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At least 217 records · Page 12

Nonlinear Dynamics of Parametric Oscillations of Polaritons in a Microcavity

The dynamics of polaritons in a microcavity in the parametric oscillator mode, when two pump polaritons turn into the signal and idler polaritons and vice versa, has been studied. The pumping is carried out using two lasers with close frequencies. Analytical solutions of the system of nonlinear differential equations have been obtained. The periodic and aperiodic modes of the transformation of a pair of pump polaritons into signal and idler polaritons have been found.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

A Nonlinear Dynamic Inversion Predictor-Based Model Reference Adaptive Controller for a Generic Transport Model

Presented here is a Predictor-Based Model Reference Adaptive Control (PMRAC) architecture for a generic transport aircraft. At its core, this architecture features a three-axis, non-linear, dynamic-inversion controller. Command inputs for this baseline controller are provided by pilot roll-rate, pitch-rate, and sideslip commands. This paper will first thoroughly present the baseline controller followed by a description of the PMRAC adaptive augmentation to this control system. Results are presented via a full-scale, nonlinear simulation of NASA s Generic Transport Model (GTM).

Campbell, Stefan F.↗

Examples of the nonlinear dynamics of ballistic capture and escape in the earth-moon system

An example of a trajectory is given which is initially captured in an elliptic resonant orbit about the earth and then ballistically escapes the earth-moon system. This is demonstrated by a numerical example in three-dimensions using a planetary ephemeris. Another example shows a mechanism of how an elliptic orbit about the earth can increase its energy by performing a complex nonlinear transition to an elliptic orbit of a larger semi-major axis. Capture is also considered. An application of ballistic capture at the moon via an unstable periodic orbit using the four-body sun-earth-moon-S/C interaction is described.

Belbruno, Edward A.↗

Edge localized mode rotation and the nonlinear dynamics of filaments

Edge Localized Modes (ELMs) rotating precursors were reported few milliseconds before an ELM crash in several tokamak experiments. Also, the reversal of the filaments rotation at the ELM crash is commonly observed. In this article, we present a mathematical model that reproduces the rotation of the ELM precursors as well as the reversal of the filaments rotation at the ELM crash. Linear ballooning theory is used to establish a formula estimating the rotation velocity of ELM precursors. The linear study together with nonlinear magnetohydrodynamic simulations give an explanation to the rotations observed experimentally. Unstable ballooning modes, localized at the pedestal, grow and rotate in the electron diamagnetic direction in the laboratory reference frame. Approaching the ELM crash, this rotation decreases corresponding to the moment when the magnetic reconnection occurs. During the highly nonlinear ELM crash, the ELM filaments are cut from the main plasma due to the strong sheared mean flow that is nonlinearly generated via the Maxwell stress tensor.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Nonlinear Dynamic Behavior of Impact Damage in a Composite Skin-Stiffener Structure

One of the key issues in composite structures for aircraft applications is the early identification of damage. Often, service induced damage does not involve visible plastic deformation, but internal matrix related damage, like delaminations. A wide range of technologies, comprising global vibration and local wave propagation methods can be employed for health monitoring purposes. Traditional low frequency modal analysis based methods are linear methods. The effectiveness of these methods is often limited since they rely on a stationary and linear approximation of the system. The nonlinear interaction between a low frequency wave field and a local impact induced skin-stiffener failure is experimentally demonstrated in this paper. The different mechanisms that are responsible for the nonlinearities (opening, closing and contact) of the distorted harmonic waveforms are separated with the help of phase portraits. A basic analytical model is employed to support the observations.

Ooijevaar, T. H.↗

Numerical investigation of bubble nonlinear dynamics characteristics

The complicated dynamical behaviors of bubble oscillation driven by acoustic wave can provide favorable conditions for many engineering applications. On the basis of Keller-Miksis model, the influences of control parameters, including acoustic frequency, acoustic pressure and radius of gas bubble, are discussed by utilizing various numerical analysis methods, Furthermore, the law of power spectral variation is studied. It is shown that the complicated dynamic behaviors of bubble oscillation driven by acoustic wave, such as bifurcation and chaos, further the stimulated scattering processes are revealed.

