Analysis of chaotic instabilities in a rotating body with internal energy dissipation

Melnikov's method is used to analytically predict the onset of chaotic instability in a rotating body with internal energy dissipation. The model has been found to exhibit chaotic instability when a harmonic disturbance torque is applied to the system for a range of forcing amplitude and frequency. Such a model may be considered to be representative of the dynamical behavior of a number of physical systems such as a spinning spacecraft. In spacecraft, disturbance torques may arise under malfunction of the control system, from an unbalanced rotor, from vibrations in appendages or from orbital variations. Chaotic instabilities arising from such disturbances could introduce uncertainties and irregularities into the motion of the multibody system and consequently could have disastrous effects on its intended operation. A comprehensive stability analysis is performed and regions of nonlinear behavior are identified. Subsequently, the closed form analytical solution for the unperturbed system is obtained in order to identify homoclinic orbits. Melnikov's method is then applied on the system once transformed into Hamiltonian form. The resulting analytical criterion for the onset of chaotic instability is obtained in terms of critical system parameters. The sufficient criterion is shown to be a useful predictor of the phenomenon via comparisons with numerical results. Finally, for the purposes of providing a complete, self-contained investigation of this fundamental system, the control of chaotic instability is demonstated using Lyapunov's method.

Prediction of chaotic instabilities in a dragline bucket swing

The occurrence of chaotic instabilities is investigated in the swing motion of a dragline bucket during operation cycles. A dragline is a large, powerful, rotating multibody system utilised in the mining industry for removal of overburden. A simplified representative model of the dragline is developed in the form of a fundamental non-linear rotating multibody system with energy dissipation. An analytical predictive criterion for the onset of chaotic instability is then obtained in terms of critical system parameters using Melnikov's method. The model is shown to exhibit chaotic instability due to a harmonic slew torque for a range of amplitudes and frequencies. These chaotic instabilities could introduce irregularities into the motion of the dragline system, rendering the system difficult to control by the operator and/or would have undesirable effects on dragline productivity and fatigue lifetime. The sufficient analytical criterion for the onset of chaotic instability is shown to be a useful predictor of the phenomenon under steady and unsteady slewing conditions via comparisons with numerical results. (c) 2005 Elsevier Ltd. All rights reserved.

Dynamical properties of a strongly correlated model for quarter-filled layered organic molecular crystals

The dynamical properties of an extended Hubbard model, which is relevant to quarter-filled layered organic molecular crystals, are analyzed. We have computed the dynamical charge correlation function, spectral density, and optical conductivity using Lanczos diagonalization and large-N techniques. As the ratio of the nearest-neighbor Coulomb repulsion, V, to the hopping integral, t, increases there is a transition from a metallic phase to a charge-ordered phase. Dynamical properties close to the ordering transition are found to differ from the ones expected in a conventional metal. Large-N calculations display an enhancement of spectral weight at low frequencies as the system is driven closer to the charge-ordering transition in agreement with Lanczos calculations. As V is increased the charge correlation function displays a collective mode which, for wave vectors close to (pi,pi), increases in amplitude and softens as the charge-ordering transition is approached. We propose that inelastic x-ray scattering be used to detect this mode. Large-N calculations predict superconductivity with d(xy) symmetry close to the ordering transition. We find that this is consistent with Lanczos diagonalization calculations, on lattices of 20 sites, which find that the binding energy of two holes becomes negative close to the charge-ordering transition.

Numerical evaluation of three dimensional effects in planar flow birefringence

The influence of three dimensional effects on isochromatic birefringence is evaluated for planar flows by means of numerical simulation. Two fluid models are investigated in channel and abrupt contraction geometries. In practice, the flows are confined by viewing windows, which alter the stresses along the optical path. The observed optical properties differ therefore from their counterpart in an ideal two-dimensional flow. To investigate the influence of these effects, the stress optical rule and the differential propagation Mueller matrix are used. The material parameters are selected so that a retardation of multiple orders is achieved, as is typical for highly birefringent melts. Errors due to three dimensional effects are mainly found on the symmetry plane, and increase significantly with the flow rate. Increasing the geometric aspect ratio improve the accuracy provided that the error on the retardation is less than one order. (C) 2004 Elsevier B.V. All rights reserved.

Finite element analysis of fault bend influence on stick-slip instability along an intra-plate fault

Earthquakes have been recognized as resulting from stick-slip frictional instabilities along the faults between deformable rocks. A three-dimensional finite-element code for modeling the nonlinear frictional contact behaviors between deformable bodies with the node-to-point contact element strategy has been developed and applied here to investigate the fault geometry influence on the nucleation and development process of the stick-slip instability along an intra-plate fault through a typical fault bend model, which has a pre-cut fault that is artificially bent by an angle of 5.6degrees at the fault center. The numerical results demonstrate that the geometry of the fault significantly affects nucleation, termination and restart of the stick-slip instability along the intra-plate fault, and all these instability phenomena can be well simulated using the current finite-element algorithm.

Theoretical investigation of convective instability in inclined and fluid-saturated three-dimensional fault zones.

