1,362 research outputs found
Quasi-conservation laws for compressible 3D Navier-Stokes flow
We formulate the quasi-Lagrangian fluid transport dynamics of mass density
and the projection q=\bom\cdot\nabla\rho of the vorticity \bom onto
the density gradient, as determined by the 3D compressible Navier-Stokes
equations for an ideal gas, although the results apply for an arbitrary
equation of state. It turns out that the quasi-Lagrangian transport of
cannot cross a level set of . That is, in this formulation, level sets of
(isopychnals) are impermeable to the transport of the projection .Comment: 2 page note, to appear in Phys Rev
Lagrangian analysis of alignment dynamics for isentropic compressible magnetohydrodynamics
After a review of the isentropic compressible magnetohydrodynamics (ICMHD)
equations, a quaternionic framework for studying the alignment dynamics of a
general fluid flow is explained and applied to the ICMHD equations.Comment: 12 pages, 2 figures, submitted to a Focus Issue of New Journal of
Physics on "Magnetohydrodynamics and the Dynamo Problem" J-F Pinton, A
Pouquet, E Dormy and S Cowley, editor
Conditional regularity of solutions of the three dimensional Navier-Stokes equations and implications for intermittency
Two unusual time-integral conditional regularity results are presented for
the three-dimensional Navier-Stokes equations. The ideas are based on
-norms of the vorticity, denoted by , and particularly
on , where for . The first result, more appropriate for the unforced case, can be stated
simply : if there exists an for which the integral condition
is satisfied () then no singularity can occur on . The
constant for large . Secondly, for the forced case, by
imposing a critical \textit{lower} bound on , no
singularity can occur in for \textit{large} initial data. Movement
across this critical lower bound shows how solutions can behave intermittently,
in analogy with a relaxation oscillator. Potential singularities that drive
over this critical value can be ruled out whereas
other types cannot.Comment: A frequency was missing in the definition of D_{m} in (I5) v3. 11
pages, 1 figur
A comparison of A-level performance in economics and business studies: how much more difficult is economics?
This paper uses ALIS data to compare academic performance in two subjects often viewed as relatively close substitutes for one another at A-level. The important role of GCSE achievement is confirmed for both subjects. There is evidence of strong gender effects and variation in outcomes across Examination Boards. A counterfactual exercise suggests that if the sample of Business Studies candidates had studied Economics nearly 40% of those who obtained a grade C or better in the former subject would not have done so in the latter. The opposite exercise uggests that 12% more Economics candidates would have achieved a grade C or better if they had taken Business Studies. In order to render a Business Studies A-level grade comparable to an Economics one in terms of relative difficulty, we estimate that a downward adjustment of 1.5 UCAS points should be applied to the former subject. This adjustment is lower than that suggested by correction factors based on conventional subject pair analysis for these two subjects
Depletion of Nonlinearity in Magnetohydrodynamic Turbulence: Insights from Analysis and Simulations
We build on recent developments in the study of fluid turbulence [Gibbon
\textit{et al.} Nonlinearity 27, 2605 (2014)] to define suitably scaled,
order- moments, , of , where
and are, respectively, the vorticity and current density in
three-dimensional magnetohydrodynamics (MHD). We show by mathematical analysis,
for unit magnetic Prandtl number , how these moments can be used to
identify three possible regimes for solutions of the MHD equations; these
regimes are specified by inequalities for and . We then
compare our mathematical results with those from our direct numerical
simulations (DNSs) and thus demonstrate that 3D MHD turbulence is like its
fluid-turbulence counterpart insofar as all solutions, which we have
investigated, remain in \textit{only one of these regimes}; this regime has
depleted nonlinearity. We examine the implications of our results for the
exponents that characterize the power-law dependences of the energy
spectra on the wave number , in the inertial range of
scales. We also comment on (a) the generalization of our results to the case
and (b) the relation between and the order- moments
of gradients of hydrodynamic fields, which are used in characterizing
intermittency in turbulent flows.Comment: 14 pages, 3 figure
Lagrangian particle paths and ortho-normal quaternion frames
Experimentalists now measure intense rotations of Lagrangian particles in
turbulent flows by tracking their trajectories and Lagrangian-average velocity
gradients at high Reynolds numbers. This paper formulates the dynamics of an
orthonormal frame attached to each Lagrangian fluid particle undergoing
three-axis rotations, by using quaternions in combination with Ertel's theorem
for frozen-in vorticity. The method is applicable to a wide range of Lagrangian
flows including the three-dimensional Euler equations and its variants such as
ideal MHD. The applicability of the quaterionic frame description to Lagrangian
averaged velocity gradient dynamics is also demonstrated.Comment: 9 pages, one figure, revise
Depletion of nonlinearity in magnetohydrodynamic turbulence: insights from analysis and simulations
Cascaded acceleration of proton beams in ultrashort laser-irradiated microtubes
A cascaded ion acceleration scheme is proposed by use of ultrashort
laser-irradiated microtubes. When the electrons of a microtube are blown away
by intense laser pulses, strong charge-separation electric fields are formed in
the microtube both along the axial and along the radial directions. By
controlling the time delay between the laser pulses and a pre-accelerated
proton beam injected along the microtube axis, we demonstrate that this proton
beam can be further accelerated by the transient axial electric field in the
laser-irradiated microtube. Moreover, the collimation of the injected proton
beam can be enhanced by the inward radial electric field. Numerical simulations
show that this cascaded ion acceleration scheme works efficiently even at
non-relativistic laser intensities, and it can be applied to injected proton
beams in the energy range from 1 to 100 MeV. Therefore, it is particularly
suitable for cascading acceleration of protons to higher energy.Comment: 13 pages, 4 figure
Developing a partcipatory approach to seed production and varietal selection
The performance of UK winter wheat varieties was tested under organic conditions involving farmer participation. Three breadmaking varieties (Hereward, Solstice and Xi19) and their mixture (1:1:1) were grown at 19 UK farms in 2003/04 and 2004/05. The variability of productivity on organic farms was illustrated with more variation among farm sites than among varieties. Seed health was generally high over all sites. Although the trials were successful, more time was needed at project initiation to improve farmer involvement. Some farmers expected more researcher visits, and were reticent about assessing the trials themselves. In contrast, some participants valued the variety performance data on their farms particularly when related to that of other growers. The balance between the goals of the researchers relative to the farmers needs to be defined at project initiation
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