We discuss a general formula which allows to automatically reproduce experimental data for Majorana neutrino mass models, while keeping the complete set of the remaining model parameters free for ...general scans, as necessary in order to provide reliable predictions for observables outside the neutrino sector. We provide a proof of this master parametrization and show how to apply it for several well-known neutrino mass models from the literature. We also discuss a list of special cases, in which the Yukawa couplings have to fulfill some particular additional conditions.
After showing that the neutrino mass matrix in all Majorana models can be described by a general master formula, we will present a master parametrization for the Yukawa matrices, also valid for all ...Majorana models, that automatically ensures agreement with neutrino oscillation data. The application of the master parametrization will be illustrated in an example model.
After introducing a master formula for the Majorana neutrino mass matrix, we present a master parametrization for the Yukawa matrices automatically in agreement with neutrino oscillation data. This ...parametrization can be used for any model that induces Majorana neutrino masses. The application of the master parametrization is also illustrated in an example model, with special focus on its lepton flavor violating phenomenology.
We present a fully relativistic numerical method for the study of cosmological problems using the Baumgarte-Shapiro-Shibata-Nakamura formalism on a dynamical Friedmann-Lemaitre-Robertson-Walker ...background. This has many potential applications, including the study of the growth of structures beyond the linear regime. We present one such application by reproducing the Lemaitre-Tolman-Bondi solution for the collapse of pressureless matter with arbitrary lapse function. The regular and smooth numerical solution at the center of coordinates proceeds in a natural way by relying on the partially implicit Runge-Kutta algorithm described in Montero and Cordero-Carrion arXiv: 1211.5930 (http://arXiv.org/abs/1211.5930). We generalize the usual radiative outer boundary condition to the case of a dynamical background and show the stability and convergence properties of the method in the study of pure gauge dynamics on a de Sitter background.
The Scheduled Relaxation Jacobi (SRJ) method is an extension of the classical Jacobi iterative method to solve linear systems of equations (Au=b) associated with elliptic problems. It inherits its ...robustness and accelerates its convergence rate computing a set of P relaxation factors that result from a minimization problem. In a typical SRJ scheme, the former set of factors is employed in cycles of M consecutive iterations until a prescribed tolerance is reached. We present the analytic form for the optimal set of relaxation factors for the case in which all of them are strictly different, and find that the resulting algorithm is equivalent to a non-stationary generalized Richardson's method where the matrix of the system of equations is preconditioned multiplying it by D=diag(A). Our method to estimate the weights has the advantage that the explicit computation of the maximum and minimum eigenvalues of the matrix A (or the corresponding iteration matrix of the underlying weighted Jacobi scheme) is replaced by the (much easier) calculation of the maximum and minimum frequencies derived from a von Neumann analysis of the continuous elliptic operator. This set of weights is also the optimal one for the general problem, resulting in the fastest convergence of all possible SRJ schemes for a given grid structure. The amplification factor of the method can be found analytically and allows for the exact estimation of the number of iterations needed to achieve a desired tolerance. We also show that with the set of weights computed for the optimal SRJ scheme for a fixed cycle size it is possible to estimate numerically the optimal value of the parameter ω in the Successive Overrelaxation (SOR) method in some cases. Finally, we demonstrate with practical examples that our method also works very well for Poisson-like problems in which a high-order discretization of the Laplacian operator is employed (e.g., a 9- or 17-points discretization). This is of interest since the former discretizations do not yield consistently ordered A matrices and, hence, the theory of Young cannot be used to predict the optimal value of the SOR parameter. Furthermore, the optimal SRJ schemes deduced here are advantageous over existing SOR implementations for high-order discretizations of the Laplacian operator in as much as they do not need to resort to multi-coloring schemes for their parallel implementation.
We present a study of the fully relativistic spherical collapse in the presence of quintessence using on numerical relativity, following the method proposed by the authors in a previous article Phys. ...Rev. D 91, 024025 (2015). We ascertain the validity of the method by studying the evolution of a spherically symmetric quintessence inhomogeneity on a de Sitter background and we find that it has an impact on the local expansion around the center of coordinates. We then proceed to compare the results of our method to those of the more largely adopted top-hat model. We find that quintessence inhomogeneities do build up under the effect that matter inhomogeneities have on the local space-time, yet remain very small due to the presence of momentum transfer from the over-dense to the background regions. We expect that these might have an even more important role in modified theories of gravitation.
