505 research outputs found
Similar sublattices of the root lattice
Similar sublattices of the root lattice are possible, according to a
result of Conway, Rains and Sloane, for each index that is the square of a
non-zero integer of the form . Here, we add a constructive
approach, based on the arithmetic of the quaternion algebra and the existence of a particular involution of the
second kind, which also provides the actual sublattices and the number of
different solutions for a given index. The corresponding Dirichlet series
generating function is closely related to the zeta function of the icosian
ring.Comment: 17 pages, 1 figure; revised version with several additions and
improvement
Characterization of the complex ion dynamics in lithium silicate glasses via computer simulations
We present results of molecular dynamics simulations on lithium metasilicate
over a broad range of temperatures for which the silicate network is frozen in
but the lithium ions can still be equilibrated. The lithium dynamics is studied
via the analysis of different correlation functions. The activation energy for
the lithium mobility agrees very well with experimental data. The correlation
of the dynamics of adjacent ions is weak. At low temperatures the dynamics can
be separated into local vibrational dynamics and hopping events between
adjacent lithium sites. The derivative of the mean square displacement displays
several characteristic time regimes. They can be directly mapped onto
respective frequency regimes for the conductivity. In particular it is possible
to identify time regimes dominated by localized dynamics and long-range
dynamics, respectively. The question of time-temperature superposition is
discussed for the mean square displacement and the incoherent scattering
function.Comment: to be published in Phys. Chem. Chem. Phy
Particle rearrangements during transitions between local minima of the potential energy landscape of a supercooled Lennard-Jones liquid
The potential energy landscape (PEL) of supercooled binary Lennard-Jones
(BLJ) mixtures exhibits local minima, or inherent structures (IS), which are
organized into meta-basins (MB). We study the particle rearrangements related
to transitions between both successive IS and successive MB for a small 80:20
BLJ system near the mode-coupling temperature T_MCT. The analysis includes the
displacements of individual particles, the localization of the rearrangements
and the relevance of string-like motion. We find that the particle
rearrangements during IS and MB transitions do not change significantly at
T_MCT. Further, it is demonstrated that IS and MB dynamics are spatially
heterogeneous and facilitated by string-like motion. To investigate the
mechanism of string-like motion, we follow the particle rearrangements during
suitable sequences of IS transitions. We find that most strings observed after
a series of transitions do not move coherently during a single transition, but
subunits of different sizes are active at different times. Several findings
suggest that the occurrence of a successful string enables the system to exit a
MB. Moreover, we show that the particle rearrangements during two consecutive
MB transitions are basically uncorrelated. Specifically, different groups of
particles are highly mobile during subsequent MB transitions. Finally, the
relation between the features of the PEL and the relaxation processes in
supercooled liquids is discussed.Comment: 13 pages, 10 figure
- …