The convective instability of pore-fluid flow in inclined and fluid-saturated three-dimensional fault zones has been theoretically investigated in this paper. Due to the consideration of the inclined three-dimensional fault zone with any values of the inclined angle, it is impossible to use the conventional linear stability analysis method for deriving the critical condition (i.e., the critical Rayleigh number) which can be used to investigate the convective instability of the pore-fluid flow in an inclined three-dimensional fault zone system. To overcome this mathematical difficulty, a combination of the variable separation method and the integration elimination method has been used to derive the characteristic equation, which depends on the Rayleigh number and the inclined angle of the inclined three-dimensional fault zone. Using this characteristic equation, the critical Rayleigh number of the system can be numerically found as a function of the inclined angle of the three-dimensional fault zone. For a vertically oriented three-dimensional fault zone system, the critical Rayleigh number of the system can be explicitly derived from the characteristic equation. Comparison of the resulting critical Rayleigh number of the system with that previously derived in a vertically oriented three-dimensional fault zone has demonstrated that the characteristic equation of the Rayleigh number is correct and useful for investigating the convective instability of pore-fluid flow in the inclined three-dimensional fault zone system. The related numerical results from this investigation have indicated that: (1) the convective pore-fluid flow may take place in the inclined three-dimensional fault zone; (2) if the height of the fault zone is used as the characteristic length of the system, a decrease in the inclined angle of the inclined fault zone stabilizes the three-dimensional fundamental convective flow in the inclined three-dimensional fault zone system; (3) if the thickness of the stratum is used as the characteristic length of the system, a decrease in the inclined angle of the inclined fault zone destabilizes the three-dimensional fundamental convective flow in the inclined three-dimensional fault zone system; and that (4) the shape of the inclined three-dimensional fault zone may affect the convective instability of pore-fluid flow in the system. (C) 2004 Published by Elsevier B.V.

QRT: A Qr-based tridiagonalization algorithm for nonsymmetric matrices

The stable similarity reduction of a nonsymmetric square matrix to tridiagonal form has been a long-standing problem in numerical linear algebra. The biorthogonal Lanczos process is in principle a candidate method for this task, but in practice it is confined to sparse matrices and is restarted periodically because roundoff errors affect its three-term recurrence scheme and degrade the biorthogonality after a few steps. This adds to its vulnerability to serious breakdowns or near-breakdowns, the handling of which involves recovery strategies such as the look-ahead technique, which needs a careful implementation to produce a block-tridiagonal form with unpredictable block sizes. Other candidate methods, geared generally towards full matrices, rely on elementary similarity transformations that are prone to numerical instabilities. Such concomitant difficulties have hampered finding a satisfactory solution to the problem for either sparse or full matrices. This study focuses primarily on full matrices. After outlining earlier tridiagonalization algorithms from within a general framework, we present a new elimination technique combining orthogonal similarity transformations that are stable. We also discuss heuristics to circumvent breakdowns. Applications of this study include eigenvalue calculation and the approximation of matrix functions.

Spin exchange and superconductivity in a t-J(')-V model for two-dimensional quarter-filled systems

The effect of antiferromagnetic spin fluctuations on two-dimensional quarter-filled systems is studied theoretically. An effective t-J(')-V model on a square lattice which accounts for checkerboard charge fluctuations and next-nearest-neighbor antiferromagnetic spin fluctuations is considered. From calculations based on large-N theory on this model it is found that the exchange interaction J(') increases the attraction between electrons in the d(xy) channel only, so that both charge and spin fluctuations work cooperatively to produce d(xy) pairing.

A parametric study of droplet deformation through a microfluidic contraction: Low viscosity Newtonian droplets

Numerical simulations are conducted to investigate how a droplet of Newtonian liquid. entrained in a higher viscosity Newtonian liquid, behaves when passing through an axisymmetric microfluidic contraction. Simulations are performed using a transient Volume of Fluid finite volume algorithm, and cover ranges of Reynolds and Weber numbers relevant to microfluidic flows. Results are presented for a droplet to surrounding fluid viscosity ratio of 0.001. In contrast to behaviour at higher viscosity ratios obtained previously by the authors, shear and interfacial tension driven instabilities often develop along the droplet Surface. leading to complex shape development, and in some instances, droplet breakup. (c) 2006 Elsevier Ltd. All rights reserved.

General foundation for the nonlinear ponderomotive four-force in laser-plasma interactions

The interaction of electromagnetic radiation with plasmas is studied in relativistic four-vector formalism. A gauge and Lorentz invariant ponderomotive four-force is derived from the time dependent nonlinear three-force of Hora (1985). This four-force, due to its Lorentz invariance, contains new magnetic field terms. A new gauge and Lorentz invariant model of the response of plasma to electromagnetic radiation is then devised. An expression for the dispersion relation is obtained from this model. It is then proved that the magnetic permeability of plasma is unity for a general reference frame. This is an important result since it has been previously assumed in many plasma models.

Adverse feedback sequences in exploited marine systems: Are deliberate interruptive actions warranted?

Several mechanisms for self-enhancing feedback instabilities in marine ecosystems are identified and briefly elaborated. It appears that adverse phases of operation may be abruptly triggered by explosive breakouts in abundance of one or more previously suppressed populations. Moreover, an evident capacity of marine organisms to accomplish extensive geographic habitat expansions may expand and perpetuate a breakout event. This set of conceptual elements provides a framework for interpretation of a sequence of events that has occurred in the Northern Benguela Current Large Marine Ecosystem (off south-western Africa). This history can illustrate how multiple feedback loops might interact with one another in unanticipated and quite malignant ways, leading not only to collapse of customary resource stocks but also to degradation of the ecosystem to such an extent that disruption of customary goods and services may go beyond fisheries alone to adversely affect other major global ecosystem concerns (e.g. proliferations of jellyfish and other slimy, stingy, toxic and/or noxious organisms, perhaps even climate change itself, etc.). The wisdom of management interventions designed to interrupt an adverse mode of feedback operation is pondered. Research pathways are proposed that may lead to improved insights needed: (i) to avoid potential 'triggers' that might set adverse phases of feedback loop operation into motion; and (ii) to diagnose and properly evaluate plausible actions to reverse adverse phases of feedback operation that might already have been set in motion. These pathways include the drawing of inferences from available 'quasi-experiments' produced either by short-term climatic variation or inadvertently in the course of biased exploitation practices, and inter-regional applications of the comparative method of science.