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Numerically computed with high accuracy are periodic travelling waves at the free surface of a two-dimensional, infinitely deep, and constant vorticity flow of an incompressible inviscid fluid, under gravity, without the effects of surface tension. Of particular interest is the angle the fluid surface of an almost extreme wave makes with the horizontal. Numerically found are the following. (i) There is a boundary layer where the angle rises sharply from $$0^\circ$$ at the crest to a local maximum, which converges to $$30.3787\ldots ^\circ$$ , independently of the vorticity, as the amplitude increases towards that of the extreme wave, which displays a corner at the crest with a $$30^\circ$$ angle. (ii) There is an outer region where the angle descends to $$0^\circ$$ at the trough for negative vorticity, while it rises to a maximum, greater than $$30^\circ$$ , and then falls sharply to $$0^\circ$$ at the trough for large positive vorticity. (iii) There is a transition region where the angle oscillates about $$30^\circ$$ , resembling the Gibbs phenomenon. Numerical evidence suggests that the amplitude and frequency of the oscillations become independent of the vorticity as the wave profile approaches the extreme form.
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Extreme matter meets extreme gravity: Ultraheavy neutron stars with phase transitions
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We solve a long-standing challenge to the integrity of votes cast without the supervision of a voting booth: ``improper influence,'' which we define as any combination of vote buying and voter coercion. In comparison with previous proposals, our system is the first in the literature to protect against a strong adversary who learns all of the voter's keys---we call this property ``extreme coercion resistance.'' Our approach allows each voter, or their trusted agents (which we call ``hedgehogs''), to ``nullify'' (effectively cancel) their vote in a way that is unstoppable and irrevocable, and such that the nullification action is forever unattributable to that voter or their hedgehog(s). We demonstrate the security of VoteXX in the {universal composability} model. Additionally we provide concrete implementations of sub-protocols---including inalienable authentication, decentralized bulletin boards, and anonymous communication channels---that are usually left as abstract assumptions in the literature. As in many other coercion-resistant systems, voters are authorized to vote with public-private keys. Each voter registers their public keys with the Election Authority (EA) in a way that convinces the EA that the voter has complete knowledge of their private keys. Voters concerned about losing their private keys can themselves, or by delegating to one or more hedgehog(s), monitor the bulletin board for malicious ballots cast with their keys, and can act to nullify these ballots in a privacy-preserving manner with zero-knowledge proofs. In comparison with previous proposals, our system makes fewer assumptions and protects against a stronger adversary. For example, votexx makes none of the following assumptions made by previous systems: the voter must complete registration before being coerced; the election will not close before the voter can cast a ballot after coercion; the voter needs to generate a fake password to evade coercion; and the voter knows an honest Election Authority official.more » « less
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Abstract Carbon fluxes at the land‐atmosphere interface are strongly influenced by weather and climate conditions. Yet what is usually known as “climate extremes” does not always translate into very high or low carbon fluxes or so‐called “carbon extremes.” To reveal the patterns of how climate extremes influence terrestrial carbon fluxes, we analyzed the interannual variations in ecosystem carbon fluxes simulated by the Terrestrial Biosphere Models (TBMs) in the Inter‐Sectoral Impact Model Intercomparison Project. At the global level, TBMs simulated reduced ecosystem net primary productivity (NPP; 18.5 ± 9.3 g C m−2 yr−1), but enhanced heterotrophic respiration (Rh; 7 ± 4.6 g C m−2 yr−1) during extremely hot events. TBMs also simulated reduced NPP (60.9 ± 24.4 g C m−2 yr−1) and reduced Rh (16.5 ± 11.4 g C m−2 yr−1) during extreme dry events. Influences of precipitation extremes on terrestrial carbon uptake were larger in the arid/semiarid zones than other regions. During hot extremes, ecosystems in the low latitudes experienced a larger reduction in carbon uptake. However, a large fraction of carbon extremes did not occur in concert with either temperature or precipitation extremes. Rather these carbon extremes are likely to be caused by the interactive effects of the concurrent temperature and precipitation anomalies. The interactive effects showed considerable spatial variations with the largest effects on NPP in South America and Africa. Additionally, TBMs simulated a stronger sensitivity of ecosystem productivity to precipitation than satellite estimates. This study provides new insights into the complex ecosystem responses to climate extremes, especially the emergent properties of carbon dynamics resulting from compound climate extremes.more » « less
