1,013 research outputs found
Visualizing Spacetime Curvature via Frame-Drag Vortexes and Tidal Tendexes II. Stationary Black Holes
When one splits spacetime into space plus time, the Weyl curvature tensor
(which equals the Riemann tensor in vacuum) splits into two spatial, symmetric,
traceless tensors: the tidal field , which produces tidal forces, and the
frame-drag field , which produces differential frame dragging. In recent
papers, we and colleagues have introduced ways to visualize these two fields:
tidal tendex lines (integral curves of the three eigenvector fields of ) and
their tendicities (eigenvalues of these eigenvector fields); and the
corresponding entities for the frame-drag field: frame-drag vortex lines and
their vorticities. These entities fully characterize the vacuum Riemann tensor.
In this paper, we compute and depict the tendex and vortex lines, and their
tendicities and vorticities, outside the horizons of stationary (Schwarzschild
and Kerr) black holes; and we introduce and depict the black holes' horizon
tendicity and vorticity (the normal-normal components of and on the
horizon). For Schwarzschild and Kerr black holes, the horizon tendicity is
proportional to the horizon's intrinsic scalar curvature, and the horizon
vorticity is proportional to an extrinsic scalar curvature. We show that, for
horizon-penetrating time slices, all these entities (, , the tendex lines
and vortex lines, the lines' tendicities and vorticities, and the horizon
tendicities and vorticities) are affected only weakly by changes of slicing and
changes of spatial coordinates, within those slicing and coordinate choices
that are commonly used for black holes. [Abstract is abbreviated.]Comment: 19 pages, 7 figures, v2: Changed to reflect published version
(changes made to color scales in Figs 5, 6, and 7 for consistent
conventions). v3: Fixed Ref
Is Growth of Eelgrass Nitrogen Limited? A Numerical Simulation of the Effects of Light and Nitrogen on the Growth Dynamics of Zostera marina
A numerical model of nitrogen uptake and growth was developed for the temperate seagrass Zostera marina L. Goals were to evaluate the relative effects of light and nitrogen availability on nitrogen uptake and partitioning between leaf and root tissue, and to estimate nitrogen concentrations in the sedment and water column required to saturate growth. Steady-state predictions are quite robust with respect to a range of parameter values justified by available data The calculations indicated that roots are probably more important in overall nitrogen acquisition in most light and nitrogen environments encountered in situ, but may contribute less than 50 % of the total uptake in low light. The model also predicted ammonium to be a much more important source of nitrogen than nitrate. Nitrogen concentrations required to saturate growth (even for nitrate) were estimated to be at least 50 % below concentrations commonly reported in situ, an indication that nitrogen limitation of Z. marina is probably very rare in nature
Visualizing Spacetime Curvature via Frame-Drag Vortexes and Tidal Tendexes III. Quasinormal Pulsations of Schwarzschild and Kerr Black Holes
In recent papers, we and colleagues have introduced a way to visualize the
full vacuum Riemann curvature tensor using frame-drag vortex lines and their
vorticities, and tidal tendex lines and their tendicities. We have also
introduced the concepts of horizon vortexes and tendexes and 3-D vortexes and
tendexes (regions where vorticities or tendicities are large). Using these
concepts, we discover a number of previously unknown features of quasinormal
modes of Schwarzschild and Kerr black holes. These modes can be classified by
mode indexes (n,l,m), and parity, which can be electric [(-1)^l] or magnetic
[(-1)^(l+1)]. Among our discoveries are these: (i) There is a near duality
between modes of the same (n,l,m): a duality in which the tendex and vortex
structures of electric-parity modes are interchanged with the vortex and tendex
structures (respectively) of magnetic-parity modes. (ii) This near duality is
perfect for the modes' complex eigenfrequencies (which are well known to be
identical) and perfect on the horizon; it is slightly broken in the equatorial
plane of a non-spinning hole, and the breaking becomes greater out of the
equatorial plane, and greater as the hole is spun up; but even out of the plane
for fast-spinning holes, the duality is surprisingly good. (iii)
Electric-parity modes can be regarded as generated by 3-D tendexes that stick
radially out of the horizon. As these "longitudinal," near-zone tendexes rotate
or oscillate, they generate longitudinal-transverse near-zone vortexes and
tendexes, and outgoing and ingoing gravitational waves. The ingoing waves act
back on the longitudinal tendexes, driving them to slide off the horizon, which
results in decay of the mode's strength. (iv) By duality, magnetic-parity modes
are driven in this same manner by longitudinal, near-zone vortexes that stick
out of the horizon. [Abstract abridged.]Comment: 53 pages with an overview of major results in the first 11 pages, 26
figures. v2: Very minor changes to reflect published version. v3: Fixed Ref
