180 research outputs found
Bispecial factors in circular non-pushy D0L languages
We study bispecial factors in fixed points of morphisms. In particular, we
propose a simple method of how to find all bispecial words of non-pushy
circular D0L-systems. This method can be formulated as an algorithm. Moreover,
we prove that non-pushy circular D0L-systems are exactly those with finite
critical exponent.Comment: 18 pages, 5 figure
Evolutionary influences on the structure of red-giant acoustic oscillation spectra from 600d of Kepler observations
Context: The Kepler space mission is reaching continuous observing times long
enough to start studying the fine structure of the observed p-mode spectra.
Aims: In this paper, we aim to study the signature of stellar evolution on the
radial and p-dominated l=2 modes in an ensemble of red giants that show
solar-type oscillations. Results: We find that the phase shift of the central
radial mode (eps_c) is significantly different for red giants at a given large
frequency separation (Dnu_c) but which burn only H in a shell (RGB) than those
that have already ignited core He burning. Even though not directly probing the
stellar core the pair of local seismic observables (Dnu_c, eps_c) can be used
as an evolutionary stage discriminator that turned out to be as reliable as the
period spacing of the mixed dipole modes. We find a tight correlation between
eps_c and Dnu_c for RGB stars and no indication that eps_c depends on other
properties of these stars. It appears that the difference in eps_c between the
two populations becomes if we use an average of several radial orders, instead
of a local, i.e. only around the central radial mode, Dnu to determine the
phase shift. This indicates that the information on the evolutionary stage is
encoded locally, in the shape of the radial mode sequence. This shape turns out
to be approximately symmetric around the central radial mode for RGB stars but
asymmetric for core He burning stars. We computed radial modes for a sequence
of RG models and find them to qualitatively confirm our findings. We also find
that, at least in our models, the local Dnu is an at least as good and mostly
better proxy for both the asymptotic spacing and the large separation scaled
from the model density than the average Dnu. Finally, we investigate the
signature of the evolutionary stage on the small frequency separation and
quantify the mass dependency of this seismic parameter.Comment: 12 pages, 9 figures, accepted for publication in A&
A Geometric Approach to the stabilisation of certain sequences of Kronecker coefficients
We give another proof, using tools from Geometric Invariant Theory, of a
result due to S. Sam and A. Snowden in 2014, concerning the stability of
Kro-necker coefficients. This result states that some sequences of Kronecker
coefficients eventually stabilise, and our method gives a nice geometric bound
from which the stabilisation occurs. We perform the explicit computation of
such a bound on two examples, one being the classical case of Murnaghan's
stability. Moreover, we see that our techniques apply to other coefficients
arising in Representation Theory: namely to some plethysm coefficients and in
the case of the tensor product of representations of the hyperoctahedral group.Comment: Manuscripta mathematica, Springer Verlag, In press,
\&\#x3008;https://doi.org/10.1007/s00229-018-1021-4\&\#x300
Large Deviation Approach to the Randomly Forced Navier-Stokes Equation
The random forced Navier-Stokes equation can be obtained as a variational
problem of a proper action. By virtue of incompressibility, the integration
over transverse components of the fields allows to cast the action in the form
of a large deviation functional. Since the hydrodynamic operator is nonlinear,
the functional integral yielding the statistics of fluctuations can be
practically computed by linearizing around a physical solution of the
hydrodynamic equation. We show that this procedure yields the dimensional
scaling predicted by K41 theory at the lowest perturbative order, where the
perturbation parameter is the inverse Reynolds number. Moreover, an explicit
expression of the prefactor of the scaling law is obtained.Comment: 24 page
Integrable systems and holomorphic curves
In this paper we attempt a self-contained approach to infinite dimensional
Hamiltonian systems appearing from holomorphic curve counting in Gromov-Witten
theory. It consists of two parts. The first one is basically a survey of
Dubrovin's approach to bihamiltonian tau-symmetric systems and their relation
with Frobenius manifolds. We will mainly focus on the dispersionless case, with
just some hints on Dubrovin's reconstruction of the dispersive tail. The second
part deals with the relation of such systems to rational Gromov-Witten and
Symplectic Field Theory. We will use Symplectic Field theory of
as a language for the Gromov-Witten theory of a closed symplectic manifold .
Such language is more natural from the integrable systems viewpoint. We will
show how the integrable system arising from Symplectic Field Theory of
coincides with the one associated to the Frobenius structure of
the quantum cohomology of .Comment: Partly material from a working group on integrable systems organized
by O. Fabert, D. Zvonkine and the author at the MSRI - Berkeley in the Fall
semester 2009. Corrected some mistake
Morphic words and equidistributed sequences
The problem we consider is the following: Given an infinite word on an
ordered alphabet, construct the sequence , equidistributed on
and such that if and only if ,
where is the shift operation, erasing the first symbol of . The
sequence exists and is unique for every word with well-defined positive
uniform frequencies of every factor, or, in dynamical terms, for every element
of a uniquely ergodic subshift. In this paper we describe the construction of
for the case when the subshift of is generated by a morphism of a
special kind; then we overcome some technical difficulties to extend the result
to all binary morphisms. The sequence in this case is also constructed
with a morphism.
At last, we introduce a software tool which, given a binary morphism
, computes the morphism on extended intervals and first elements of
the equidistributed sequences associated with fixed points of
On the critical exponent of generalized Thue-Morse words
For certain generalized Thue-Morse words t, we compute the "critical
exponent", i.e., the supremum of the set of rational numbers that are exponents
of powers in t, and determine exactly the occurrences of powers realizing it.Comment: 13 pages; to appear in Discrete Mathematics and Theoretical Computer
Science (accepted October 15, 2007
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