7,033 research outputs found
Multiple-Time Higher-Order Perturbation Analysis of the Regularized Long-Wavelength Equation
By considering the long-wave limit of the regularized long wave (RLW)
equation, we study its multiple-time higher-order evolution equations. As a
first result, the equations of the Korteweg-de Vries hierarchy are shown to
play a crucial role in providing a secularity-free perturbation theory in the
specific case of a solitary-wave solution. Then, as a consequence, we show that
the related perturbative series can be summed and gives exactly the
solitary-wave solution of the RLW equation. Finally, some comments and
considerations are made on the N-soliton solution, as well as on the
limitations of applicability of the multiple scale method in obtaining uniform
perturbative series.Comment: 15 pages, RevTex, no figures (to appear in Phys. Rev. E
Perturbative analysis of wave interactions in nonlinear systems
This work proposes a new way for handling obstacles to asymptotic
integrability in perturbed nonlinear PDEs within the method of Normal Forms -
NF - for the case of multi-wave solutions. Instead of including the whole
obstacle in the NF, only its resonant part is included, and the remainder is
assigned to the homological equation. This leaves the NF intergable and its
solutons retain the character of the solutions of the unperturbed equation. We
exploit the freedom in the expansion to construct canonical obstacles which are
confined to te interaction region of the waves. Fo soliton solutions, e.g., in
the KdV equation, the interaction region is a finite domain around the origin;
the canonical obstacles then do not generate secular terms in the homological
equation. When the interaction region is infifnite, or semi-infinite, e.g., in
wave-front solutions of the Burgers equation, the obstacles may contain
resonant terms. The obstacles generate waves of a new type, which cannot be
written as functionals of the solutions of the NF. When an obstacle contributes
a resonant term to the NF, this leads to a non-standard update of th wave
velocity.Comment: 13 pages, including 6 figure
Elastic amplitudes studied with the LHC measurements at 7 and 8 TeV
Recent measurements of the differential cross sections in the forward region
of pp elastic scattering at 7 and 8 TeV show precise form of the
dependence. We propose a detailed analysis of these measurements including the
structures of the real and imaginary parts of the scattering amplitude. A good
description is achieved, confirming in all experiments the existence of a zero
in the real part in the forward region close to the origin, in agreement with
the prediction of a theorem by A. Martin, with important role in the observed
form of . Universal value for the position of this zero and
regularity in other features of the amplitudes are found, leading to
quantitative predictions for the forward elastic scattering at 13 TeV.Comment: 22 pages, 17 figures and 4 table
Evolution of Cosmological Perturbations in the Universe dominated by Multiple Scalar Fields
By efforts of several authors, it is recently established that the dynamical
behavior of the cosmological perturbation on superhorizon scales is well
approximated in terms of that in the long wavelength limit, and the latter can
be constructed from the evolution of corresponding exactly homogeneous
universe. Using these facts, we investigate the evolution of the cosmological
perturbation on superhorizon scales in the universe dominated by oscillating
multiple scalar fields which are generally interacting with each other, and the
ratio of whose masses is incommensurable. Since the scalar fields oscillate
rapidly around the local minimum of the potential, we use the action angle
variables. We found that this problem can be formulated as the canonical
perturbation theory in which the perturbed part appearing as the result of the
expansion of the universe and the interaction of the scalar fields is bounded
by the negative power ot time. We show that by constructing the canonical
transformations properly, the transformed hamiltonian becomes simple enough to
be solved. As the result of the invetigation using the long wavelength limit
and the canonical perturbation theory, under the sufficiently general
conditions, we prove that for the adiabatic growing mode the Bardeen parameter
stays constant and that for all the other modes the Bardeen parameter decays.
From the viewpoint of the ergodic theory, it is discussed that as for the
Bardeen parameter, the sigularities appear probabilistically. This analysis
serves the understanding of the evolution of the cosmological perturbations on
superhorizon scales during reheating.Comment: 31 Pages; Latex, No figure
KP solitons in shallow water
The main purpose of the paper is to provide a survey of our recent studies on
soliton solutions of the Kadomtsev-Petviashvili (KP) equation. The
classification is based on the far-field patterns of the solutions which
consist of a finite number of line-solitons. Each soliton solution is then
defined by a point of the totally non-negative Grassmann variety which can be
parametrized by a unique derangement of the symmetric group of permutations.
Our study also includes certain numerical stability problems of those soliton
solutions. Numerical simulations of the initial value problems indicate that
certain class of initial waves asymptotically approach to these exact solutions
of the KP equation. We then discuss an application of our theory to the Mach
reflection problem in shallow water. This problem describes the resonant
interaction of solitary waves appearing in the reflection of an obliquely
incident wave onto a vertical wall, and it predicts an extra-ordinary four-fold
amplification of the wave at the wall. There are several numerical studies
confirming the prediction, but all indicate disagreements with the KP theory.
Contrary to those previous numerical studies, we find that the KP theory
actually provides an excellent model to describe the Mach reflection phenomena
when the higher order corrections are included to the quasi-two dimensional
approximation. We also present laboratory experiments of the Mach reflection
recently carried out by Yeh and his colleagues, and show how precisely the KP
theory predicts this wave behavior.Comment: 50 pages, 25 figure
A Photometrically Detected Forming Cluster of Galaxies at Redshift 1.6 in the GOODS Field
We report the discovery of a localized overdensity at z~1.6 in the
GOODS-South Field, presumably a poor cluster in the process of formation. The
three-dimensional galaxy density has been estimated on the basis of well
calibrated photometric redshifts from the multiband photometric GOODS-MUSIC
catalog using the (2+1)D technique. The density peak is embedded in the larger
scale overdensity of galaxies known to exist at z=1.61 in the area. The
properties of the member galaxies are compared to those of the surrounding
field and we found that the two populations are significantly different
supporting the reality of the structure. The reddest galaxies, once evolved
according to their best fit models, have colors consistent with the red
sequence of lower redshift clusters. The estimated M_200 total mass of the
cluster is in the range 1.3 x 10^14 - 5.7x 10^14 Msun, depending on the assumed
bias factor b. An upper limit for the 2-10 keV X-ray luminosity, based on the
1Ms Chandra observations, is L_X=0.5 x 10^43 erg s^-1, suggesting that the
cluster has not yet reached the virial equilibrium.Comment: 6 pages, 5 figures (1 in color), uses emulateapj.cls Latex class
file, accepted for publication in Ap
Additional symmetries and solutions of the dispersionless KP hierarchy
The dispersionless KP hierarchy is considered from the point of view of the
twistor formalism. A set of explicit additional symmetries is characterized and
its action on the solutions of the twistor equations is studied. A method for
dealing with the twistor equations by taking advantage of hodograph type
equations is proposed. This method is applied for determining the orbits of
solutions satisfying reduction constraints of Gelfand--Dikii type under the
action of additional symmetries.Comment: 21 page
Homogeneity of Stellar Populations in Early-Type Galaxies with Different X-ray Properties
We have found the stellar populations of early-type galaxies are homogeneous
with no significant difference in color or Mg2 index, despite the dichotomy
between X-ray extended early-type galaxies and X-ray compact ones. Since the
X-ray properties reflect the potential gravitational structure and hence the
process of galaxy formation, the homogeneity of the stellar populations implies
that the formation of stars in early-type galaxies predat es the epoch when the
dichotomy of the potential structure was established.Comment: 6 pages, 5 figures, accepted for publication in Ap
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