1,406 research outputs found
Euler Obstruction and Defects of Functions on Singular Varieties
Several authors have proved Lefschetz type formulae for the local Euler
obstruction. In particular, a result of this type is proved in [BLS].The
formula proved in that paper turns out to be equivalent to saying that the
local Euler obstruction, as a constructible function, satisfies the local Euler
condition (in bivariant theory) with respect to general linear forms.
The purpose of this work is to understand what prevents the local Euler
obstruction of satisfying the local Euler condition with respect to functions
which are singular at the considered point. This is measured by an invariant
(or ``defect'') of such functions that we define below. We give an
interpretation of this defect in terms of vanishing cycles, which allows us to
calculate it algebraically. When the function has an isolated singularity, our
invariant can be defined geometrically, via obstruction theory. We notice that
this invariant unifies the usual concepts of {\it the Milnor number} of a
function and of the {\it local Euler obstruction} of an analytic set.Comment: 18 page
Small resolutions of Schubert varieties and Kazhdan-Lusztig polynomials
This article does not have an abstract
Small resolutions of Schubert varieties in symplectie and orthogonal Grassmannians
This article does not have an abstract
Accidental SUSY: Enhanced Bulk Supersymmetry from Brane Back-reaction
We compute how bulk loops renormalize both bulk and brane effective
interactions for codimension-two branes in 6D gauged chiral supergravity, as
functions of the brane tension and brane-localized flux. We do so by explicitly
integrating out hyper- and gauge-multiplets in 6D gauged chiral supergravity
compactified to 4D on a flux-stabilized 2D rugby-ball geometry, specializing
the results of a companion paper, arXiv:1210.3753, to the supersymmetric case.
While the brane back-reaction generically breaks supersymmetry, we show that
the bulk supersymmetry can be preserved if the amount of brane-localized flux
is related in a specific BPS-like way to the brane tension, and verify that the
loop corrections to the brane curvature vanish in this special case. In these
systems it is the brane-bulk couplings that fix the size of the extra
dimensions, and we show that in some circumstances the bulk geometry
dynamically adjusts to ensure the supersymmetric BPS-like condition is
automatically satisfied. We investigate the robustness of this residual
supersymmetry to loops of non-supersymmetric matter on the branes, and show
that supersymmetry-breaking effects can enter only through effective brane-bulk
interactions involving at least two derivatives. We comment on the relevance of
this calculation to proposed applications of codimension-two 6D models to
solutions of the hierarchy and cosmological constant problems.Comment: 49 pages + appendices. This is the final version to appear in JHE
Order and Disorder in AKLT Antiferromagnets in Three Dimensions
The models constructed by Affleck, Kennedy, Lieb, and Tasaki describe a
family of quantum antiferromagnets on arbitrary lattices, where the local spin
S is an integer multiple M of half the lattice coordination number. The equal
time quantum correlations in their ground states may be computed as finite
temperature correlations of a classical O(3) model on the same lattice, where
the temperature is given by T=1/M. In dimensions d=1 and d=2 this mapping
implies that all AKLT states are quantum disordered. We consider AKLT states in
d=3 where the nature of the AKLT states is now a question of detail depending
upon the choice of lattice and spin; for sufficiently large S some form of Neel
order is almost inevitable. On the unfrustrated cubic lattice, we find that all
AKLT states are ordered while for the unfrustrated diamond lattice the minimal
S=2 state is disordered while all other states are ordered. On the frustrated
pyrochlore lattice, we find (conservatively) that several states starting with
the minimal S=3 state are disordered. The disordered AKLT models we report here
are a significant addition to the catalog of magnetic Hamiltonians in d=3 with
ground states known to lack order on account of strong quantum fluctuations.Comment: 7 pages, 2 figure
Comprehensive review of various corrosion behaviours on 316 stainless steel
Corrosion is a destructive process that converts the pure metal into a chemically stabled form by hydroxide or sulphide and it is a slow process of destruction on the material by the chemical or electrochemical reaction in the environmental space. This kind of destruction has been typically produced from oxides or salt content on the material and it results in distinctive orange coloration. The classifications of corrosion act on atmospheric air and liquids as well as on contact of two solids. To resist the corrosion rate, stainless steel 316 has been chosen because of the presence of 2-3% molybdenum content and the presence of molybdenum plays a vital role in corrosion resistance. In this study, literature related to various works has been reviewed to explain the corrosion behaviour on cavitation, crevice, electrochemical, erosion, fatigue, galvanic, uniform, pitting, and stress corrosion which act on 316 stainless steel. In the present work, several coating processes and the additives, that have been added to SS 316 to enhance the outcomes according to various corrosion causes, are discussed
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