Search results for "conservation law"
showing 10 items of 86 documents
Elementary Newtonian Mechanics
2010
This chapter deals with the kinematics and the dynamics of a finite number of mass points that are subject to internal, and possibly external, forces, but whose motions are not further constrained by additional conditions on the coordinates. Constraints such as requiring some mass points to follow given curves in space, to keep their relative distance fixed, or the like, are introduced in Chap. 2. Unconstrained mechanical systems can be studied directly by means of Newton’s equations and do not require the introduction of new, generalized coordinates that incorporate the constraints and are dynamically independent. This is what is meant by “elementary” in the heading of this chapter — thoug…
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…
Historischer Überblick zur mathematischen Theorie von Unstetigkeitswellen seit Riemann und Christoffel
1981
We give a brief historical account of the development of the mathematical theory of propagation of discontinuities in gases, fluids or elastic materials. The theory was initiated by Riemann who investigated the propagation of shocks in one-dimensional isentropic gas flow. Riemann’s results were used by Christoffel to treat, more generally, the propagation of (first order) discontinuity surfaces in three-dimensional flows of perfect fluids. Subsequently Christoffel applied his general theory to first order waves in certain elastic materials. Independently of Riemann and Christoffel significant contributions were made by Hugoniot. The theory was completed in Hadamard’s celebrated monograph [3…
Applications of Harten’s Framework for Multiresolution: From Conservation Laws to Image Compression
2002
We briefly review Harten’s framework for multiresolution decompositions and describe two situations in which two different instances of the general framework have been used with success.
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…
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…
Multiresolution-based adaptive schemes for Hyperbolic Conservation Laws
2006
Starting in the early nineties, wavelet and wavelet-like techniques have been successfully used to design adaptive schemes for the numerical solution of certain types of PDE. In this paper we review two representative examples of the development of such techniques for Hyperbolic Conservation Laws.
Adaptive mesh reconstruction for hyperbolic conservation laws with total variation bound
2012
We consider 3-point numerical schemes, that resolve scalar conservation laws, that are oscillatory either to their dispersive or anti-diffusive nature. The spatial discretization is performed over non-uniform adaptively redefined meshes. We provide a model for studying the evolution of the extremes of the oscillations. We prove that proper mesh reconstruction is able to control the oscillations; we provide bounds for the Total Variation (TV) of the numerical solution. We, moreover, prove under more strict assumptions that the increase of the TV, due to the oscillatory behavior of the numerical schemes, decreases with time; hence proving that the overall scheme is TV Increase-Decreasing (TVI…
Spectral WENO schemes with Adaptive Mesh Refinement for models of polydisperse sedimentation
2012
The sedimentation of a polydisperse suspension with particles belonging to N size classes (species) can be described by a system of N nonlinear, strongly coupled scalar first-order conservation laws. Its solutions usually exhibit kinematic shocks separating areas of different composition. Based on the so-called secular equation [J. Anderson, Lin. Alg. Appl. 246, 49–70 (1996)], which provides access to the spectral decomposition of the Jacobian of the flux vector for this class of models, Burger et al. [J. Comput. Phys. 230, 2322–2344 (2011)] proposed a spectral weighted essentially non-oscillatory (WENO) scheme for the numerical solution of the model. It is demonstrated that the efficiency …
Partial self-consistency and analyticity in many-body perturbation theory: Particle number conservation and a generalized sum rule
2016
We consider a general class of approximations which guarantees the conservation of particle number in many-body perturbation theory. To do this we extend the concept of $\Phi$-derivability for the self-energy $\Sigma$ to a larger class of diagrammatic terms in which only some of the Green's function lines contain the fully dressed Green's function $G$. We call the corresponding approximations for $\Sigma$ partially $\Phi$-derivable. A special subclass of such approximations, which are gauge-invariant, is obtained by dressing loops in the diagrammatic expansion of $\Phi$ consistently with $G$. These approximations are number conserving but do not have to fulfill other conservation laws, such…