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Inverse problems of symbolic dynamics
This paper reviews some results regarding symbolic dynamics, correspondence
between languages of dynamical systems and combinatorics. Sturmian sequences
provide a pattern for investigation of one-dimensional systems, in particular
interval exchange transformation. Rauzy graphs language can express many
important combinatorial and some dynamical properties. In this case
combinatorial properties are considered as being generated by substitutional
system, and dynamical properties are considered as criteria of superword being
generated by interval exchange transformation. As a consequence, one can get a
morphic word appearing in interval exchange transformation such that
frequencies of letters are algebraic numbers of an arbitrary degree.
Concerning multydimensional systems, our main result is the following. Let
P(n) be a polynomial, having an irrational coefficient of the highest degree. A
word (w=(w_n), n\in \nit) consists of a sequence of first binary numbers
of i.e. . Denote the number of different subwords
of of length by .
\medskip {\bf Theorem.} {\it There exists a polynomial , depending only
on the power of the polynomial , such that for sufficiently
great .
Non-relativistic limit of multidimensional gravity: exact solutions and applications
It is found the exact solution of the Poisson equation for the
multidimensional space with topology . This
solution describes smooth transition from the newtonian behavior for
distances bigger than periods of tori (the extra dimension sizes) to
multidimensional behavior in opposite limit. In the case of
one extra dimension , the gravitational potential is expressed via compact
and elegant formula. These exact solutions are applied to some practical
problems to get the gravitational potentials for considered configurations.
Found potentials are used to calculate the acceleration for point masses and
gravitational self-energy.It is proposed models where the test masses are
smeared over some (or all) extra dimensions. In 10-dimensional spacetime with 3
smeared extra dimensions, it is shown that the size of 3 rest extra dimensions
can be enlarged up to submillimeter for the case of 1TeV fundamental Planck
scale . In the models where all extra dimensions are smeared, the
gravitational potential exactly coincides with the newtonian one regardless of
size of the extra dimensions. Nevertheless, the hierarchy problem can be solved
in these models.Comment: LaTex file, 18 pages, 4 figure
Picosecond strain dynamics in GeSbTe monitored by time-resolved x-ray diffraction
Coherent phonons (CP) generated by laser pulses on the femtosecond scale have
been proposed as a means to achieve ultrafast, non-thermal switching in
phase-change materials such as GeSbTe(GST). Here we use
ultrafast optical pump pulses to induce coherent acoustic phonons and
stroboscopically measure the corresponding lattice distortions in GST using 100
ps x-ray pulses from the ESRF storage ring. A linear-chain model provides a
good description of the observed changes in the diffraction signal, however,
the magnitudes of the measured shifts are too large to be explained by thermal
effects alone implying the presence of transient non-equilibrium electron
heating in addition to temperature driven expansion. The information on the
movement of atoms during the excitation process can lead to greater insight
into the possibilities of using CP-induced phase-transitions in GST.Comment: 7 pages, 4 figures, Phys. Rev. B, in pres
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