353 research outputs found
On the Formation Age of the First Planetary System
Recently, it has been observed the extreme metal-poor stars in the Galactic
halo, which must be formed just after Pop III objects. On the other hand, the
first gas clouds of mass are supposed to be formed at 10, 20, and 30 for the , and , where the
density perturbations are assumed of the standard CDM cosmology. If we
could apply this gaussian distribution to the extreme small probability, the
gas clouds would be formed at 40, 60, and 80 for the ,
, and . The first gas clouds within our galaxy must be formed
around . Even if the gas cloud is metal poor, there is a lot of
possibility to form the planets around such stars. The first planetary systems
could be formed within years after the Big Bang in the
universe. Even in our galaxies, it could be formed within
years. It is interesting to wait the observations of planets around metal-poor
stars. For the panspermia theory, the origin of life could be expected in such
systems.Comment: 5 pages,Proceedings IAU Symposium No. 249, 2007, Exoplanets:Y-S. Sun,
S. Ferraz-Mello and J.-L, Zhou, eds. (p325
Local Runup Amplification By Resonant Wave Interactions
Until now the analysis of long wave runup on a plane beach has been focused
on finding its maximum value, failing to capture the existence of resonant
regimes. One-dimensional numerical simulations in the framework of the
Nonlinear Shallow Water Equations (NSWE) are used to investigate the Boundary
Value Problem (BVP) for plane and non-trivial beaches. Monochromatic waves, as
well as virtual wave-gage recordings from real tsunami simulations, are used as
forcing conditions to the BVP. Resonant phenomena between the incident
wavelength and the beach slope are found to occur, which result in enhanced
runup of non-leading waves. The evolution of energy reveals the existence of a
quasi-periodic state for the case of sinusoidal waves, the energy level of
which, as well as the time required to reach that state, depend on the incident
wavelength for a given beach slope. Dispersion is found to slightly reduce the
value of maximum runup, but not to change the overall picture. Runup
amplification occurs for both leading elevation and depression waves.Comment: 10 pages, 7 Figures. Accepted to Physical Review Letters. Other
author's papers can be downloaded at http://www.lama.univ-savoie.fr/~dutykh
Star product formula of theta functions
As a noncommutative generalization of the addition formula of theta
functions, we construct a class of theta functions which are closed with
respect to the Moyal star product of a fixed noncommutative parameter. These
theta functions can be regarded as bases of the space of holomorphic
homomorphisms between holomorphic line bundles over noncommutative complex
tori.Comment: 12 page
-Algebras, the BV Formalism, and Classical Fields
We summarise some of our recent works on -algebras and quasi-groups
with regard to higher principal bundles and their applications in twistor
theory and gauge theory. In particular, after a lightning review of
-algebras, we discuss their Maurer-Cartan theory and explain that any
classical field theory admitting an action can be reformulated in this context
with the help of the Batalin-Vilkovisky formalism. As examples, we explore
higher Chern-Simons theory and Yang-Mills theory. We also explain how these
ideas can be combined with those of twistor theory to formulate maximally
superconformal gauge theories in four and six dimensions by means of
-quasi-isomorphisms, and we propose a twistor space action.Comment: 19 pages, Contribution to Proceedings of LMS/EPSRC Durham Symposium
Higher Structures in M-Theory, August 201
On open-closed extension of boundary string field theory
We investigate a classical open-closed string field theory whose open string
sector is given by boundary string field theory. The open-closed interaction is
introduced by the overlap of a boundary state with a closed string field. With
the help of the Batalin-Vilkovisky formalism, the closed string sector is
determined to be the HIKKO closed string field theory. We also discuss the
gauge invariance of this theory in both open and closed string sides.Comment: 25 pages, 2 figures, comments and a reference added, typos correcte
Solitons on Noncommutative Torus as Elliptic Calogero Gaudin Models, Branes and Laughlin Wave Functions
For the noncommutative torus , in case of the N.C. parameter
, we construct the basis of Hilbert space {\caH}_n\thetaz_in{\cal A}_nZ_n
\times Z_n\thetagsu(n)transform covariantly by the global gauge
transformation of By acting on we establish the
isomorphism of . We embed this into the -matrix of the
elliptic Gaudin andsu_n({\cal T})D(k, u)spectral curve
describes the brane configuration, with the dynamical
variables of N.C. solitons asT^{\otimes n} / S_nthe N.C. cotangent bundle with marked points. The
eigenfunction of the Gaudin differential -operators as the
Laughli$wavefunction is solved by Bethe ansatz.Comment: 25 pages, plain latex, no figure
Comparison between three-dimensional linear and nonlinear tsunami generation models
The modeling of tsunami generation is an essential phase in understanding
tsunamis. For tsunamis generated by underwater earthquakes, it involves the
modeling of the sea bottom motion as well as the resulting motion of the water
above it. A comparison between various models for three-dimensional water
motion, ranging from linear theory to fully nonlinear theory, is performed. It
is found that for most events the linear theory is sufficient. However, in some
cases, more sophisticated theories are needed. Moreover, it is shown that the
passive approach in which the seafloor deformation is simply translated to the
ocean surface is not always equivalent to the active approach in which the
bottom motion is taken into account, even if the deformation is supposed to be
instantaneous.Comment: 39 pages, 16 figures; Accepted to Theoretical and Computational Fluid
Dynamics. Several references have been adde
Cohomology Groups of Deformations of Line Bundles on Complex Tori
The cohomology groups of line bundles over complex tori (or abelian
varieties) are classically studied invariants of these spaces. In this article,
we compute the cohomology groups of line bundles over various holomorphic,
non-commutative deformations of complex tori. Our analysis interpolates between
two extreme cases. The first case is a calculation of the space of
(cohomological) theta functions for line bundles over constant, commutative
deformations. The second case is a calculation of the cohomologies of
non-commutative deformations of degree-zero line bundles.Comment: 24 pages, exposition improved, typos fixe
Tachyon Condensation on Noncommutative Torus
We discuss noncommutative solitons on a noncommutative torus and their
application to tachyon condensation. In the large B limit, they can be exactly
described by the Powers-Rieffel projection operators known in the mathematical
literature. The resulting soliton spectrum is consistent with T-duality and is
surprisingly interesting. It is shown that an instability arises for any
D-branes, leading to the decay into many smaller D-branes. This phenomenon is
the consequence of the fact that K-homology for type II von Neumann factor is
labeled by R.Comment: LaTeX, 17 pages, 1 figur
Matrix Factorizations, Minimal Models and Massey Products
We present a method to compute the full non-linear deformations of matrix
factorizations for ADE minimal models. This method is based on the calculation
of higher products in the cohomology, called Massey products. The algorithm
yields a polynomial ring whose vanishing relations encode the obstructions of
the deformations of the D-branes characterized by these matrix factorizations.
This coincides with the critical locus of the effective superpotential which
can be computed by integrating these relations. Our results for the effective
superpotential are in agreement with those obtained from solving the A-infinity
relations. We point out a relation to the superpotentials of Kazama-Suzuki
models. We will illustrate our findings by various examples, putting emphasis
on the E_6 minimal model.Comment: 32 pages, v2: typos corrected, v3: additional comments concerning the
bulk-boundary crossing constraint, some small clarifications, typo
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