Elliptic partial differential equations (ePDEs) appear in a wide variety of areas of mathematics, physics and engineering. Typically, ePDEs must be solved numerically, which sets an ever growing ...demand for efficient and highly parallel algorithms to tackle their computational solution. The Scheduled Relaxation Jacobi (SRJ) is a promising class of methods, atypical for combining simplicity and efficiency, that has been recently introduced for solving linear Poisson-like ePDEs. The SRJ methodology relies on computing the appropriate parameters of a multilevel approach with the goal of minimizing the number of iterations needed to cut down the residuals below specified tolerances. The efficiency in the reduction of the residual increases with the number of levels employed in the algorithm. Applying the original methodology to compute the algorithm parameters with more than 5 levels notably hinders obtaining optimal SRJ schemes, as the mixed (non-linear) algebraic-differential system of equations from which they result becomes notably stiff. Here we present a new methodology for obtaining the parameters of SRJ schemes that overcomes the limitations of the original algorithm and provide parameters for SRJ schemes with up to 15 levels and resolutions of up to 215 points per dimension, allowing for acceleration factors larger than several hundreds with respect to the Jacobi method for typical resolutions and, in some high resolution cases, close to 1000. Most of the success in finding SRJ optimal schemes with more than 10 levels is based on an analytic reduction of the complexity of the previously mentioned system of equations. Furthermore, we extend the original algorithm to apply it to certain systems of non-linear ePDEs.
•We compute new optimal parameters of the Scheduled Relaxation Jacobi method.•The new parameters are calculated for SRJ schemes with P=6 to P=15 levels.•We reduce the stiffness in the computation of optimal SRJ parameters analytically.•We provide a grid of optimal parameters for different P and numerical resolutions.•We benchmark SRJ methods against other algorithms to solve linear systems.
Tests of General Relativity with GW170817 Allen, G; Angelova, S V; Appert, S ...
Physical review letters,
2019-Jul-03, Letnik:
123, Številka:
1
Journal Article, Web Resource
Recenzirano
Odprti dostop
The recent discovery by Advanced LIGO and Advanced Virgo of a gravitational wave signal from a binary neutron star inspiral has enabled tests of general relativity (GR) with this new type of source. ...This source, for the first time, permits tests of strong-field dynamics of compact binaries in the presence of matter. In this Letter, we place constraints on the dipole radiation and possible deviations from GR in the post-Newtonian coefficients that govern the inspiral regime. Bounds on modified dispersion of gravitational waves are obtained; in combination with information from the observed electromagnetic counterpart we can also constrain effects due to large extra dimensions. Finally, the polarization content of the gravitational wave signal is studied. The results of all tests performed here show good agreement with GR.
Current interferometric gravitational-wave detectors are limited by quantum noise over a wide range of their measurement bandwidth. One method to overcome the quantum limit is the injection of ...squeezed vacuum states of light into the interferometer's dark port. Here, we report on the successful application of this quantum technology to improve the shot noise limited sensitivity of the Advanced Virgo gravitational-wave detector. A sensitivity enhancement of up to 3.2±0.1 dB beyond the shot noise limit is achieved. This nonclassical improvement corresponds to a 5%-8% increase of the binary neutron star horizon. The squeezing injection was fully automated and over the first 5 months of the third joint LIGO-Virgo observation run O3 squeezing was applied for more than 99% of the science time. During this period several gravitational-wave candidates have been recorded.
We present our current best estimate of the plausible observing scenarios for the Advanced LIGO, Advanced Virgo and KAGRA gravitational-wave detectors over the next several years, with the intention ...of providing information to facilitate planning for multi-messenger astronomy with gravitational waves. We estimate the sensitivity of the network to transient gravitational-wave signals for the third (O3), fourth (O4) and fifth observing (O5) runs, including the planned upgrades of the Advanced LIGO and Advanced Virgo detectors. We study the capability of the network to determine the sky location of the source for gravitational-wave signals from the inspiral of binary systems of compact objects, that is binary neutron star, neutron star–black hole, and binary black hole systems. The ability to localize the sources is given as a sky-area probability, luminosity distance, and comoving volume. The median sky localization area (90% credible region) is expected to be a few hundreds of square degrees for all types of binary systems during O3 with the Advanced LIGO and Virgo (HLV) network. The median sky localization area will improve to a few tens of square degrees during O4 with the Advanced LIGO, Virgo, and KAGRA (HLVK) network. During O3, the median localization volume (90% credible region) is expected to be on the order of
10
5
,
10
6
,
10
7
Mpc
3
for binary neutron star, neutron star–black hole, and binary black hole systems, respectively. The localization volume in O4 is expected to be about a factor two smaller than in O3. We predict a detection count of
1
-
1
+
12
(
10
-
10
+
52
) for binary neutron star mergers, of
0
-
0
+
19
(
1
-
1
+
91
) for neutron star–black hole mergers, and
17
-
11
+
22
(
79
-
44
+
89
) for binary black hole mergers in a one-calendar-year observing run of the HLV network during O3 (HLVK network during O4). We evaluate sensitivity and localization expectations for unmodeled signal searches, including the search for intermediate mass black hole binary mergers.
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