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Composite drill stem of epoxy fiber glass reinforced with boron filaments and a retrievable core liner/sample return container for the Apollo lunar surface drill
Composite drill stem of epoxy fiber glass and boron filaments and lunar core sampling system for Apollo lunar surface dril
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
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
Depletion of nonlinearity in magnetohydrodynamic turbulence: insights from analysis and simulations
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
Blocking by fixed and variable stimuli: effects of stimulus distribution on blocking
An experiment with rats compared the ability of fixed and variable duration cues to produce blocking. Rats in Group B (Blocking) were trained that both fixed- (F) and variable- (V) duration cues would be followed by food delivery. In a subsequent training stage F and V continued to be reinforced, but F was accompanied by X, and V by Y. In the test phase responding to X and Y was examined. Control Group O (Overshadowing) received identical treatment, except that F and V were nonreinforced in the first training stage. In Group B there was evidence for blocking, but only of X which had been conditioned in compound with the fixed-duration F; there was no evidence for blocking of Y, which had been conditioned in compound with the variable duration V. It is suggested that this result may occur because fixed cues reach a higher, more stable asymptote of associative strength than their variable equivalents
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
Measurement of Magnetic-Field Structures in a Laser-Wakefield Accelerator
Experimental measurements of magnetic fields generated in the cavity of a
self-injecting laser-wakefield accelerator are presented. Faraday rotation is
used to determine the existence of multi-megagauss fields, constrained to a
transverse dimension comparable to the plasma wavelength and several plasma
wavelengths longitudinally. The fields are generated rapidly and move with the
driving laser. In our experiment, the appearance of the magnetic fields is
correlated to the production of relativistic electrons, indicating that they
are inherently tied to the growth and wavebreaking of the nonlinear plasma
wave. This evolution is confirmed by numerical simulations, showing that these
measurements provide insight into the wakefield evolution with high spatial and
temporal resolution
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