Magnetohydrodynamic convectons

Numerical continuation is used to compute branches of spatially localized structures in convection in an imposed vertical magnetic field. In periodic domains with finite spatial period, these branches exhibit slanted snaking and consist of localized states of even and odd parity. The properties of these states are analysed and related to existing asymptotic approaches valid either at small amplitude (Cox and Matthews, Physica D, vol. 149, 2001, p. 210), or in the limit of small magnetic diffusivity (Dawes, J. Fluid Mech., vol. 570, 2007, p. 385). The transition to standard snaking with increasing domain size is explored

Extended Self Similarity works for the Burgers equation and why

Extended Self-Similarity (ESS), a procedure that remarkably extends the range of scaling for structure functions in Navier--Stokes turbulence and thus allows improved determination of intermittency exponents, has never been fully explained. We show that ESS applies to Burgers turbulence at high Reynolds numbers and we give the theoretical explanation of the numerically observed improved scaling at both the infrared and ultraviolet end, in total a gain of about three quarters of a decade: there is a reduction of subdominant contributions to scaling when going from the standard structure function representation to the ESS representation. We conjecture that a similar situation holds for three-dimensional incompressible turbulence and suggest ways of capturing subdominant contributions to scaling.Comment: 10 pages, 1 figure, submitted to J. Fluid Mech. (fasttrack

Swift-Hohenberg model for magnetoconvection

A model system of partial differential equations in two dimensions is derived from the three-dimensional equations for thermal convection in a horizontal fluid layer in a vertical magnetic field. The model consists of an equation of Swift-Hohenberg type for the amplitude of convection, coupled to an equation for a large-scale mode representing the local strength of the magnetic field. The model facilitates both analytical and numerical studies of magnetoconvection in large domains. In particular, we investigate the phenomenon of flux separation, where the domain divides into regions of strong convection with a weak magnetic field and regions of weak convection with a strong field. Analytical predictions of flux separation based on weakly nonlinear analysis are extended into the fully nonlinear regime through numerical simulations. The results of the model are compared with simulations of the full three-dimensional magnetoconvection problem.S. M. Cox, P. C. Matthews, and S. L. Pollicot

The Structure of Global Attractors for Dissipative Zakharov Systems with Forcing on the Torus

The Zakharov system was originally proposed to study the propagation of Langmuir waves in an ionized plasma. In this paper, motivated by earlier work of the first and third authors, we numerically and analytically investigate the dynamics of the dissipative Zakharov system on the torus in 1 dimension. We find an interesting family of stable periodic orbits and fixed points, and explore bifurcations of those points as we take weaker and weaker dissipation.Comment: 16 pages, 7 figure

Do teachers differ by certification route? novice teachers' sense of self-efficacy, commitment to teaching, and preparedness to teach

Alternative teacher certification (ATC) programs are one method created to help alleviate teacher shortages (Cox, Matthews, & Assoc, 2001; Hallinan & Khmelkov, 2001). While much debate has arisen over ATC programs, very few have empirically examined their impact on the teaching pool (Darling-Hammond, Berry, & Thoreson, 2001; Darling-Hammond, Chung, & Frelow, 2002; Goldhaber, 2000; Ingersoll, 1999; Shen, 1997, 1999). The present study was designed to explore differences by certification type and program characteristics based on novice teachers' demographics, educational attainment, sense of self-efficacy, and sense of preparedness to enter the classroom. Results from the present study suggest ATC programs are somewhat diversifying the teaching population by bringing in more minorities and science majors, but do not appear to be bringing in more experienced scientists and mathematicians nor do they appear to be alleviating the teacher shortage. In this sample, traditionally certified teachers felt better prepared than ATC teachers with the biggest differences on Promoting Student Learning. Regardless of certification route, prior classroom experience was a strong predictor of Overall Preparedness and a teacher's perception of his or her ability to be an effective teacher. For ATC teachers, a positive mentoring experience was a strong predictor of Overall Preparedness. The discussion of whether or not ATC programs should exist should now be replaced with a discussion of how to ensure that these programs produce better teachers and improve student learning. The underlying theme from the present study was that, in order to feel prepared and have high self-efficacy, novice teachers needed instruction in the majority of the components identified by research and by the National Commission on Teaching and America's Future (1996), including positive mentoring experiences, field based experiences, and curriculum based on child development, learning theory, cognition, motivation, and subject matter pedagogy. Results from the present study support the assertion that teacher preparation programs, program components, mentoring experiences, and field-based experiences do impact teacher effectiveness in the classroom

A spectral Petrov-Galerkin formulation for pipe flow II: Nonlinear transitional stages

This work is devoted to the study of the nonlinear evolution of perturbations of Hagen-Poiseuille or pipe flow. We make use of a solenoidal spectral Petrov-Galerkin method for the spatial discretization of the Navier-Stokes equations for the perturbation field. For the time evolution, we use a semi-implicit time integration scheme. Special attention is given to the explicit treatment and efficient evaluation of the nonlinear terms. The hydrodynamic stability analysis is focused on the streak breakdown process by which two-dimensional streamwise-independent perturbations transiently modulate the basic flow, resulting in a profile which is linearly unstable with respect to three-dimensional perturbations. This mechanism is one possible route of transition to turbulence in subcritical shear flows