In the context of a ghost free f(R,G) model, we present a non-singular cosmological scenario in which the universe initially contracts through an ekpyrotic phase having a bouncing like behaviour, and ...following the bounce, it smoothly transits to a matter or radiation like deceleration era which is further smoothly connected to the dark energy era at present epoch. The ghost free character of the model is ensured by the presence of a Lagrange multiplier, and we consider the Gauss–Bonnet (GB) coupling function in such a way that it gets compatible with the event GW170817. Using suitable reconstruction technique, we obtain the non-trivial scalar field potential as well as the GB coupling function. Such scalar potential and GB coupling function source a smooth unified scenario from an ekpyrotic bounce to the dark energy era with an intermediate deceleration era. The occurrence of ekpyrotic contraction phase justifies the resolution of the anisotropic problem (also known as BKL instability) in the background evolution. Consequently we determine the background Hubble parameter and the corresponding effective equation of state parameter, and discussed several qualitative features of the model. The Hubble radius shows an asymmetric behaviour around the bounce, in particular, the evolution of the Hubble radius leads to the generation era of the primordial perturbation modes far before the bounce in the deep sub-Hubble regime. Accordingly we perform the scalar and tensor perturbation evolution in the present context, and as a result, the scalar power spectrum at large scale modes is found to be problematic. Thus an extended scenario is proposed where we consider a pre-ekpyrotic phase having the equation of state parameter is less than unity, and re-examine the scalar and tensor power spectra, on large scales that cross the Hubble radius during the pre-ekpyrotic stage. In this regard, the GB coupling function shows considerable effects in reducing the tensor to scalar ratio compared to the case where the GB coupling is absent. Furthermore the dark energy epoch is consistent with the Planck+SNe+BAO data.
Valuable information about the local environment of the aluminum nucleus can be obtained through (27)Al Nuclear Magnetic Resonance (NMR) parameters like the isotropic chemical shift, scalar and ...quadrupolar coupling constants, and relaxation rate. With nearly 250 scientific articles per year dealing with (27)Al NMR spectroscopy, this analytical tool has become popular because of the recent progress that has made the acquisition and interpretation of the NMR data much easier. The application of (27)Al NMR techniques to various classes of compounds, either in solution or solid-state, has been shown to be extremely informative concerning local structure and chemistry of aluminum in its various environments. The development of experimental methodologies combined with theoretical approaches and modeling has contributed to major advances in spectroscopic characterization especially in materials sciences where long-range periodicity and classical local NMR probes are lacking. In this review we will present an overview of results obtained by (27)Al NMR as well as the most relevant methodological developments over the last 25years, concerning particularly on progress in the application of liquid- and solid-state (27)Al NMR to the study of aluminum-based materials such as aluminum polyoxoanions, zeolites, aluminophosphates, and metal-organic-frameworks.
Abstract
We investigate a form of
f
(
R
)
=
R
1
+
δ
/
R
c
δ
and study the viability of the model for inflation in the Jordan and the Einstein frames. We have extended this form to
f
(
R
)
=
R
+
R
1
+
...δ
/
R
c
δ
in an attempt to solve the problems of the former model. This model is further analyzed by using the power spectrum indices of inflation and the reheating temperature. During the inflationary evolution, the model predicts a value of the
δ
parameter very close to one (
δ
= 0.98), while the reheating temperature
T
re
∼
10
16
GeV at
δ
= 0.98 is consistent with the standard approach to inflation and observations. We calculate the slow roll parameters for the minimally coupled scalar field within the framework of our models. It is found that the values of the scalar spectral index and tensor-to-scalar ratio are very close to the recent observational data, including those released by Planck. Further, we find the scalar spectral index and the tensor-to-scalar ratio are exactly the same in the first model because the Jordan and the Einstein frames are conformally equivalent. We also attempt to provide a constraint through the non-Gaussianity parameter.
We study the long time behavior of an advection–diffusion equation with a random shear flow which depends on a stationary Ornstein–Uhlenbeck (OU) process in parallel-plate channels ...enforcing the no-flux boundary conditions. We derive a closed form formula for the long time asymptotics of the arbitrary N-point correlator using the ground state eigenvalue perturbation approach proposed in Bronski and McLaughlin (1997). In turn, appealing to the conclusion of the Hausdorff moment problem (Shohat and Tamarkin, 1943), we discover a diffusion equation with a random drift and deterministic enhanced diffusion possessing the exact same probability density function at long times. The strategy we presented is not only restricted to the parallel-plate channel domain. The same methods can derive effective equations for a straight channel with uniform arbitrary cross-section. Such equations enjoy many ergodic properties which immediately translate to ergodicity results for the original problem. In particular, we establish that the first two Aris moments using a single realization of the random field can be used to explicitly construct all ensemble averaged moments. Also, the first two ensemble averaged moments explicitly predict any long time centered Aris moment. Our formulae quantitatively depict the dependence of the deterministic effective diffusion on the interaction between spatial structure of flow and random temporal fluctuation. Further, this approximation provides many identities regarding the stationary OU process dependent time integral. We derive explicit formulae for the decaying passive scalar’s long time limiting probability density function (PDF) for different types of initial conditions (e.g. deterministic and random).
•A diffusing passive scalar advected by a random shear flow with finite correlation is studied.•Ground state perturbation theory is used to compute the long time N-point correlator.•Finite time flow correlation effects are assessed for Ornstein–Uhlenbeck processes.•Passive Scalar probability density function with no-flux walls is calculated analytically.•Establish ergodicity like identity yielding deterministic effective diffusivity.
