Limiting stable currents in bounded electron and ion streams

The classical static analysis of the infinite planar diode has been extended to include the effects of finite transverse beam size. Simple expressions have been found for the increase in maximum stable current density over that of an infinite stream for finite cylindrical and strip streams flowing between plates of infinite diodes. The results are also given in terms of stream perveance. The effect of a nonuniform distribution of current across the stream is shown to be relatively small. Experimental values of maximum stable current agree with those obtained from the analysis. A further extension of the static analysis has been made to include the effects of additional conducting plane boundaries parallel to the stream motion. For length-to-width ratios L/D less than 0.25 the tube is adequately described by the results for the infinite planar diode and for L/D greater than 4, the infinitely-long drift tube theory suffices. At intermediate values of L/D, the maximum amount of current that can be stably passed through the tube is greater than that predicted by either asymptotic theory

Transverse instability and its long-term development for solitary waves of the (2+1)-Boussinesq equation

The stability properties of line solitary wave solutions of the (2+1)-dimensional Boussinesq equation with respect to transverse perturbations and their consequences are considered. A geometric condition arising from a multi-symplectic formulation of this equation gives an explicit relation between the parameters for transverse instability when the transverse wavenumber is small. The Evans function is then computed explicitly, giving the eigenvalues for transverse instability for all transverse wavenumbers. To determine the nonlinear and long time implications of transverse instability, numerical simulations are performed using pseudospectral discretization. The numerics confirm the analytic results, and in all cases studied, transverse instability leads to collapse.Comment: 16 pages, 8 figures; submitted to Phys. Rev.

Does Families and Schools Together (FAST) achieve its goals: an evaluation of the Rice Lake, Wisconsin FAST program

Includes bibliographical references

Limitations on the extent of off-center displacements in TbMnO3 from EXAFS measurements

We present EXAFS data at the Mn K and Tb L3 edges that provide upper limits on the possible displacements of any atoms in TbMnO3. The displacements must be less than 0.005-0.01A for all atoms which eliminates the possibility of moderate distortions (0.02A) with a small c-axis component, but for which the displacements in the ab plane average to zero. Assuming the polarization arises from a displacement of the O2 atoms along the c-axis, the measured polarization then leads to an O2 displacement that is at least 6X10^{-4}A, well below our experimental limit. Thus a combination of the EXAFS and the measured electrical polarization indicate that the atomic displacements likely lie in the range 6X10^{-4} - 5X10^{-3}A.Comment: submitted to PRB; 11 pages (preprint form) 7 figure

Coordinating academic programmes of secondary schooling and higher education institutions of Kazakhstan in the context of the international experience

The international research project "Coordinating Academic Programmes of Secondary Schooling and Higher Education Institutions of Kazakhstan in the Context ofthe International Experience" grew out of a partnership between the newly established Nazarbayev University Graduate School of Education (NUGSE) and the University of Cambridge Faculty of Education. The principal investigators are Kairat Kurakbayev (NUGSE) and David Bridges (Cambridge)

The rocks from space initiative and the space safari

This paper reports the successes of a new initiative in the UK using electronic resources, such as virtual learning environments and e-classrooms, for planetary and space science public engagement activities

Standing Waves in a Non-linear 1D Lattice : Floquet Multipliers, Krein Signatures, and Stability

We construct a class of exact commensurate and incommensurate standing wave (SW) solutions in a piecewise smooth analogue of the discrete non-linear Schr\"{o}dinger (DNLS) model and present their linear stability analysis. In the case of the commensurate SW solutions the analysis reduces to the eigenvalue problem of a transfer matrix depending parametrically on the eigenfrequency. The spectrum of eigenfrequencies and the corresponding eigenmodes can thereby be determined exactly. The spatial periodicity of a commensurate SW implies that the eigenmodes are of the Bloch form, characterised by an even number of Floquet multipliers. The spectrum is made up of bands that, in general, include a number of transition points corresponding to changes in the disposition of the Floquet multipliers. The latter characterise the different band segments. An alternative characterisation of the segments is in terms of the Krein signatures associated with the eigenfrequencies. When one or more parameters characterising the SW solution is made to vary, one occasionally encounters collisions between the band-edges or the intra-band transition points and, depending on the the Krein signatures of the colliding bands or segments, the spectrum may stretch out in the complex plane, leading to the onset of instability. We elucidate the correlation between the disposition of Floquet multipliers and the Krein signatures, presenting two specific examples where the SW possesses a definite window of stability, as distinct from the SW's obtained close to the anticontinuous and linear limits of the DNLS model.Comment: 31 pages, 11 figure