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A square-free monomial ideal
is said to be an
-ideal if the facet complex and non-face complex associated with
have the same
-vector. We show that
-ideal if and only if its Newton complementary dual
is also an
-ideal. Because of this duality, previous results about some classes of
-ideals can be extended to a much larger class of
-ideals. An interesting by-product of our work is an alternative formulation of the Kruskal–Katona theorem for
-vectors of simplicial complexes.
The northwestern sector of the Amery Ice Shelf, East Antarctica, has a layered structure, due to the presence of both meteoric ice and a marine ice layer resulting from sub-shelf freezing processes. Crystal orientation fabric and grain-size data are presented for ice cores obtained from two boreholes ˜70 km apart on approximately the same flowline. Multiple-maxima crystal orientation fabrics and large mean grain sizes in the meteoric ice are indicative of stress relaxation and subsequent grain growth in ice that has flowed into the Amery Ice Shelf. Strongly anisotropic single-maximum crystal orientation fabrics and rectangular textures near the base of the ˜200 m thick marine ice layer suggest accretion occurs by the accumulation of frazil ice platelets. Crystal orientation fabrics in older marine ice exhibit vertical large circle girdle patterns, influenced by the complex stress configurations that exist towards the margins of the ice shelf. Post-accumulation grain growth and fabric development in the marine ice layer are restricted by a high concentration of brine and insoluble particulate inclusions. Differences in the meteoric and marine ice crystallography are indicative of the contrasting rheological properties of these layers, which must be considered in relation to large-scale ice-shelf dynamics.
Laboratory creep deformation experiments have been conducted on initially isotropic laboratory-made samples of polycrystalline ice. Steady-state tertiary creep rates, , were determined at strains exceeding 10% in either uniaxial-compression or simple-shear experiments. Isotropic minimum strain rates, , determined at ˜1 % strain, provide a reference for comparing the relative magnitude of tertiary creep rates in shear and compression through the use of strain-rate enhancement factors, E, defined as the ratio of corresponding tertiary and isotropic minimum creep rates, i.e. . The magnitude of strain-rate enhancement in simple shear was found to exceed that in uniaxial compression by a constant factor of 2.3. Results of experiments conducted at octahedral shear stresses of to = 0.040.80 MPa indicate a creep power-law stress exponent of n = 3 for isotropic minimum creep rates and n = 3.5 for tertiary creep rates. The difference in stress exponents for minimum and tertiary creep regimes can be interpreted as a t0 stress-dependent level of strain-rate enhancement, i.e. .The implications of these results for deformation in complex multicomponent stress configurations and at stresses below those used in the current experiments are discussed.
In this study we compare the anisotropic flow relations for polycrystalline ice of Azuma and Goto-Azuma (1996), Thorsteinsson (2002), Placidi and others (2010) and Budd and others (2013). Observations from the Dome Summit South (DSS) ice-coring site at Law Dome, East Antarctica, are used to model the vertical distribution of deviatoric stress components at the borehole site. The flow relations in which the anisotropic rheology is parameterized by a scalar function, so that the strain-rate and deviatoric stress tensor components are collinear, provide simple shear and vertical compression deviatoric stress profiles that are most consistent with laboratory observations of tertiary creep in combined stress configurations. Those flow relations where (1) the anisotropy is derived from the magnitude of applied stresses resolved onto the basal planes of individual grains and (2) the macroscopic deformation is obtained via homogenization of individual grain responses provide stress estimates less consistent with laboratory observations. This is most evident in combined simple shear and vertical compression flow regimes where shear is dominant. Our results highlight the difficulties associated with developing flow relations which incorporate a physically based description of microdeformation processes. In particular, this requires that all relevant microdeformation, recrystallization and recovery processes are adequately parameterized.
The generalized (Glen) flow relation for ice, involving the second invariants of the stress deviator and strain-rate tensors, is only expected to hold for isotropic polycrystalline ice. Previous single-stress experiments have shown that for the steady-state flow, which develops at large strains, the tertiary strain rate is greater than the minimum (secondary creep) value by an enhancement factor which is larger for shear than compression. Previous experiments combining shear with compression normal to the shear plane have shown that enhancement of the tertiary octahedral strain rate increases monotonically from compression alone to shear alone. Additional experiments and analyses presented here were conducted to further investigate how the separate tertiary shear and compression strain-rate components are related in combined stress situations. It is found that tertiary compression rates are more strongly influenced by the addition of shear than is given by a Glen-type flow relation, whereas shear is less influenced by additional compression. A scalar function formulation of the flow relation is proposed, which fits the tertiary creep data well and is readily adapted to a generalized form that can be extended to other stress configurations and applied in ice mass modelling.
In the West, the bloody and costly Napoleonic Wars (1803–15) were followed by economic depression, political reform, famine in Ireland, civil war and imperial assertion. But the immediate global political consequence was the creation of the ‘nation state’ at the Congress of Vienna (1815–16), where Europe was carved up into countries that mirrored the languages, religions and traditions of the people who would rule them. The newly created governments were eager to justify their legitimacy as nations by employing historians to celebrate their ‘imagined community’.
Shortly after Samuel Richardson published the second installment of his tragedy Clarissa (1747–8), one reader warned that its heroine's death would hit her ‘like a mortifying stroke’. Another insisted that ‘the desire of having your piece end happily (as ’tis called) will ever be the test of a wrong head, and a vain mind’. Both readers sought to use their aesthetic reactions to display their moral sentiments, believing that the practice of reading led to important social consequences. For the first reader, sentimental fiction aroused her moral abilities; for the second, such claims to sensitivity only suggested one's inability to recognize true right and wrong.
It has become something of a classroom cliché to depict eighteenth-century readers voicing moral reactions to sentimental novels, and a scholarly truism that the source of the connection between moral feelings and literary response was celebrated (if not defined) by David Hume's theory of sympathy in A Treatise of Human Nature (1739–40). This would seem to be straightforward both in terms of the Treatise 's theoretical positions and of the psychology it depicts – for when Hume presented the now-famous ‘philosophical melancholy and delirium’ that was brought on by his relentless scepticism, it was non-cognitive ‘lively impressions of my senses’ that restored him to ‘a relaxed frame of mind’. Earlier in the same book, Hume had defined the provision of such lively impressions as the unique ability of eloquent authors who are thus like our close friends – that is, like those with whom we sympathize. So it would seem that Hume had epistemological and even therapeutic reasons for celebrating the moral value of powerful fiction. Yet this chapter will argue that Hume's aesthetic theory from the early 1740s provides a fresh interpretive context for making sense of contemporary aesthetic claims to moral practice. This argument will clarify not only why Hume's theory of fiction serves as a weak source of belief at the level of his own philosophy, but also why it is important to recognize Hume as a theorist of the kind of self-conscious reading that ultimately makes reading a process of adjustment and response rather than of credulous reaction.