Capturing naturally occurring emotional suppression as it unfolds in couple interactions
Most research examining the consequences of suppressing emotional expression has focused on either experimentally manipulated and conscious suppression, or self-reported suppression behavior. This study examined suppression as it naturally occurred in couple (n= 105) discussions regarding a challenging topic. A Suppression Index (SI) was created by calculating the difference between continuous self-reports of emotional experience, obtained using cued video recall, and coders’ continuous ratings of expressed emotion. Suppression was common for both men and women, though there was also substantial individual variation. Autocorrelations of the SIwere used to tap Suppressive Rigidity (Srig), or the tendency to inflexibly use suppression throughout the discussions. Srigscores were consistent within individuals across repeated conversations and varied across individuals, suggesting that Srigcaptures stable individual differences. Women’s greater suppression of negative emotions combined with more rigid use of suppression was associated with their own lower relationship satisfaction but not their partners’. These findings indicate that suppressive behavior may be linked to relationship quality, and that it is not just the use of suppression that may matter but how rigidly one applies this regulatory approach
Frame-Dragging Vortexes and Tidal Tendexes Attached to Colliding Black Holes: Visualizing the Curvature of Spacetime
When one splits spacetime into space plus time, the spacetime curvature (Weyl
tensor) gets split into an "electric" part E_{jk} that describes tidal gravity
and a "magnetic" part B_{jk} that describes differential dragging of inertial
frames. We introduce tools for visualizing B_{jk} (frame-drag vortex lines,
their vorticity, and vortexes) and E_{jk} (tidal tendex lines, their tendicity,
and tendexes), and also visualizations of a black-hole horizon's (scalar)
vorticity and tendicity. We use these tools to elucidate the nonlinear dynamics
of curved spacetime in merging black-hole binaries.Comment: 4 pages, 5 figure
Frame-Dragging Vortexes and Tidal Tendexes Attached to Colliding Black Holes: Visualizing the Curvature of Spacetime
When one splits spacetime into space plus time, the spacetime curvature (Weyl
tensor) gets split into an "electric" part E_{jk} that describes tidal gravity
and a "magnetic" part B_{jk} that describes differential dragging of inertial
frames. We introduce tools for visualizing B_{jk} (frame-drag vortex lines,
their vorticity, and vortexes) and E_{jk} (tidal tendex lines, their tendicity,
and tendexes), and also visualizations of a black-hole horizon's (scalar)
vorticity and tendicity. We use these tools to elucidate the nonlinear dynamics
of curved spacetime in merging black-hole binaries.Comment: 4 pages, 5 figure
Visualizing Spacetime Curvature via Frame-Drag Vortexes and Tidal Tendexes I. General Theory and Weak-Gravity Applications
When one splits spacetime into space plus time, the Weyl curvature tensor
(vacuum Riemann tensor) gets split into two spatial, symmetric, and trace-free
(STF) tensors: (i) the Weyl tensor's so-called "electric" part or tidal field,
and (ii) the Weyl tensor's so-called "magnetic" part or frame-drag field. Being
STF, the tidal field and frame-drag field each have three orthogonal
eigenvector fields which can be depicted by their integral curves. We call the
integral curves of the tidal field's eigenvectors tendex lines, we call each
tendex line's eigenvalue its tendicity, and we give the name tendex to a
collection of tendex lines with large tendicity. The analogous quantities for
the frame-drag field are vortex lines, their vorticities, and vortexes. We
build up physical intuition into these concepts by applying them to a variety
of weak-gravity phenomena: a spinning, gravitating point particle, two such
particles side by side, a plane gravitational wave, a point particle with a
dynamical current-quadrupole moment or dynamical mass-quadrupole moment, and a
slow-motion binary system made of nonspinning point particles. [Abstract is
abbreviated; full abstract also mentions additional results.]Comment: 25 pages, 20 figures, matches the published versio
Gravitomagnetism in the Kerr-Newman-Taub-NUT spacetime
We study the motion of test particles and electromagnetic waves in the
Kerr-Newman-Taub-NUT spacetime in order to elucidate some of the effects
associated with the gravitomagnetic monopole moment of the source. In
particular, we determine in the linear approximation the contribution of this
monopole to the gravitational time delay and the rotation of the plane of the
polarization of electromagnetic waves. Moreover, we consider "spherical" orbits
of uncharged test particles in the Kerr-Taub-NUT spacetime and discuss the
modification of the Wilkins orbits due to the presence of the gravitomagnetic
monopole.Comment: 12 pages LaTeX iopart style, uses PicTex for 1 Figur
Larval control of Anopheles (Nyssorhinchus) darlingiusing granular formulation of Bacillus sphaericus in abandoned gold-miners excavation pools in the Brazilian Amazon Rainforest
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