1,869 research outputs found
Symmetry, singularities and integrability in complex dynamics III: approximate symmetries and invariants
The different natures of approximate symmetries and their corresponding first
integrals/invariants are delineated in the contexts of both Lie symmetries of
ordinary differential equations and Noether symmetries of the Action Integral.
Particular note is taken of the effect of taking higher orders of the
perturbation parameter. Approximate symmetries of approximate first
integrals/invariants and the problems of calculating them using the Lie method
are considered
Consequences of a covariant Description of Heavy Ion Reactions at intermediate Energies
Heavy ion collisions at intermediate energies are studied by using a new RQMD
code, which is a covariant generalization of the QMD approach. We show that
this new implementation is able to produce the same results in the
nonrelativistic limit (i.e. 50MeV/nucl.) as the non-covariant QMD. Such a
comparison is not available in the literature. At higher energies (i.e. 1.5
GeV/nucl. and 2 GeV/nucl.) RQMD and QMD give different results in respect to
the time evolution of the phase space, for example for the directed transverse
flow. These differences show that consequences of a covariant description of
heavy ion reactions within the framework of RQMD are existing even at
intermediate energies.Comment: LaTex-file, 28 pages, 8 figures (available upon request), accepted
for publication in Physical Review
Time and Observables in Unimodular General Relativity
A cosmological time variable is emerged from the hamiltonian formulation of
unimodular theory of gravity to measure the evolution of dynamical observables
in the theory. A set of constants of motion has been identified for the theory
on the null hypersurfaces that its evolution is with respect to the volume
clock introduced by the cosmological time variable.Comment: 16 page
Proof of the Thin Sandwich Conjecture
We prove that the Thin Sandwich Conjecture in general relativity is valid,
provided that the data satisfy certain geometric
conditions. These conditions define an open set in the class of possible data,
but are not generically satisfied. The implications for the ``superspace''
picture of the Einstein evolution equations are discussed.Comment: 8 page
Planck Scale Physics of the Single Particle Schr\"{o}dinger Equation with Gravitational Self-Interaction
We consider the modification of a single particle Schr\"{o}dinger equation by
the inclusion of an additional gravitational self-potential term which follows
from the prescription that the' mass-density'that enters this term is given by
, where is the wavefunction and
is the mass of the particle. This leads to a nonlinear equation, the '
Newton Schrodinger' equation, which has been found to possess stationary
self-bound solutions, whose energy can be determined exactly using an
asymptotic method. We find that such a particle strongly violates superposition
and becomes a black hole as its mass approaches the Planck mass.Comment: 16 pages, Revtex, No figure, Submitted to Physics Letters
Detection of Multiple Variants of Grapevine Fanleaf Virus in Single Xiphinema index Nematodes
Grapevine fanleaf virus (GFLV) is responsible for a widespread disease in vineyards
worldwide. Its genome is composed of two single-stranded positive-sense RNAs, which both show
a high genetic diversity. The virus is transmitted from grapevine to grapevine by the ectoparasitic
nematode Xiphinema index. Grapevines in diseased vineyards are often infected by multiple genetic
variants of GFLV but no information is available on the molecular composition of virus variants
retained in X. index following nematodes feeding on roots. In this work, aviruliferous X. index were
fed on three naturally GFLV-infected grapevines for which the virome was characterized by RNAseq.
Six RNA-1 and four RNA-2 molecules were assembled segregating into four and three distinct
phylogenetic clades of RNA-1 and RNA-2, respectively. After 19 months of rearing, single and pools
of 30 X. index tested positive for GFLV. Additionally, either pooled or single X. index carried multiple
variants of the two GFLV genomic RNAs. However, the full viral genetic diversity found in the leaves
of infected grapevines was not detected in viruliferous nematodes, indicating a genetic bottleneck.
Our results provide new insights into the complexity of GFLV populations and the putative role of X.
index as reservoirs of virus diversity
Diffeomorphisms, Noether Charges and Canonical Formalism in 2D Dilaton Gravity
We carry out a parallel study of the covariant phase space and the
conservation laws of local symmetries in two-dimensional dilaton gravity. Our
analysis is based on the fact that the Lagrangian can be brought to a form that
vanishes on-shell giving rise to a well-defined covariant potential for the
symplectic current. We explicitly compute the symplectic structure and its
potential and show that the requirement to be finite and independent of the
Cauchy surface restricts the asymptotic symmetries.Comment: 14 pages, latex with psfig macro, one figur
Conserved charges for gravity with locally AdS asymptotics
A new formula for the conserved charges in 3+1 gravity for spacetimes with
local AdS asymptotic geometry is proposed. It is shown that requiring the
action to have an extremum for this class of asymptotia sets the boundary term
that must be added to the Lagrangian as the Euler density with a fixed weight
factor. The resulting action gives rise to the mass and angular momentum as
Noether charges associated to the asymptotic Killing vectors without requiring
specification of a reference background in order to have a convergent
expression. A consequence of this definition is that any negative constant
curvature spacetime has vanishing Noether charges. These results remain valid
in the limit of vanishing cosmological constant.Comment: 5 pages, 2 Columns, revtex. Last version for Phys. Rev. Let
Quasi-Local Gravitational Energy
A dynamically preferred quasi-local definition of gravitational energy is
given in terms of the Hamiltonian of a `2+2' formulation of general relativity.
The energy is well-defined for any compact orientable spatial 2-surface, and
depends on the fundamental forms only. The energy is zero for any surface in
flat spacetime, and reduces to the Hawking mass in the absence of shear and
twist. For asymptotically flat spacetimes, the energy tends to the Bondi mass
at null infinity and the \ADM mass at spatial infinity, taking the limit along
a foliation parametrised by area radius. The energy is calculated for the
Schwarzschild, Reissner-Nordstr\"om and Robertson-Walker solutions, and for
plane waves and colliding plane waves. Energy inequalities are discussed, and
for static black holes the irreducible mass is obtained on the horizon.
Criteria for an adequate definition of quasi-local energy are discussed.Comment: 16 page
The Relativistic N-body Problem in a Separable Two-Body Basis
We use Dirac's constraint dynamics to obtain a Hamiltonian formulation of the
relativistic N-body problem in a separable two-body basis in which the
particles interact pair-wise through scalar and vector interactions. The
resultant N-body Hamiltonian is relativistically covariant. It can be easily
separated in terms of the center-of-mass and the relative motion of any
two-body subsystem. It can also be separated into an unperturbed Hamiltonian
with a residual interaction. In a system of two-body composite particles, the
solutions of the unperturbed Hamiltonian are relativistic two-body internal
states, each of which can be obtained by solving a relativistic
Schr\"odinger-like equation. The resultant two-body wave functions can be used
as basis states to evaluate reaction matrix elements in the general N-body
problem. We prove a relativistic version of the post-prior equivalence which
guarantees a unique evaluation of the reaction matrix element, independent of
the ways of separating the Hamiltonian into unperturbed and residual
interactions. Since an arbitrary reaction matrix element involves composite
particles in motion, we show explicitly how such matrix elements can be
evaluated in terms of the wave functions of the composite particles and the
relevant Lorentz transformations.Comment: 42 pages, 2 figures, in LaTe
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