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Figure 14.

The three-periodic cubic P 118 R L ( cosh 1 ( 7 3 / 2 ) ) chain-mail weaving [ Casadei Lizard Slingback Pumps Clearance Comfortable Manchester Cheap Price Free Shipping Eastbay b3dUEIyJ
], the inter-growth of closed loops in a three-periodic chain-mail arrangement. (–) The array as it lies on the surface, with various combinations of components shown. () A unit cell of an ideal conformation. () Extended fragment of an ideal conformation. (Online version in colour.)

We turn our attention to ideal embeddings of two- and three-periodic nets and arrays of inter-woven nets. The ‘equilibrium placement’ concept of O'Keeffe Delgado-Friedrichs [ Ralph Lauren Purple Label Patent Leather Slingback Sandals Finishline sF5NIxP
] leads to canonical embeddings of crystallographic nets [ Miu Miu Leather Moto Boots Outlet Cheap Online y3l9nkaxM
]. In fact, equilibrium placement allows a continuum of embeddings of a crystallographic net, as the unit cell parameters are arbitrary. However, two of those embeddings are most useful, and are explicitly computed by the SyStRe algorithm [ 78 ]. The first is a ‘barycentric’ embedding, which places each vertex at the barycentre of its neighbours. The second is a ‘uniform’ embedding, where the variance of the edge lengths is minimized, favouring uniform edge lengths. Despite the evident power of the SyStRe algorithm, there remain many nets for which it gives no canonical form, including those with edge and vertex collisions, where multiple edges or vertices occupy the same location in the equilibrium placement, and non-crystallographic nets. Additionally, SyStRe cannot produce canonical embeddings for patterns containing multiple interwoven nets. Given those limitations, it is worthwhile exploring ideal tight embeddings of nets via the PB-SONO algorithm. (Ideal configurations of many of these nets are published in [ 27 ].)

Consider first the ideal configurations of the simplest three-periodic regular nets, that are edge-1 and vertex-1 transitive [ Cheap Cheap Online Adidas adidas Originals Campus LowTop Sneakers Discounts Sale Online Pay With Visa Cheap Price Cheap Price From China Cheapest aXzfk
]: srs , dia and pcu [ 80 ]. On tightening, these nets are equivalent to both the barycentric and the uniform embeddings given by SyStRe. These ideal conformations, which realize all possible symmetries of their graph topologies, are shown in Free Shipping Pictures André Assous Woven Leather Wedge Sandals Discounts Cheap Price AZ1zUvd4u3
.

Figure 15.

Ideal embeddings of the simplest three-periodic nets: () srs , () dia , () pcu , and of two simple two-periodic nets () hcb , () (4,4,8,8). The edge diameter has been decreased to show the ideal form [ 27 ]. (Online version in colour.)

Consider next, ideal forms of two-periodic graphs. In its ideal form ( Cheap Sale Countdown Package Clearance 2018 Unisex Manolo Blahnik Cashmere KneeHigh Boots Amazon Sale Online bmDYz
d ), the regular hcb (graphene) net has equal edges and ropelength L / D =2.89, with a hexagonal 2-periodic unit cell ( a = b =1; γ = π /3), which is equivalent to both of the SyStRe embeddings. For the (4,4,8,8) two-periodic net, the barycentric embedding and the uniform embeddings given by SySrRe are distinct. The ideal embedding found by PB-SONO, shown in figure 15 e , is equivalent to the uniform embedding and not the barycentric embedding. This ideal embedding has ropelength L / D =6.05, with lattice parameters a = b =1; γ = π /2.

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Figure 4.

() Unfiltered time series of the along-stream average mean latitude anomaly of ACC transport, (blue line), and the SAM (green) and Niño 3.4 (red) indices. () Time series of (blue) and SAM (green) smoothed with a 2 year wide triangle filter. For , the mean dynamic topography from Aviso is used [ 44 , 45 ]. (Online version in colour.)

Also shown in MM6 Maison Margiela Leather KneeHigh Boots New Sale Hot Sale 1G3bF
a are time series of the SAM (green) and Niño 3.4 (red) indices, here computed by interpolating monthly climate indices onto the dates of the weekly Aviso altimetry. On monthly time scales, there is no evidence of a statistically significant correlation between the ACC position variability in figure 4 and either climate index.

In figure 4 b , the and SAM time series have been filtered using a 2-year wide triangle filter. This smoothing removes high-frequency fluctuations leaving only interannual signals, and in this case, the SAM is weakly anti-correlated with , at roughly the 90% significance level. These results are sensitive to the choice of mean dynamic topography. More anomalous spikes in transport latitude appear when EGM08/DNSC08B mean dynamic topography is used, and in that case, the signals are anti-correlated at only about the 65% significance level. In neither case is a significant correlation found between the Niño 3.4 index and .

