373,599 research outputs found
Infinitesimal rigidity of convex surfaces through the second derivative of the Hilbert-Einstein functional II: Smooth case
The paper is centered around a new proof of the infinitesimal rigidity of
smooth closed surfaces with everywhere positive Gauss curvature. We use a
reformulation that replaces deformation of an embedding by deformation of the
metric inside the body bounded by the surface. The proof is obtained by
studying derivatives of the Hilbert-Einstein functional with boundary term.
This approach is in a sense dual to proving the Gauss infinitesimal rigidity,
that is rigidity with respect to the Gauss curvature parametrized by the Gauss
map, by studying derivatives of the volume bounded by the surface. We recall
that Blaschke's classical proof of the infinitesimal rigidity is also related
to the Gauss infinitesimal rigidity, but in a different way: while Blaschke
uses Gauss rigidity of the same surface, we use the Gauss rigidity of the polar
dual. In the spherical and in the hyperbolic-de Sitter space, there is a
perfect duality between the Hilbert-Einstein functional and the volume, as well
as between both kinds of rigidity. We also indicate directions for future
research, including the infinitesimal rigidity of convex cores of hyperbolic
3--manifolds.Comment: 60 page
Comparative analysis of rigidity across protein families
We present a comparative study in which 'pebble game' rigidity analysis is applied to multiple protein crystal structures, for each of six different protein families. We find that the main-chain rigidity of a protein structure at a given hydrogen bond energy cutoff is quite sensitive to small structural variations, and conclude that the hydrogen bond constraints in rigidity analysis should be chosen so as to form and test specific hypotheses about the rigidity of a particular protein. Our comparative approach highlights two different characteristic patterns ('sudden' or 'gradual') for protein rigidity loss as constraints are removed, in line with recent results on the rigidity transitions of glassy networks
De Jure Rigidity
The rigid designation of proper names and natural kind terms is the most well-known doctrine of Kripkeâs Naming and Necessity (1981). On the basis of rigidity, Kripke has shown that proper names and natural kind terms do not refer via a description as argued by descriptivists. In response to Kripke several people have argued that all general terms could be interpreted rigidly, which would make the notion of rigidity trivial. This leads to the ârigidity problemâ: the notion of rigidity cannot be used to argue against descriptivism anymore. I will show that the rigidity problem appears on a larger scale: firstly, because it appears independently of the trivialisation problem, secondly, because it appears for descriptions acting like singular terms as well. I will argue, however, that proper names and natural kind terms differ in an important manner from rigid descriptions. While the first are de jure rigid, the latter are de facto rigid. I will show that the rigidity problem indeed appears for de facto rigidity, but not for de jure rigidity, with the result that Kripkeâs argument against descriptivism can withstand
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Monetary policy rules, real rigidity and endogenous persistence
The bulk of literature on real rigidity attempts to identify sources of real rigidity in
market imperfections while assuming that the money supply is exogenously set. This
paper shows that monetary policy preferences affect the responsiveness of marginal
cost to output and through this channel they are shown to determine (i) the degree of
real rigidity and (ii) the degree of endogenous persistence. We find that substantial
levels of real rigidity and persistence can be generated using plausible parameters
values, without relying on market imperfections or other sources of real rigidity
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