53 research outputs found
Finite subgroups of automorphisms of K3 surfaces
We give a complete classification of finite subgroups of automorphisms of K3
surfaces up to deformation. The classification is in terms of Hodge theoretic
data associated to certain conjugacy classes of finite subgroups of the
orthogonal group of the K3 lattice. The moduli theory of K3 surfaces, in
particular the surjectivity of the period map and the strong Torelli theorem
allow us to interpret this datum geometrically. Our approach is computer aided
and involves hermitian lattices over number fields.Comment: 50 pages, for ancillary files see
https://doi.org/10.5281/zenodo.654447
Computing isomorphisms between lattices
Let K be a number field, let A be a finite dimensional semisimple K-algebra
and let Lambda be an O_K-order in A. It was shown in previous work that, under
certain hypotheses on A, there exists an algorithm that for a given (left)
Lambda-lattice X either computes a free basis of X over Lambda or shows that X
is not free over Lambda. In the present article, we generalise this by showing
that, under weaker hypotheses on A, there exists an algorithm that for two
given Lambda-lattices X and Y either computes an isomorphism X -> Y or
determines that X and Y are not isomorphic. The algorithm is implemented in
Magma for A=Q[G], Lambda=Z[G] and Lambda-lattices X and Y contained in Q[G],
where G is a finite group satisfying certain hypotheses. This is used to
investigate the Galois module structure of rings of integers and ambiguous
ideals of tamely ramified Galois extensions of Q with Galois group isomorphic
to Q_8 x C_2, the direct product of the quaternion group of order 8 and the
cyclic group of order 2.Comment: 30 pages; v3 revised and accepted version to appear in Mathematics of
Computation; v2 has many minor corrections with additional explanation in
section 1
Capillary rise of water in hydrophilic nanopores
We report on the capillary rise of water in three-dimensional networks of
hydrophilic silica pores with 3.5nm and 5nm mean radii, respectively (porous
Vycor monoliths). We find classical square root of time Lucas-Washburn laws for
the imbibition dynamics over the entire capillary rise times of up to 16h
investigated. Provided we assume two preadsorbed strongly bound layers of water
molecules resting at the silica walls, which corresponds to a negative velocity
slip length of -0.5nm for water flow in silica nanopores, we can describe the
filling process by a retained fluidity and capillarity of water in the pore
center. This anticipated partitioning in two dynamic components reflects the
structural-thermodynamic partitioning in strongly silica bound water layers and
capillary condensed water in the pore center which is documented by sorption
isotherm measurements.Comment: 4 pages, 3 figure
Molecular dynamics of n-hexane: A quasi-elastic neutron scattering study on the bulk and spatially nanochannel-confined liquid
We present incoherent quasi-elastic neutron scattering measurements in a
wavevector transfer range from 0.4 AA^{-1} to 1.6AA^{-1} on liquid n-hexane
confined in cylindrical, parallel-aligned nanochannels of 6 nm mean diameter
and 260 micrometer length in monolithic, mesoporous silicon. They are
complemented with, and compared to, measurements on the bulk system in a
temperature range from 50K to 250K. The time-of-flight spectra of the bulk
liquid can be modeled by microscopic translational as well as fast localized
rotational, thermally-excited, stochastic motions of the molecules. In the
nano-confined state of the liquid, which was prepared by vapor condensation, we
find two molecular populations with distinct dynamics, a fraction which is
immobile on the time scale of 1ps to 100ps probed in our experiments and a
second component with a self-diffusion dynamics slightly slower than observed
for the bulk liquid. No hints of an anisotropy of the translational diffusion
with regard to the orientation of the channels' long axes have been found. The
immobile fraction amounts to about 5% at 250K, gradually increases upon cooling
and exhibits an abrupt increase at 160K (20K below bulk crystallization), which
indicates pore freezingComment: 10 pages, 7 figure
Melting and freezing of argon in a granular packing of linear mesopore arrays
Freezing and melting of Ar condensed in a granular packing of template-grown
arrays of linear mesopores (SBA-15, mean pore diameter 8 nanometer) has been
studied by specific heat measurements C as a function of fractional filling of
the pores. While interfacial melting leads to a single melting peak in C,
homogeneous and heterogeneous freezing along with a delayering transition for
partial fillings of the pores result in a complex freezing mechanism
explainable only by a consideration of regular adsorption sites (in the
cylindrical mesopores) and irregular adsorption sites (in niches of the rough
external surfaces of the grains, and at points of mutual contact of the powder
grains). The tensile pressure release upon reaching bulk liquid/vapor
coexistence quantitatively accounts for an upward shift of the
melting/freeezing temperature observed while overfilling the mesopores.Comment: 4 pages, 4 figures, to appear as a Letter in Physical Review Letter
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