42 ENGINEERING↗

Nonlinear dynamics of C–terminal tails in cellular microtubules

The mechanical and electrical properties, and information processing capabilities of microtubules are the permanent subject of interest for carrying out experiments in vitro and in silico, as well as for theoretical attempts to elucidate the underlying processes. In this paper, we developed a new model of the mechano–electrical waves elicited in the rows of very flexible C–terminal tails which decorate the outer surface of each microtubule. The fact that C–terminal tails play very diverse roles in many cellular functions, such as recruitment of motor proteins and microtubule–associated proteins, motivated us to consider their collective dynamics as the source of localized waves aimed for communication between microtubule and associated proteins. Our approach is based on the ferroelectric liquid crystal model and it leads to the effective asymmetric double-well potential which brings about the conditions for the appearance of kink–waves conducted by intrinsic electric fields embedded in microtubules. These kinks can serve as the signals for control and regulation of intracellular traffic along microtubules performed by processive motions of motor proteins, primarly from kinesin and dynein families. On the other hand, they can be precursors for initiation of dynamical instability of microtubules by recruiting the proper proteins responsible for the depolymerization process.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Nonlinear dynamics of mini-satellite respinup by weak internal controllable torques

Contemporary space engineering advanced new problem before theoretical mechanics and motion control theory: a spacecraft directed respinup by the weak restricted control internal forces. The paper presents some results on this problem, which is very actual for energy supply of information mini-satellites (for communication, geodesy, radio- and opto-electronic observation of the Earth et al.) with electro-reaction plasma thrusters and gyro moment cluster based on the reaction wheels or the control moment gyros. The solution achieved is based on the methods for synthesis of nonlinear robust control and on rigorous analytical proof for the required spacecraft rotation stability by Lyapunov function method. These results were verified by a computer simulation of strongly nonlinear oscillatory processes at respinuping of a flexible spacecraft.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Nonlinear Dynamic Analyses of STS-1 Forward RCS Oxidizer Tank Structural Failure

At liftoff of the first Space Shuttle mission, a strong ignition overpressure pulse excited the stack. The frequency of the experienced pressure wave exceeded pre-launch predictions, and resulted in high, alternating normal accelerations along the length of the vehicle. As result of this unexpected loading, an oxidizer tank support strut in the orbiter’s forward reaction control system module failed in buckling under axial compression, which could have led to loss of the mission, crew, and vehicle. This incident is investigated in more detail using linear and nonlinear finite element analyses, complementing previous analyses with classical structural mechanics. The results of these analyses are examined to provide additional insight into the accident and to better inform future design decisions for modern space vehicle systems and structures.

Space Shuttle↗

Nonlinear Dynamic Analyses of STS-1 Forward RCS Oxidizer Tank Structural Failure

At liftoff of the first Space Shuttle mission, a strong ignition overpressure pulse excited the stack. The frequency of the experienced pressure wave exceeded pre-launch predictions, and resulted in high, alternating normal accelerations along the length of the vehicle. As result of this unexpected loading, an oxidizer tank support strut in the orbiter’s forward reaction control system module failed in buckling under axial compression, which could have led to loss of the mission, crew, and vehicle. This incident is investigated in more detail using linear and nonlinear finite element analyses, complementing previous analyses with classical structural mechanics. The results of these analyses are examined to provide additional insight into the accident and to better inform future design decisions for modern space vehicle systems and structures.