The results of this analysis suggest that latitudinal shifts in the circumpolarly integrated ACC transport are more correlated with the SAM than with the Niño 3.4 index, implying that zonally averaged Southern Hemisphere winds have more impact on the mean latitude of the ACC than do remote tropical teleconnections. The low correlation with Niño 3.4 is not surprising since ENSO impacts are not expected to be zonally coherent. The findings should be interpreted with caution, because even on interannual scales, the correlation between the SAM and does not pass a rigorous 95% statistical significance test. Coherence analysis or lagged correlations would make it possible to assess time lags in the relationships between and climate indices, but that is beyond the scope of this short paper.

5. Summary and conclusions

This study has used altimeter data to examine temporal shifts in the position of the ACC. In contrast to earlier altimeter-based studies [ Buy Cheap Low Cost Rag amp; Bone 2018 Harrow Leather Ankle Boots Offer SAHtBh4J36
, 50 52 ], this analysis has not focused on latitudinal shifts in SSH contours, which are potentially sensitive to large-scale steric expansion associated with warming of the Southern Ocean, and which therefore do not provide clear insights into driving mechanisms. Instead, this study has explored an alternate measure of ACC displacement, in this case, based on the latitude of the mean, meridionally averaged transport, . This transport latitude index is designed to minimize large-scale steric height signals, though it is sensitive to the definition of endpoints and to some extent to the MDT.

On the basis of the position index, , the zonally averaged latitude of ACC transport shows no long-term trend, in contrast with SSH-contour based measures of ACC variability. This leaves open the questions of what mechanisms account for the long-term warming observed in the Southern Ocean in recent decades and whether more warm circumpolar seep water is reaching the Antarctic ice edge. Analyses of hydrographic data suggest that the Southern Ocean warming signal is too deep to be explained trivially through air–sea fluxes [ Céline Canvas Slingback Wedges Brand New Unisex Sale Outlet Store Latest Collections REAu5ohugT
]. While it remains possible that the ACC fronts have shifted poleward in a way that has not yet been convincingly diagnosed, an alternative is that enhanced meridional heat transport, perhaps via eddy heat fluxes, may account for the observed warming. Further analysis of the ocean heat budget will be needed to unravel these mechanisms.

The zonally averaged position index is uncorrelated with the Niño 3.4 index on any timescales. By contrast, does correlate with the Niño 3.4 index, with differing correlations as a function of longitude. The nature of the Niño 3.4 correlation suggests that tropical Pacific influences on the Southern Ocean are regional and not circumpolarly coherent. The circumpolarly averaged value is weakly anti-correlated with the SAM index, implying that changes in the latitude and strength of the wind that are represented by the increasing SAM might be able to displace the mean transport of the ACC poleward. Taken together, these results are suggestive of a two-mechanism system, in which regional effects associated with upper ocean temperatures, air–sea fluxes, and even ice melt may respond to changes in the tropical Pacific [ 21 APC Leather LaceUp Boots Choice Cheap Online nfT0SbD
], but the latitude at which the zonally averaged ACC carries its mean transport might be more dependent on the SAM-related winds than on teleconnections with the equatorial Pacific.

Funding statement

Work has been supported by a number of funding sources, including NOAA award NA10OAR4310139, NSF grant no. OCE-1234473 and NASA grant no. NNX13AE44G.

Acknowledgements

The altimeter products were produced by Ssalto/Duacs and distributed by Aviso with support from CNES. The DNSC08B-EGM08 dynamic ocean topography is made available by the National Geospatial-Intelligence Agency ( Shopping Online Outlet Sale Cheap View Alice Olivia Leather Ankle Boots Fashion Style Cheap Online Free Shipping Best Clearance Store For Sale Ypcpr3g
). Ocean climate indices for SAM and ENSO for this study were distributed by the Ocean Observations Panel for Climate (OOPC) and the JCOMM Observations Programme ( Kate Spade New York RoundToe LowTop Sneakers Good Selling Reliable Cheap Online Online Sale Red Pre Order Eastbay Cheap Clearance Store bWsBo8
). The work discussed here has benefited from discussions with Angelica Gilroy, Doug Martinson, Matt Mazloff, Rosemary Morrow, Dean Roemmich, Uriel Zajaczkovski, and Nathalie Zilberman. Many thanks also to the anonymous reviewers for their insightful suggestions.

Footnotes

One contribution of 12 to a Theo Murphy Meeting Issue ‘ New models and observations of the Southern Ocean, its role in global climate and the carbon cycle ’.

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