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.