Space Shuttle↗

Nonlinear Dynamic Analysis of Deploying Flexible Space Booms

A fundamental investigation of the planar deployment and lock-up of two flexible boom type appendages which have attached tip masses and are connected to a central rigid body through a rotational spring is presented. Nondimensional parameters are identified and it is shown that, in general, the solution depends only on two mass ratios and one nondimensional stiffness parameter. Results are presented for boom tip deflections, deployment time and root moments at lock-up. A threshold value of the nondimensional stiffness parameter is identified beyond which boom deflections become large. Also, a thorough examination of the effect of nonlinear terms in the equations governing the deployment phase is performed. Nonlinear terms in the deployment equations due to kinematics and structural deformation are required to predict more accurately boom deflections, but retention of an inconsistent set of nonlinear terms leads to erroneous results. In particular, retaining nonlinear kinematic terms while neglecting nonlinear structural terms can produce inaccurate results even below the threshold stiffness value.

Mcgowan, P. E.↗

Nonlinear dynamic analysis of flexible multibody systems

Two approaches are developed to analyze the dynamic behavior of flexible multibody systems. In the first approach each body is modeled with a modal methodology in a local non-inertial frame of reference, whereas in the second approach, each body is modeled with a finite element methodology in the inertial frame. In both cases, the interaction among the various elastic bodies is represented by constraint equations. The two approaches were compared for accuracy and efficiency: the first approach is preferable when the nonlinearities are not too strong but it becomes cumbersome and expensive to use when many modes must be used. The second approach is more general and easier to implement but could result in high computation costs for a large system. The constraints should be enforced in a time derivative fashion for better accuracy and stability.

Bauchau, Olivier A.↗

A concept for a magnetic field detector underpinned by the nonlinear dynamics of coupled multiferroic devices

Multiferroic (MF) composites, in which magnetic and ferroelectric orders coexist, represent a very attractive class of materials with promising applications in areas, such as spintronics, memories, and sensors. One of the most important multiferroics is the perovskite phase of bismuth ferrite, which exhibits weak magnetoelectric properties at room temperature; its properties can be enhanced by doping with other elements such as dysprosium. A recent paper has demonstrated that a thin film of Bi{sub 0.7}Dy{sub 0.3}FeO{sub 3} shows good magnetoelectric coupling. In separate work it has been shown that a carefully crafted ring connection of N (N odd and N ≥ 3) ferroelectric capacitors yields, past a critical point, nonlinear oscillations that can be exploited for electric (E) field sensing. These two results represent the starting point of our work. In this paper the (electrical) hysteresis, experimentally measured in the MF material Bi{sub 0.7}Dy{sub 0.3}FeO{sub 3}, is characterized with the applied magnetic field (B) taken as a control parameter. This yields a “blueprint” for a magnetic (B) field sensor: a ring-oscillator coupling of N = 3 Sawyer-Tower circuits each underpinned by a mutliferroic element. In this configuration, the changes induced in the ferroelectric behavior by the external or “target” B-field are quantified, thus providing a pathway for very low power and high sensitivity B-field sensing.

36 MATERIALS SCIENCE↗

Nonlinear Dynamic Inversion Baseline Control Law: Architecture and Performance Predictions

A model reference dynamic inversion control law has been developed to provide a baseline control law for research into adaptive elements and other advanced flight control law components. This controller has been implemented and tested in a hardware-in-the-loop simulation; the simulation results show excellent handling qualities throughout the limited flight envelope. A simple angular momentum formulation was chosen because it can be included in the stability proofs for many basic adaptive theories, such as model reference adaptive control. Many design choices and implementation details reflect the requirements placed on the system by the nonlinear flight environment and the desire to keep the system as basic as possible to simplify the addition of the adaptive elements. Those design choices are explained, along with their predicted impact on the handling qualities.

