6,009 research outputs found
The equivalence problem and rigidity for hypersurfaces embedded into hyperquadrics
We consider the class of Levi nondegenerate hypersurfaces in \bC^{n+1}
that admit a local (CR transversal) embedding, near a point , into a
standard nondegenerate hyperquadric in with codimension
small compared to the CR dimension of . We show that, for hypersurfaces
in this class, there is a normal form (which is closely related to the
embedding) such that any local equivalence between two hypersurfaces in normal
form must be an automorphism of the associated tangent hyperquadric. We also
show that if the signature of and that of the standard hyperquadric in
\bC^{N+1} are the same, then the embedding is rigid in the sense that any
other embedding must be the original embedding composed with an automorphism of
the quadric
Deformation of generic submanifolds in a complex manifold
This paper shows that an arbitrary generic submanifold in a complex manifold
can be deformed into a 1-parameter family of generic submanifolds satisfying
strong nondegeneracy conditions. The proofs use a careful analysis of the jet
spaces of embeddings satisfying certain nondegeneracy properties, and also make
use of the Thom transversality theorem, as well as the stratification of
real-algebraic sets. Optimal results on the order of nondegeneracy are given.Comment: 24 page
Experimental evidence of ageing and slow restoration of the weak-contact configuration in tilted 3D granular packings
Granular packings slowly driven towards their instability threshold are
studied using a digital imaging technique as well as a nonlinear acoustic
method. The former method allows us to study grain rearrangements on the
surface during the tilting and the latter enables to selectively probe the
modifications of the weak-contact fraction in the material bulk. Gradual ageing
of both the surface activity and the weak-contact reconfigurations is observed
as a result of repeated tilt cycles up to a given angle smaller than the angle
of avalanche. For an aged configuration reached after several consecutive tilt
cycles, abrupt resumption of the on-surface activity and of the weak-contact
rearrangements occurs when the packing is subsequently inclined beyond the
previous maximal tilting angle. This behavior is compared with literature
results from numerical simulations of inclined 2D packings. It is also found
that the aged weak-contact configurations exhibit spontaneous restoration
towards the initial state if the packing remains at rest for tens of minutes.
When the packing is titled forth and back between zero and near-critical
angles, instead of ageing, the weak-contact configuration exhibits "internal
weak-contact avalanches" in the vicinity of both the near-critical and zero
angles. By contrast, the stronger-contact skeleton remains stable
Quantitative Simulation of the Superconducting Proximity Effect
A numerical method is developed to calculate the transition temperature of
double or multi-layers consisting of films of super- and normal conductors. The
approach is based on a dynamic interpretation of Gorkov's linear gap equation
and is very flexible. The mean free path of the different metals, transmission
through the interface, ratio of specular reflection to diffusive scattering at
the surfaces, and fraction of diffusive scattering at the interface can be
included. Furthermore it is possible to vary the mean free path and the BCS
interaction NV in the vicinity of the interface. The numerical results show
that the normalized initial slope of an SN double layer is independent of
almost all film parameters except the ratio of the density of states. There are
only very few experimental investigations of this initial slope and they
consist of Pb/Nn double layers (Nn stands for a normal metal). Surprisingly the
coefficient of the initial slope in these experiments is of the order or less
than 2 while the (weak coupling) theory predicts a value of about 4.5. This
discrepancy has not been recognized in the past. The autor suggests that it is
due to strong coupling behavior of Pb in the double layers. The strong coupling
gap equation is evaluated in the thin film limit and yields the value of 1.6
for the coefficient. This agrees much better with the few experimental results
that are available.
PACS: 74.45.+r, 74.62.-c, 74.20.F
Quasiclassical approach to the spin-Hall effect in the two-dimensional electron gas
We study the spin-charge coupled transport in a two-dimensional electron
system using the method of quasiclassical (-integrated) Green's functions.
In particular we derive the Eilenberger equation in the presence of a generic
spin-orbit field. The method allows us to study spin and charge transport from
ballistic to diffusive regimes and continuity equations for spin and charge are
automatically incorporated. In the clean limit we establish the connection
between the spin-Hall conductivity and the Berry phase in momentum space. For
finite systems we solve the Eilenberger equation numerically for the special
case of the Rashba spin-orbit coupling and a two-terminal geometry. In
particular, we calculate explicitly the spin-Hall induced spin polarization in
the corners, predicted by Mishchenko et al. [13]. Furthermore we find universal
spin currents in the short-time dynamics after switching on the voltage across
the sample, and calculate the corresponding spin-Hall polarization at the
edges. Where available, we find perfect agreement with analytical results.Comment: 9 pages, 6 figure
Artificial Intelligence as a Culturological Problem
The article poses the question of cultural interpretation of artificial intelligence. It is revealed that in relation to artificial intelligence in modern culture there are at least two conflicting strategies. The first strategy is based on the idea of the superiority of artificial intelligence over the human intellect, and as a response serves as a breeding ground for the ideas of techno-apocalypse. The second strategy, which arose and developed within the framework of the Soviet Information Society project, sees in artificial intelligence the possibility of building a more perfect and just society.
Keywords: information society, artificial intelligence, induction of artificial intelligence, cultural problem, intercultural spac
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