319 research outputs found
Equivariant cohomology over Lie groupoids and Lie-Rinehart algebras
Using the language and terminology of relative homological algebra, in
particular that of derived functors, we introduce equivariant cohomology over a
general Lie-Rinehart algebra and equivariant de Rham cohomology over a locally
trivial Lie groupoid in terms of suitably defined monads (also known as
triples) and the associated standard constructions. This extends a
characterization of equivariant de Rham cohomology in terms of derived functors
developed earlier for the special case where the Lie groupoid is an ordinary
Lie group, viewed as a Lie groupoid with a single object; in that theory over a
Lie group, the ordinary Bott-Dupont-Shulman-Stasheff complex arises as an a
posteriori object. We prove that, given a locally trivial Lie groupoid G and a
smooth G-manifold f over the space B of objects of G, the resulting
G-equivariant de Rham theory of f boils down to the ordinary equivariant de
Rham theory of a vertex manifold relative to the corresponding vertex group,
for any vertex in the space B of objects of G; this implies that the
equivariant de Rham cohomology introduced here coincides with the stack de Rham
cohomology of the associated transformation groupoid whence this stack de Rham
cohomology can be characterized as a relative derived functor. We introduce a
notion of cone on a Lie-Rinehart algebra and in particular that of cone on a
Lie algebroid. This cone is an indispensable tool for the description of the
requisite monads.Comment: 47 page
Water wave propagation and scattering over topographical bottoms
Here I present a general formulation of water wave propagation and scattering
over topographical bottoms. A simple equation is found and is compared with
existing theories. As an application, the theory is extended to the case of
water waves in a column with many cylindrical steps
Molecular cloning and transcriptional regulation of ompT , a ToxR-repressed gene in Vibrio cholerae
Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/72189/1/j.1365-2958.2000.01699.x.pd
Nanoscale Mechanical Characterisation of Amyloid Fibrils Discovered in a Natural Adhesive
Using the atomic force microscope, we have investigated the nanoscale mechanical response of the attachment adhesive of the terrestrial alga Prasiola linearis (Prasiolales, Chlorophyta). We were able to locate and extend highly ordered mechanical structures directly from the natural adhesive matrix of the living plant. The in vivo mechanical response of the structured biopolymer often displayed the repetitive sawtooth force-extension characteristics of a material exhibiting high mechanical strength at the molecular level. Mechanical and histological evidence leads us to propose a mechanism for mechanical strength in our sample based on amyloid fibrils. These proteinaceous, pleated β-sheet complexes are usually associated with neurodegenerative diseases. However, we now conclude that the amyloid protein quaternary structures detected in our material should be considered as a possible generic mechanism for mechanical strength in natural adhesives
Scale-free static and dynamical correlations in melts of monodisperse and Flory-distributed homopolymers: A review of recent bond-fluctuation model studies
It has been assumed until very recently that all long-range correlations are
screened in three-dimensional melts of linear homopolymers on distances beyond
the correlation length characterizing the decay of the density
fluctuations. Summarizing simulation results obtained by means of a variant of
the bond-fluctuation model with finite monomer excluded volume interactions and
topology violating local and global Monte Carlo moves, we show that due to an
interplay of the chain connectivity and the incompressibility constraint, both
static and dynamical correlations arise on distances . These
correlations are scale-free and, surprisingly, do not depend explicitly on the
compressibility of the solution. Both monodisperse and (essentially)
Flory-distributed equilibrium polymers are considered.Comment: 60 pages, 49 figure
Rapid and highly variable warming of lake surface waters around the globe
In this first worldwide synthesis of in situ and satellite-derived lake data, we find that lake summer surface water temperatures rose rapidly (global mean = 0.34°C decade−1) between 1985 and 2009. Our analyses show that surface water warming rates are dependent on combinations of climate and local characteristics, rather than just lake location, leading to the counterintuitive result that regional consistency in lake warming is the exception, rather than the rule. The most rapidly warming lakes are widely geographically distributed, and their warming is associated with interactions among different climatic factors—from seasonally ice-covered lakes in areas where temperature and solar radiation are increasing while cloud cover is diminishing (0.72°C decade−1) to ice-free lakes experiencing increases in air temperature and solar radiation (0.53°C decade−1). The pervasive and rapid warming observed here signals the urgent need to incorporate climate impacts into vulnerability assessments and adaptation efforts for lakes.Peer reviewe
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