1,789 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
Gauging kinematical and internal symmetry groups for extended systems: the Galilean one-time and two-times harmonic oscillators
The possible external couplings of an extended non-relativistic classical
system are characterized by gauging its maximal dynamical symmetry group at the
center-of-mass. The Galilean one-time and two-times harmonic oscillators are
exploited as models. The following remarkable results are then obtained: 1) a
peculiar form of interaction of the system as a whole with the external gauge
fields; 2) a modification of the dynamical part of the symmetry
transformations, which is needed to take into account the alteration of the
dynamics itself, induced by the {\it gauge} fields. In particular, the
Yang-Mills fields associated to the internal rotations have the effect of
modifying the time derivative of the internal variables in a scheme of minimal
coupling (introduction of an internal covariant derivative); 3) given their
dynamical effect, the Yang-Mills fields associated to the internal rotations
apparently define a sort of Galilean spin connection, while the Yang-Mills
fields associated to the quadrupole momentum and to the internal energy have
the effect of introducing a sort of dynamically induced internal metric in the
relative space.Comment: 32 pages, LaTex using the IOP preprint macro package (ioplppt.sty
available at: http://www.iop.org/). The file is available at:
http://www.fis.unipr.it/papers/1995.html The file is a uuencoded tar gzip
file with the IOP preprint style include
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
The Quantum States and the Statistical Entropy of the Charged Black Hole
We quantize the Reissner-Nordstr\"om black hole using an adaptation of
Kucha\v{r}'s canonical decomposition of the Kruskal extension of the
Schwarzschild black hole. The Wheeler-DeWitt equation turns into a functional
Schroedinger equation in Gaussian time by coupling the gravitational field to a
reference fluid or dust. The physical phase space of the theory is spanned by
the mass, , the charge, , the physical radius, , the dust proper time,
, and their canonical momenta. The exact solutions of the functional
Schroedinger equation imply that the difference in the areas of the outer and
inner horizons is quantized in integer units. This agrees in spirit, but not
precisely, with Bekenstein's proposal on the discrete horizon area spectrum of
black holes. We also compute the entropy in the microcanonical ensemble and
show that the entropy of the Reissner-Nordstr\"om black hole is proportional to
this quantized difference in horizon areas.Comment: 31 pages, 3 figures, PHYZZX macros. Comments on the wave-functional
in the interior and one reference added. To appear in Phys. Rev.
Correlation between nucleotide composition and folding energy of coding sequences with special attention to wobble bases
Background: The secondary structure and complexity of mRNA influences its
accessibility to regulatory molecules (proteins, micro-RNAs), its stability and
its level of expression. The mobile elements of the RNA sequence, the wobble
bases, are expected to regulate the formation of structures encompassing coding
sequences.
Results: The sequence/folding energy (FE) relationship was studied by
statistical, bioinformatic methods in 90 CDS containing 26,370 codons. I found
that the FE (dG) associated with coding sequences is significant and negative
(407 kcal/1000 bases, mean +/- S.E.M.) indicating that these sequences are able
to form structures. However, the FE has only a small free component, less than
10% of the total. The contribution of the 1st and 3rd codon bases to the FE is
larger than the contribution of the 2nd (central) bases. It is possible to
achieve a ~ 4-fold change in FE by altering the wobble bases in synonymous
codons. The sequence/FE relationship can be described with a simple algorithm,
and the total FE can be predicted solely from the sequence composition of the
nucleic acid. The contributions of different synonymous codons to the FE are
additive and one codon cannot replace another. The accumulated contributions of
synonymous codons of an amino acid to the total folding energy of an mRNA is
strongly correlated to the relative amount of that amino acid in the translated
protein.
Conclusion: Synonymous codons are not interchangable with regard to their
role in determining the mRNA FE and the relative amounts of amino acids in the
translated protein, even if they are indistinguishable in respect of amino acid
coding.Comment: 14 pages including 6 figures and 1 tabl
Quasigroups, Asymptotic Symmetries and Conservation Laws in General Relativity
A new quasigroup approach to conservation laws in general relativity is
applied to study asymptotically flat at future null infinity spacetime. The
infinite-parametric Newman-Unti group of asymptotic symmetries is reduced to
the Poincar\'e quasigroup and the Noether charge associated with any element of
the Poincar\'e quasialgebra is defined. The integral conserved quantities of
energy-momentum and angular momentum are linear on generators of Poincar\'e
quasigroup, free of the supertranslation ambiguity, posess the flux and
identically equal to zero in Minkowski spacetime.Comment: RevTeX4, 5 page
Relativistic conservation laws and integral constraints for large cosmological perturbations
For every mapping of a perturbed spacetime onto a background and with any
vector field we construct a conserved covariant vector density ,
which is the divergence of a covariant antisymmetric tensor density, a
"superpotential". is linear in the energy-momentum tensor
perturbations of matter, which may be large; does not contain the
second order derivatives of the perturbed metric. The superpotential is
identically zero when perturbations are absent.
By integrating conserved vectors over a part \Si of a hypersurface of
the background, which spans a two-surface \di\Si, we obtain integral
relations between, on the one hand, initial data of the perturbed metric
components and the energy-momentum perturbations on \Si and, on the other
hand, the boundary values on \di\Si. We show that there are as many such
integral relations as there are different mappings, 's, \Si's and
\di\Si's. For given boundary values on \di\Si, the integral relations may
be interpreted as integral constraints (e.g., those of Traschen) on local
initial data including the energy-momentum perturbations. Conservation laws
expressed in terms of Killing fields \Bar\xi of the background become
"physical" conservation laws.
In cosmology, to each mapping of the time axis of a Robertson-Walker space on
a de Sitter space with the same spatial topology there correspond ten
conservation laws. The conformal mapping leads to a straightforward
generalization of conservation laws in flat spacetimes. Other mappings are also
considered. ...Comment: This paper, published 7 years ago, was found useful by some
researchers but originally was not put on the gr-qc website. Now it has been
retyped with very minor changes: few wordings have been modified and several
misprints occurring in the printed version correcte
Energy Distribution of a Stationary Beam of Light
Aguirregabiria et al showed that Einstein, Landau and Lifshitz, Papapetrou,
and Weinberg energy-momentum complexes coincide for all Kerr-Schild metric.
Bringely used their general expression of the Kerr-Schild class and found
energy and momentum densities for the Bonnor metric. We obtain these results
without using Aguirregabiria et al results and verify that Bringley's results
are correct. This also supports Aguirregabiria et al results as well as
Cooperstock hypothesis. Further, we obtain the energy distribution of the
space-time under consideration.Comment: Latex, no figures [Admin note: substantial overlap with gr-qc/9910015
and hep-th/0308070
Two-spinor Formulation of First Order Gravity coupled to Dirac Fields
Two-spinor formalism for Einstein Lagrangian is developed. The gravitational
field is regarded as a composite object derived from soldering forms. Our
formalism is geometrically and globally well-defined and may be used in
virtually any 4m-dimensional manifold with arbitrary signature as well as
without any stringent topological requirement on space-time, such as
parallelizability. Interactions and feedbacks between gravity and spinor fields
are considered. As is well known, the Hilbert-Einstein Lagrangian is second
order also when expressed in terms of soldering forms. A covariant splitting is
then analysed leading to a first order Lagrangian which is recognized to play a
fundamental role in the theory of conserved quantities. The splitting and
thence the first order Lagrangian depend on a reference spin connection which
is physically interpreted as setting the zero level for conserved quantities. A
complete and detailed treatment of conserved quantities is then presented.Comment: 16 pages, Plain TE
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