies on the interrelationship between soil structure, plants and AMF. Non-linearity in functional responses, spatial and temporal heterogeneity, and indirect effects can be invoked on a theoretical basis and experimentally tested in laboratory and field experiments in order to account for and buffer the local instability of the simplest of current scenarios. This first model presented here may generate interest in more explicitly representing the role of biota in soil physical structure, a phenomenon that is typically viewed in a more process- and management-focused context. (C) 2011 Elsevier Ltd. All rights reserved.

Dynamical role of system-environment correlations in non-Markovian dynamics

We analyze the role played by system-environment correlations in the emergence of non-Markovian dynamics. By working within the framework developed in Breuer et al. [Phys. Rev. Lett. 103, 210401 (2009)], we unveil a fundamental connection between non-Markovian behavior and dynamics of system-environment correlations. We derive an upper bound to the rate of change of the distinguishability between different states of the system that explicitly depends on the establishment of correlations between system and environment. We illustrate our results using a fully solvable spin-chain model, which allows us to gain insight into the mechanisms triggering non-Markovian evolution. © 2012 American Physical Society.

Dynamical symmetries and crossovers in a three-spin system with collective dissipation

We consider the non-equilibrium dynamics of a simple system consisting of interacting spin-1/2 particles subjected to a collective damping. The model is close to situations that can be engineered in hybrid electro/opto-mechanical settings. Making use of large-deviation theory, we find a Gallavotti-Cohen symmetry in the dynamics of the system as well as evidence for the coexistence of two dynamical phases with different activity levels. We show that additional damping processes smooth out this behavior. Our analytical results are backed up by Monte Carlo simulations that reveal the nature of the trajectories contributing to the different dynamical phases.

Dynamical and steady-state requirements for effective entanglement transfer

Entanglement transfer processes from a continuous-variable (CV) to a qubit system have primary importance in quantum information processing due to some practical implications in the realization of a quantum network. A CV system can propagate entanglement while a qubit system is easy to manipulate. We study conditions to entangle two atomic qubits with a two-mode squeezed field driving two cavities containing the atoms.

Dynamical entanglement transfer for quantum-information networks

A key element in the architecture of a quantum-information processing network is a reliable physical interface between fields and qubits. We study a process of entanglement transfer engineering, where two remote qubits respectively interact with an entangled two-mode continuous-variable (CV) field. We quantify the entanglement induced in the qubit state at the expenses of the loss of entanglement in the CV system. We discuss the range of mixed entangled states which can be obtained with this setup. Furthermore, we suggest a protocol to determine the residual entangling power of the light fields inferring, thus, the entanglement left in the field modes which, after the interaction, are no longer in a Gaussian state. Two different setups are proposed: a cavity-QED system and an interface between superconducting qubits and field modes. We address in detail the practical difficulties inherent in these two proposals, showing that the latter is promising in many aspects.

Enhanced dynamical entanglement transfer with multiple qubits

We present two strategies to enhance the dynamical entanglement transfer from continuous-variable (CV) to finite-dimensional systems by employing multiple qubits. First, we consider the entanglement transfer to a composite finite-dimensional system of many qubits simultaneously interacting with a bipartite CV field. We show that, considering realistic conditions in the generation of CV entanglement, a small number of qubits resonantly coupled to the CV system are sufficient for an almost complete dynamical transfer of the entanglement. Our analysis also sheds further light on the transition between the microscopic and macroscopic behaviors of composite finite-dimensional systems coupled to bosonic fields (like atomic clouds interacting with light). Furthermore, we present a protocol based on sequential interactions of the CV system with some ancillary qubit systems and on subsequent measurements, allowing us to probabilistically convert CV entanglement into "almost-perfect" Bell pairs of two qubits. Our proposals are suited for realizations in various experimental settings, ranging from cavity-QED to cavity-integrated superconducting devices.

Time operators and shift representation of dynamical systems

We introduce and characterise time operators for unilateral shifts and exact endomorphisms. The associated shift representation of evolution is related to the spectral representation by a generalized Fourier transform. We illustrate the results for a simple exact system, namely the Renyi map.

Disturbance attenuation in linear systems via dynamical compensators: A parametric eigenstructure assignment approach

A simple approach is proposed for disturbance attenuation in multivariable linear systems via dynamical output compensators based on complete parametric eigenstructure assignment. The basic idea is to minimise the H-2 norm of the disturbance-output transfer function using the design freedom provided by eigenstructure assignment. For robustness, the closed-loop system is restricted to be nondefective. Besides the design parameters, the closed-loop eigenvalues are also optimised within desired regions on the left-half complex plane to ensure both closed-loop stability and dynamical performance. With the proposed approach, additional closed-loop specifications can be easily achieved. As a demonstration, robust pole assignment, in the sense that the closed-loop eigenvalues are as insensitive as possible to open-loop system parameter perturbations, is treated. Application of the proposed approach to robust control of a magnetic bearing with a pair of opposing electromagnets and a rigid rotor is discussed.

WASP-8b: a retrograde transiting planet in a multiple system

We report the discovery of WASP-8b, a transiting planet of 2.25 ± 0.08 MJup on a strongly inclined eccentric 8.15-day orbit, moving in a retrograde direction to the rotation of its late-G host star. Evidence is found that the star is in a multiple stellar system with two other companions. The dynamical complexity of the system indicates that it may have experienced secular interactions such as the Kozai mechanism or a formation that differs from the “classical” disc-migration theory.