5,504 research outputs found
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)
Recommended from our members
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
- …