104,223 research outputs found
Probabilistic cellular automata and random fields with i.i.d. directions
Let us consider the simplest model of one-dimensional probabilistic cellular
automata (PCA). The cells are indexed by the integers, the alphabet is {0, 1},
and all the cells evolve synchronously. The new content of a cell is randomly
chosen, independently of the others, according to a distribution depending only
on the content of the cell itself and of its right neighbor. There are
necessary and sufficient conditions on the four parameters of such a PCA to
have a Bernoulli product invariant measure. We study the properties of the
random field given by the space-time diagram obtained when iterating the PCA
starting from its Bernoulli product invariant measure. It is a non-trivial
random field with very weak dependences and nice combinatorial properties. In
particular, not only the horizontal lines but also the lines in any other
direction consist in i.i.d. random variables. We study extensions of the
results to Markovian invariant measures, and to PCA with larger alphabets and
neighborhoods
Structural and magnetic properties of Mn3-xCdxTeO6 (x = 0, 1, 1.5 and 2)
Mn3TeO6 exhibits a corundum-related A3TeO6 structure and a complex magnetic
structure involving two magnetic orbits for the Mn atoms [*]. Mn3-xCdxTeO6
(x=0, 1, 1.5 and 2) ceramics were synthesized by solid state reaction and
investigated using X-ray powder diffraction, electron microscopy, calorimetric
and magnetic measurements. Cd2+ replaces Mn2+ cations without greatly affecting
the structure of the compound. The Mn and Cd cations were found to be randomly
distributed over the A-site. Magnetization measurements indicated that the
samples order antiferromagnetically at low temperature with a transition
temperature that decreases with increasing Cd doping. The nuclear and magnetic
structure of one specially prepared 114Cd containing sample:
Mn1.5(114Cd)1.5TeO6, was studied using neutron powder diffraction over the
temperature range 2 to 295 K. Mn1.5(114Cd)1.5TeO6 was found to order in an
incommensurate helical magnetic structure, very similar to that of Mn3TeO6 [*].
However, with a lower transition temperature and the extension of the ordered
structure confined to order 240(10) {\AA}. [*] S. A. Ivanov et al. Mater. Res.
Bull. 46 (2011) 1870.Comment: 20 pages, 8 figure
Interpretation of some Yb-based valence-fluctuating crystals as approximants to a dodecagonal quasicrystal
The hexagonal ZrNiAl-type (space group: P-62m) and the tetragonal
Mo2FeB2-type (space group: P4/mbm) structures, which are frequently formed in
the same Yb-based alloys and exhibit physical properties related to
valence-fluctuation, can be regarded as approximants of a hypothetical
dodecagonal quasicrystal. Using Pd-Sn-Yb system as an example, a model of
quasicrystal structure has been constructed, of which 5-dimensional crystal
(space group: P12/mmm, aDD=5.66 {\AA} and c=3.72 {\AA}) consists of four types
of acceptance regions located at the following crystallographic sites; Yb
[00000], Pd[1/3 0 1/3 0 1/2], Pd[1/3 1/3 1/3 1/3 0] and Sn[1/2 00 1/2 1/2]. In
the 3-dimensional space, the quasicrystal is composed of three types of
columns, of which c-projections correspond to a square, an equilateral triangle
and a 3-fold hexagon. They are fragments of two known crystals, the hexagonal
{\alpha}-YbPdSn and the tetragonal Yb2Pd2Sn structures. The model of the
hypothetical quasicrystal may be applicable as a platform to treat in a unified
manner the heavy fermion properties in the two types of Yb-based crystals.Comment: 19 pages, 6 figure
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