Dynamical boson stars Liebling, Steven L.; Palenzuela, Carlos
Living reviews in relativity,
02/2023, Volume:
26, Issue:
1
Journal Article
Peer reviewed
Open access
The idea of stable, localized bundles of energy has strong appeal as a model for particles. In the 1950s, John Wheeler envisioned such bundles as smooth configurations of electromagnetic energy that ...he called
geons
, but none were found. Instead, particle-like solutions were found in the late 1960s with the addition of a scalar field, and these were given the name
boson stars
. Since then, boson stars find use in a wide variety of models as sources of dark matter, as black hole mimickers, in simple models of binary systems, and as a tool in finding black holes in higher dimensions with only a single Killing vector. We discuss important varieties of boson stars, their dynamic properties, and some of their uses, concentrating on recent efforts.
Branch Prediction Attack on Blinded Scalar Multiplication Bhattacharya, Sarani; Maurice, Clementine; Bhasin, Shivam ...
I.E.E.E. transactions on computers/IEEE transactions on computers,
2020-May-1, 2020-5-1, 2020-05-01, Volume:
69, Issue:
5
Journal Article
Peer reviewed
Open access
In recent years, performance counters have been used as a side channel source to monitor branch mispredictions, in order to attack cryptographic algorithms. However, the literature considers blinding ...techniques as effective countermeasures against such attacks. In this article, we present the first template attack on the branch predictor. We target blinded scalar multiplications with a side-channel attack that uses branch misprediction traces. Since an accurate model of the branch predictor is a crucial element of our attack, we first reverse-engineer the branch predictor. Our attack proceeds with a first online acquisition step, followed by an offline template attack with a template building phase and a template matching phase. During the template matching phase, we use a strategy we call Deduce & Remove , to first infer the candidate values from templates based on a model of the branch predictor, and subsequently eliminate erroneous observations. This last step uses the properties of the target blinding technique to remove wrong guesses and thus naturally provides error correction in key retrieval. In the later part of this article, we demonstrate a template attack on Curve1174 where the double-and-add always algorithm implementation is free from conditional branching on the secret scalar. In that case, we target the data-dependent branching based on the modular reduction operations of long integer multiplications. Such implementations still exist in open source software and can be vulnerable, even if top level safeguards like blinding are used. We provide experimental results on scalar splitting, scalar randomization, and point blinding to show that the secret scalar can be correctly recovered with high confidence. Finally, we conclude with recommendations on countermeasures to thwart such attacks.
In this paper a numerical procedure to simulate low diffusivity scalar turbulence is presented. The method consists of using a grid for the advected scalar with a higher spatial resolution than that ...of the momentum. The latter usually requires a less refined mesh and integrating both fields on a single grid tailored to the most demanding variable produces an unnecessary computational overhead. A multiple resolution approach is used also in the time integration in order to maintain the stability of the scalars on the finer grid. The method is the more advantageous the less diffusive the scalar is with respect to momentum, therefore it is particularly well suited for large Prandtl or Schmidt number flows. However, even in the case of equal diffusivities the present procedure gives CPU time and memory occupation savings, due to the increased gradients and more intermittent behaviour of the scalars when compared to momentum.
On the basis of the general relativistic statistical and kinetic theory, a consistent closed cosmological model is formulated. It is based on a statistical system of scalar-charged fermions ...interacting by means of classical and phantom scalar fields. Based on the study of the microscopic dynamics of scalar-charged particles, within the framework of the Lagrangian an Hamiltonian formalisms, a function of the dynamical mass of scalar-charged particles is constructed and it is shown that the nonnegativity condition for this function has to be removed for the consistency of the theory. On the basis of the Lagrangian formalism, equations of gravitational and scalar fields with singular sources are formulated and microscopic conservation laws are obtained. Within the framework of the general relativistic kinetic theory, macroscopic equations of gravitational and scalar fields are formulated and macroscopic conservation laws are obtained. The full correspondence of these equations to microscopic equations with singular sources is demonstrated. On the basis of the obtained equations, a cosmological model for a degenerate system of scalar-charged fermions is formulated. An exact solution of the constitutive equations for a degenerate scalar-charged plasma in the cosmological model is obtained, which allows significantly simplifying the original system of equations. On the basis of the obtained solution of the constitutive equations, two fundamentally different cosmological models are formulated, one of which has two types of single-scalar-charged fermions and the other has one kind of fermions charged with two charges of various nature. A qualitative analysis of the obtained 6-dimensional dynamical system for a two-component model is carried out. It is shown that in such models, acceleration deceleration modes become possible at the late stages of the evolution of the Universe.
We present the library Collier for the numerical evaluation of one-loop scalar and tensor integrals in perturbative relativistic quantum field theories. The code provides numerical results for ...arbitrary tensor and scalar integrals for scattering processes in general quantum field theories. For tensor integrals either the coefficients in a covariant decomposition or the tensor components themselves are provided. Collier supports complex masses, which are needed in calculations involving unstable particles. Ultraviolet and infrared singularities are treated in dimensional regularization. For soft and collinear singularities mass regularization is available as an alternative.
Program title:Collier
Program Files doi:http://dx.doi.org/10.17632/dmdn2ph3x2.1
Licensing provisions: GNU GPL version 3
Programming language: Fortran95
Nature of problem: Evaluation of general one-loop multi-leg scalar and tensor integrals occurring in the calculation of one-loop corrections to scattering amplitudes in relativistic quantum field theories.
Solution method: Scalar integrals are evaluated using explicit analytical expressions. Tensor integrals are numerically reduced to scalar integrals via different methods. Depending on the specific kinematical variables, an appropriate method is automatically chosen to optimize the resulting numerical accuracy.
Restrictions: real momenta
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