Miller, Christopher J.↗

Experimental nonlinear dynamical studies in cesium magneto-optical trap using time-series analysis

A magneto-optical trap of neutral atoms is essentially a dissipative quantum system. The fast thermal atoms continuously dissipate their energy to the environment via spontaneous emissions during the cooling. The atoms are, therefore, strongly coupled with the vacuum reservoir and the laser field. The vacuum fluctuations as well as the field fluctuations are imparted to the atoms as random photon recoils. Consequently, the external and internal dynamics of atoms becomes stochastic. In this paper, we have investigated the stochastic dynamics of the atoms in a magneto-optical trap during the loading process. The time series analysis of the fluorescence signal shows that the dynamics of the atoms evolves, like all dissipative systems, from deterministic to the chaotic regime. The subsequent disappearance and revival of chaos was attributed to chaos synchronization between spatially different atoms in the magneto-optical trap.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Robust Control Design for Uncertain Nonlinear Dynamic Systems

Robustness to parametric uncertainty is fundamental to successful control system design and as such it has been at the core of many design methods developed over the decades. Despite its prominence, most of the work on robust control design has focused on linear models and uncertainties that are non-probabilistic in nature. Recently, researchers have acknowledged this disparity and have been developing theory to address a broader class of uncertainties. This paper presents an experimental application of robust control design for a hybrid class of probabilistic and non-probabilistic parametric uncertainties. The experimental apparatus is based upon the classic inverted pendulum on a cart. The physical uncertainty is realized by a known additional lumped mass at an unknown location on the pendulum. This unknown location has the effect of substantially altering the nominal frequency and controllability of the nonlinear system, and in the limit has the capability to make the system neutrally stable and uncontrollable. Another uncertainty to be considered is a direct current motor parameter. The control design objective is to design a controller that satisfies stability, tracking error, control power, and transient behavior requirements for the largest range of parametric uncertainties. This paper presents an overview of the theory behind the robust control design methodology and the experimental results.

Kenny, Sean P.↗

Nonlinear dynamics of multiple Alfvén modes driven by trapped energetic ions in tokamaks: A triplet paradigm

Non-linear dynamics of multiple infernal Alfvén eigenmodes—a subset of global Alfvén eigenmodes in tokamak plasmas with extended low-shear central core [Marchenko et al., Phys. Plasmas 16, 092502 (2009)]—is studied. The analysis is carried out for a mode triplet with toroidal mode-numbers n=1, 2, 3. It was assumed that the n = 1 mode was linearly unstable due to precession resonance with trapped fast ions, whereas the other modes were linearly damped. The modes were coupled due to a non-linearity in a bounce-averaged drift kinetic equation for the distribution function of fast ions. Nonlinear equations for the mode amplitudes and phases are derived and solved numerically. It is found that the temporal evolution of the amplitudes and the phase (responsible for the frequency chirping) of the modes exhibit Hopf bifurcations to stable limit cycles. This can explain a synchronous cyclic destabilization of multiple modes in Alfvén avalanches (sudden growth of amplitudes of the mode cluster with different n and approximately equal frequency spacing) in NSTX and bursting modes in MAST—events, which resulted in enhanced loss of fast ions.

Marchenko, V. S. (ORCID:0000000261480533)↗

Understanding the nonlinear dynamics of driven particles in supercooled liquids in terms of an effective temperature

In active microrheology, the mechanical properties of a material are tested by adding probe particles which are pulled by an external force. In case of supercooled liquids, strong forcing leads to a thinning of the host material which becomes more pronounced as the system approaches the glass transition. In this work, we provide a quantitative theoretical description of this thinning behavior based on the properties of the Potential Energy Landscape (PEL) of a model glass-former. A key role plays the trap-like nature of the PEL. We find that the mechanical properties in the strongly driven system behave the same as in a quiescent system at an enhanced temperature, giving rise to a well-characterized effective temperature. Furthermore, this effective temperature turns out to be independent of the chosen observable and individually shows up in the thermodynamic and dynamic properties of the system. Based on this underlying theoretical understanding, we can estimate its dependence on temperature and force by the PEL-properties of the quiescent system. We furthermore critically discuss the relevance of effective temperatures obtained by scaling relations for the description of out-of-equilibrium situations.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