Search results for "conservation law"
showing 10 items of 86 documents
A Revised Experimental Upper Limit on the Electric Dipole Moment of the Neutron
2015
We present for the first time a detailed and comprehensive analysis of the experimental results that set the current world sensitivity limit on the magnitude of the electric dipole moment (EDM) of the neutron. We have extended and enhanced our earlier analysis to include recent developments in the understanding of the effects of gravity in depolarizing ultracold neutrons (UCN); an improved calculation of the spectrum of the neutrons; and conservative estimates of other possible systematic errors, which are also shown to be consistent with more recent measurements undertaken with the apparatus. We obtain a net result of $d_\mathrm{n} = -0.21 \pm 1.82 \times10^{-26}$ $e$cm, which may be inter…
On the implementation of weno schemes for a class of polydisperse sedimentation models
2011
The sedimentation of a polydisperse suspension of small rigid spheres of the same density, but which belong to a finite number of species (size classes), can be described by a spatially one-dimensional system of first-order, nonlinear, strongly coupled conservation laws. The unknowns are the volume fractions (concentrations) of each species as functions of depth and time. Typical solutions, e.g. for batch settling in a column, include discontinuities (kinematic shocks) separating areas of different composition. The accurate numerical approximation of these solutions is a challenge since closed-form eigenvalues and eigenvectors of the flux Jacobian are usually not available, and the characte…
Capturing Shock Reflections: An Improved Flux Formula
1996
Godunov type schemes, based on exact or approximate solutions to the Riemann problem, have proven to be an excellent tool to compute approximate solutions to hyperbolic systems of conservation laws. However, there are many instances in which a particular scheme produces inappropriate results. In this paper we consider several situations in which Roe's scheme gives incorrect results (or blows up all together) and we propose an alternative flux formula that produces numerical approximations in which the pathological behavior is either eliminated or reduced to computationally acceptable levels.
Power ENO methods: a fifth-order accurate Weighted Power ENO method
2004
In this paper we introduce a new class of ENO reconstruction procedures, the Power ENO methods, to design high-order accurate shock capturing methods for hyperbolic conservation laws, based on an extended class of limiters, improving the behavior near discontinuities with respect to the classical ENO methods. Power ENO methods are defined as a correction of classical ENO methods [J. Comput. Phys. 71 (1987) 231], by applying the new limiters on second-order differences or higher. The new class of limiters includes as a particular case the minmod limiter and the harmonic limiter used for the design of the PHM methods [see SIAM J. Sci. Comput. 15 (1994) 892]. The main features of these new ENO…
A Flux-Split Algorithm Applied to Relativistic Flows
1998
The equations of RFD can be written as a hyperbolic system of conservation laws by choosing an appropriate vector of unknowns. We give an explicit formulation of the full spectral decomposition of the Jacobian matrices associated with the fluxes in each spatial direction, which is the essential ingredient of the techniques we propose in this paper. These techniques are based on the recently derived flux formula of Marquina, a new way to compute the numerical flux at a cell interface which leads to a conservative, upwind numerical scheme. Using the spectral decompositions in a fundamental way, we construct high order versions of the basic first-order scheme described by R. Donat and A. Marqu…
Weighted ENO interpolation and applications
2004
Abstract Data-dependent interpolatory techniques such as essentially non-oscillatory (ENO) technique [J. Comput. Phys. 71 (1987) 231] have long been used as a reconstruction process in multiresolution schemes. In this work we analyze the weighted ENO (WENO) technique introduced by Liu et al. in the context of conservation laws [J. Comput. Phys. 115 (1994) 200] and improved by Jiang and Shu [J. Comput. Phys. 126 (1996) 202], and apply it to the compression of images, using multiresolution techniques.
Hyperbolic character of the angular moment equations of radiative transfer and numerical methods
2000
We study the mathematical character of the angular moment equations of radiative transfer in spherical symmetry and conclude that the system is hyperbolic for general forms of the closure relation found in the literature. Hyperbolicity and causality preservation lead to mathematical conditions allowing to establish a useful characterization of the closure relations. We apply numerical methods specifically designed to solve hyperbolic systems of conservation laws (the so-called Godunov-type methods), to calculate numerical solutions of the radiation transport equations in a static background. The feasibility of the method in any kind of regime, from diffusion to free-streaming, is demonstrat…
A fresh look into the interacting dark matter scenario
2018
The elastic scattering between dark matter particles and radiation represents an attractive possibility to solve a number of discrepancies between observations and standard cold dark matter predictions, as the induced collisional damping would imply a suppression of small-scale structures. We consider this scenario and confront it with measurements of the ionization history of the Universe at several redshifts and with recent estimates of the counts of Milky Way satellite galaxies. We derive a conservative upper bound on the dark matter-photon elastic scattering cross section of $\sigma_{\gamma \rm{DM}} < 8 \times 10^{-10} \, \sigma_T \, \left(m_{\rm DM}/{\rm GeV}\right)$ at $95\%$~CL, abou…
Testing WWγ vertex in radiative muon decay
2019
Large numbers of muons will be produced at facilities developed to probe the lepton-flavor-violating process μ→eγ. We show that by constructing a suitable asymmetry, radiative muon decay μ→eγνμν̄e can also be used to test the WWγ vertex at such facilities. The process has two missing neutrinos in the final state, and upon integrating their momenta the partial differential decay rate shows no radiation-amplitude zero. However, we establish that an easily separable part of the normalized differential decay rate that is odd under the exchange of photon and electron energies does have a zero in the case of the standard model (SM). This new type of zero has hitherto not been studied in the liter…
Bound-state dark matter and Dirac neutrino mass
2018
We propose a simple theory for the idea that cosmological dark matter (DM) may be present today mainly in the form of stable neutral hadronic thermal relics. In our model neutrino masses arise radiatively from the exchange of colored DM constituents, giving a common origin for both dark matter and neutrino mass. The exact conservation of $B-L$ symmetry ensures dark matter stability and the Dirac nature of neutrinos. The theory can be falsified by dark matter nuclear recoil direct detection experiments, leading also to possible signals at a next generation hadron collider.