168 research outputs found
A first-order purely frame-formulation of General Relativity
In the gauge natural bundle framework a new space is introduced and a
first-order purely frame-formulation of General Relativity is obtained.Comment: 9 Pages, Submitted to Classical and Quantum Gravit
Critical exact solutions for self-gravitating Dirac fields
We consider the Einstein-Dirac field equations describing a self-gravitating
massive neutrino, looking for axially-symmetric exact solutions; in the search
of general solutions, we find some that are specific and which have critical
features, such as the fact that the space-time curvature turns out to be flat
and the spinor field gives rise to a vanishing bi-linear scalar
with non-vanishing bi-linear pseudo-scalar
: because in quantum field theory general
computational methods are built on plane-wave solutions, for which bi-linear
pseudo-scalar vanishes while the bi-linear scalar does not vanish, then the
solutions we found cannot be treated with the usual machinery of quantum field
theory. This means that for the Einstein-Dirac system there exist admissible
solutions which nevertheless cannot be quantized with the common prescriptions;
we regard this situation as yet another issue of tension between Einstein
gravity and quantum principles. Possible ways to quench this tension can be
seen either in enlarging the validity of quantum field theory or by restricting
the space of the solutions of the Einstein-Dirac system of field equations.Comment: 12 page
Exact solutions for Weyl fermions with gravity
We consider the single-handed spinor field in interaction with its own
gravitational field described by the set of field equations given by Weyl field
equations written in terms of derivatives that are covariant with respect to
the gravitational connection plus Einstein field equations soured with the
energy tensor of the spinor: for the Weyl spinor and the ensuing spacetime of
Weyl-Lewis-Papapetrou structure, we will find all exact solutions. The obtained
solution for the metric tensor is that of a PP-wave spacetime while the spinor
field is a flag-dipole.Comment: 12 page
Updated F(T) gravity constraints from high redshift cosmography
In the last dozen years a wide and variegated mass of observational data
revealed that the universe is now expanding at an accelerated rate. In the
absence of a well-based theory to interpret the observations, cosmography
provides information about the evolution of the Universe from measured
distances, only assuming that the geometry of the can be described by the
Friedmann-Lemaitre-Robertson -Walker metric. We perform a high-redshift
analysis allows us to put constraints on the cosmographic parameters up to the
5fth order, thus inducing indirect constraints on any gravity theory. Here we
are interested in the so called teleparallel gravity theory, f(T). Actually we
use the analytical expressions of the present day values of f(T) and its
derivatives as functions of the cosmographic parameters to map the cosmography
region of confidences into confidence ranges for f(T) and its derivative.
Moreover, we show how these can be used to test some teleparallel gravity
models without solving the dynamical equations. Our analysis is based on the
Union2 Type Ia Supernovae (SNIa) data set, a set of 28 measurements of the
Hubble parameter, the Hubble diagram constructed from some Gamma Ray Bursts
(GRB) luminosity distance indicators, and gaussian priors on the distance from
the Baryon Acoustic Oscillations (BAO), and the Hubble constant h. To perform
our statistical analysis and to explore the probability distributions of the
cosmographic parameters we use the Markov Chain Monte Carlo Method (MCMC).Comment: International Journal of Modern Physics D, 20 pages, 5 figure
Modeling and Estimation of Thermal Flows Based on Transport and Balance Equations
Heat transfer in counterflow heat exchangers is modeled by using transport and balance equations with the temperatures of cold fluid, hot fluid, and metal pipe as state variables distributed along the entire pipe length. Using such models, boundary value problems can be solved to estimate the temperatures over all the length by means of measurements taken only at the boundaries. Conditions for the stability of the estimation error given by the difference between the temperatures and their estimates are established by using a Lyapunov approach. Toward this end, a method to construct nonlinear Lyapunov functionals is addressed by relying on a polynomial diagonal structure. This stability analysis is extended in case of the presence of bounded modeling uncertainty. The theoretical findings are illustrated with numerical results, which show the effectiveness of the proposed approach
Effect of graded interphase on the coefficient of thermal expansion for composites with spherical inclusions
Financial support of this research by the Royal Society of Edinburgh (UK) and the Italian Academy of Science under the International Exchanges Bilateral Programme is gratefully acknowledged.Peer reviewedPostprin
Analytical Solutions of One-Dimensional Contaminant Transport in Soils with Source Production-Decay
An analytical solution in closed form of the advection-dispersion equation in
one-dimensional contaminated soils is proposed in this paper. This is valid for non-conservative
solutes with first order reaction, linear equilibrium sorption, and a time-dependent Robin boundary
condition. The Robin boundary condition is expressed as a combined production-decay function
representing a realistic description of the source release phenomena in time. The proposed
model is particularly useful to describe sources as the contaminant release due to the failure in
underground tanks or pipelines, Non Aqueous Phase Liquid pools, or radioactive decay series.
The developed analytical model tends towards the known analytical solutions for particular values
of the rate constants
Integrability of Dirac equations in static spherical space-times
We consider the Dirac equations in static spherically-symmetric space-times,
and we present a type of spinor field whose structure allows the separation of
elevation angle and radial coordinate in very general situations. We
demonstrate that after such a separation of variables the Dirac equations
reduce to two equations that can always be integrated, at least in principle.
To prove that ours is a fully-working method, we find an explicit exact
solution in the special case of the de Sitter universe.Comment: 10 page
Hashinâs bounds for elastic properties of particle-reinforced composites with graded interphase
Financial support of this research by the Royal Society of Edinburgh and the Italian Academy of Sciences International Exchange Bilateral Programme grant is gratefully acknowledged.Peer reviewedPostprin
A Simulation of One Dimensional Contaminant Transport
In this note we present some simulations and some analytical solutions, in closed form, of the advection dispersion equation in one-dimensional domain. These solutions are obtained for not-conservative solutes by considering time-dependent, third type (Robin) boundary condition for first order reaction and linear equilibrium absorption. The Robin boundary condition models a combined production-decay function. The model is useful to describe sources as the contaminant release due to the failure of an underground pipelines or radioactive decay series. The developed analytical model gives rise to analytical solutions not present in the literature. Further, we remark that, for particular values of the rate constants involved in the model, our results furnish values which are in agreement with results present in the literature
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