On velocities beyond the speed of light cc

From a mathematical point of view velocities can be larger than $c$. Lorentz transformations are easily extended in Minkowski space to discuss velocities beyond the speed of light. Energy and momentum conservation fixes the relation between masses and velocities larger than $c$, and some interesting consequences are drawn. Current data make neutrinos as possible candidates for having speed larger than $c$. Assuming this is true, a well known enigma on the arrival times of the neutrino bursts from the SN1987A supernova can be explained quite naturally. Finally, experimental research is proposed to verify the theory

hp-adaptive celatus enriched discontinuous Galerkin method for second-order elliptic source problems

This paper presents a new way to enrich finite element methods with nonpolynomial functions without adding any function to the finite element space. For this reason, the method is called celatus, which is a Latin word meaning ``hidden from view."" Since no nonpolynomial function is added to the finite element space, many issues with standard enriched methods are avoided, among which there is the worsening of the condition of the linear system. In the present work, we focus on second-order elliptic source problems with reentering corners and show that the new method is more computationally efficient than standard finite element methods when used with hp-adaptivity

An a posteriori error estimator for hp-adaptive continuous Galerkin methods for photonic crystal applications

In this paper we propose and analyse an error estimator suitable for $hp$-adaptive continuous finite element methods for computing the band structure and the isolated modes of 2D photonic crystal (PC) applications. The error estimator that we propose is based on the residual of the discrete problem and we show that it leads to very fast convergence in all considered examples when used with $hp$-adaptive refinement techniques. In order to show the flexibility and robustness of the error estimator we present an extensive collection of numerical experiments inspired by real applications. In particular we are going to consider PCs with point defects, PCs with line defects, bended waveguides and semi-infinite PCs

Multi-hp adaptive discontinuous Galerkin methods for simplified PN approximations of 3D radiative transfer in non-gray media

In this paper we present a multi-hp adaptive discontinuous Galerkin method for 3D simplified approximations of radiative transfer in non-gray media capable of reaching accuracies superior to most of methods in the literature. The simplified models are a set of differential equations derived based on asymptotic expansions for the integro-differential radiative transfer equation. In a non-gray media the optical spectrum is divided into a finite set of bands with constant absorption coefficients and the simplified approximations are solved for each band in the spectrum. At high temperature, boundary layers with different magnitudes occur for each wavelength in the spectrum and developing a numerical solver to accurately capture them is challenging for the conventional finite element methods. Here we propose a class of high-order adaptive discontinuous Galerkin methods using space error estimators. The proposed method is able to solve problems where 3D meshes contain finite elements of different kind with the number of equations and polynomial orders of approximation varying locally on the finite element edges, faces, and interiors. The proposed method has also the potential to perform both isotropic and anisotropic adaptation for each band in the optical spectrum. Several numerical results are presented to illustrate the performance of the proposed method for 3D radiative simulations. The computed results confirm its capability to solve 3D simplified approximations of radiative transfer in non-gray media

An A Posteriori Error Estimator for Hp-Adaptive Discontinuous Galerkin Methods for Elliptic Eigenvalue Problems

In this paper we present a residual-based a posteriori error estimator for hp-adaptive discontinuous Galerkin methods for elliptic eigenvalue problems. In particular, we use as a model problem the Laplace eigenvalue problem on bounded domains in ℝd, d = 2, 3, with homogeneous Dirichlet boundary conditions. Analogous error estimators can be easily obtained for more complicated elliptic eigenvalue problems. We prove the reliability and efficiency of the residual-based error estimator also for non-convex domains and use numerical experiments to show that, under an hp-adaptation strategy driven by the error estimator, exponential convergence can be achieved, even for non-smooth eigenfunctions

Adaptive finite element methods for computing band gaps in photonic crystals

In this paper we propose and analyse adaptive finite element methods for computing the band structure of 2D periodic photonic crystals. The problem can be reduced to the computation of the discrete spectra of each member of a family of periodic Hermitian eigenvalue problems on a unit cell, parametrised by a two-dimensional parameter - the quasimomentum. These eigenvalue problems involve non-coercive elliptic operators with generally discontinuous coefficients and are solved by adaptive finite elements. We propose an error estimator of residual type and show it is reliable and efficient for each eigenvalue problem in the family. In particular we prove that if the error estimator converges to zero then the distance of the computed eigenfunction from the true eigenspace also converges to zero and the computed eigenvalue converges to a true eigenvalue with double the rate. We also prove that if the distance of a computed sequence of approximate eigenfunctions from the true eigenspace approaches zero, then so must the error estimator. The results hold for eigenvalues of any multiplicity. We illustrate the benefits of the resulting adaptive method in practice, both for fully periodic structures and also for the computation of eigenvalues in the band gap of structures with defect, using the supercell method

Solving Elliptic Eigenproblems with Adaptive Multimesh hp-FEM

This paper proposes a novel adaptive higher-order nite element (hp-FEM) method for solving elliptic eigenvalue problems, where n eigenpairs are calculated simultaneously, but on individual higher-order nite element meshes. The meshes are automatically hp-rened independently of each other, with the goal to use an optimal mesh sequence for each eigenfunction. The method and the adaptive algorithm are described in detail. Numerical examples clearly demonstrate the superiority of the novel method over the standard approach where all eigenfunctions are approximated on the same nite element mesh

Will I Get In? Using Predictive Analytics to Develop Student-Facing Tools to Estimate University Admissions Decisions

A sizable number of low-income high school graduates enroll in colleges less selective than their academic qualifications would allow or forgo postsecondary altogether despite being college-ready. One potential cause of this “undermatching” is that some students have limited access to information about their college options. We hypothesize that providing students with more and better information about the relationship between their academic preparation and college options may promote college-going. The purpose of this study was to develop a predictive model of admissions to public 4-year institutions using data from Texas’ statewide longitudinal data system in order to build a student-facing tool that predicts admissions decisions. We sought to include only variables for which students have some control over, namely academic characteristics, but compared the predictive accuracy of this reduced model to more complex models that include demographic variables commonly used in higher education research. We show the reduced model successfully predicts admissions decisions for approximately 85% of applications. The addition of demographic variables, despite showing a statistically significant better fit of the data, do not substantively change the predictive accuracy of the model. We include a demonstration of a data visualization tool built on this predictive model using the open-source R statistical software that can be used by students, parents, and educators. We also discuss causes for both optimism and caution when using predictive modeling to develop student-facing tools

GEANT4 simulation of phase rotation for neutrino factory

We discuss a GEANT4 simulation of the phase rotation system for a neutrino factory. The comparison with the beam transport code PATH shows a good agreement. Preliminary results for the energy disposition in the cryostat of the superconducting 1.8 T solenoid are briefly presented