Intermediate behavior of Kerr tails

The numerical investigation of wave propagation in the asymptotic domain of Kerr spacetime has only recently been possible thanks to the construction of suitable hyperboloidal coordinates. The asymptotics revealed an apparent puzzle in the decay rates of scalar fields: the late-time rates seemed to depend on whether finite distance observers are in the strong field domain or far away from the rotating black hole, an apparent phenomenon dubbed "splitting". We discuss far-field "splitting" in the full field and near-horizon "splitting" in certain projected modes using horizon-penetrating, hyperboloidal coordinates. For either case we propose an explanation to the cause of the "splitting" behavior, and we determine uniquely decay rates that previous studies found to be ambiguous or immeasurable. The far-field "splitting" is explained by competition between projected modes. The near-horizon "splitting" is due to excitation of lower multipole modes that back excite the multipole mode for which "splitting" is observed. In both cases "splitting" is an intermediate effect, such that asymptotically in time strong field rates are valid at all finite distances. At any finite time, however, there are three domains with different decay rates whose boundaries move outwards during evolution. We then propose a formula for the decay rate of tails that takes into account the inter--mode excitation effect that we study.Comment: 16 page

Testing weighted splitting schemes on a one-column transport-chemistry model

In many transport-chemistry models, a huge system of ODE’s of the advection-diffusion-reaction type has to be integrated in time. Typically, this is done with the help of operator splitting. Rosenbrock schemes combined with approximate matrix factorization (ROS-AMF) are an alternative to operator splitting which does not suffer from splitting errors. However, implementation of ROS-AMF schemes often requires serious changes in the code. In this paper we test another classical second order splitting introduced by Strang in 1963, which, unlike the popular Strang splitting, seemed to be forgotten and rediscovered recently (partially due to its intrinsic parallellism). This splitting, called symmetrically weighted sequential (SWS) splitting, is simple and straightforward to apply, independent of the order of the operators and has an operator-level parallelism. In the experiments, the SWS scheme compares favorably to the Strang splitting, but is less accurate than ROS-AMF

Solving Vertical Transport and Chemistry in Air Pollution Models.

For the time integration of stiff transport-chemistry problems from air pollution modelling, standard ODE solvers are not feasible due to the large number of species and the 3D nature. The popular alternative, standard operator splitting, introduces artificial transients for short-lived species. This complicates the chemistry solution, easily causing large errors for such species. In the framework of an operational global air pollution model, we focus on the problem formed by chemistry and vertical transport, which is based on diffusion, cloud-related vertical winds, and wet deposition. Its specific nature leads to full Jacobian matrices, ruling out standard implicit integration. We compare Strang operator splitting with two alternatives: source splitting and an (unsplit) Rosenbrock method with approximate matrix factorization, all having equal computational cost. The comparison is performed with real data. All methods are applied with half-hour time steps, and give good accuracies. Rosenbrock is the most accurate, and source splitting is more accurate than Strang splitting. Splitting errors concentrate in short-lived species sensitive to solar radiation and species with strong emissions and depositions

CLASSICAL SPLITTING OF FUNDAMENTAL STRINGS

We find exact solutions of the string equations of motion and constraints describing the {\em classical}\ splitting of a string into two. We show that for the same Cauchy data, the strings that split have {\bf smaller} action than the string without splitting. This phenomenon is already present in flat space-time. The mass, energy and momentum carried out by the strings are computed. We show that the splitting solution describes a natural decay process of one string of mass $M$ into two strings with a smaller total mass and some kinetic energy. The standard non-splitting solution is contained as a particular case. We also describe the splitting of a closed string in the background of a singular gravitational plane wave, and show how the presence of the strong gravitational field increases (and amplifies by an overall factor) the negative difference between the action of the splitting and non-splitting solutions.Comment: 27 pages, revtex

Finite-Frequency SKS Splitting: Measurement and Sensitivity Kernels

Splitting of SKS waves caused by anisotropy may be analyzed by measuring the splitting intensity, i.e., the amplitude of the transverse signal relative to the radial signal in the SKS time window. This quantity is simply related to structural parameters. Extending the widely used cross-correlation method for measuring travel-time anomalies to anisotropic problems, we propose to measure the SKS-splitting intensity by a robust cross-correlation method that can be automated to build large high-quality datasets. For weak anisotropy, the SKS-splitting intensity is retrieved by cross-correlating the radial signal with the sum of the radial and transverse signals. The cross-correlation method is validated based upon a set of Californian seismograms. We investigate the sensitivity of the SKS-splitting intensity to general anisotropy in the mantle based upon a numerical technique (the adjoint spectral-element method) considering the full physics of wave propagation. The computations reveal a sensitivity remarkably focused on a small number of elastic parameters and on a small region of the upper mantle. These fundamental properties and the practical advantages of the measurement make the cross-correlation SKS-splitting intensity particularly well adapted for finite-frequency imaging of upper-mantle anisotropy

Time bucket size and lot-splitting approach

We address the problem of lot splitting for various time bucket lengths in MRP systems. Two approaches for lot splitting can be applied: either use the same (equal) or a variable number of subbatches. Equal subbatching strategies have logistical and computational advantages. Literature states that variable batching strategies are only marginal better. However, these results do not take into account the sensitivity for changes in time bucket length. Managers have reduced time bucket lengths in planning systems. We examine the sensitivity of lot splitting for these changes. Our study reveals that it is not cost-effective to disregard time bucket length when deciding on the number of subbatches. Using the same number of subbatches per time bucket for all products results in substantial cost-differences, where the magnitude is affected by the discontinuity of the total cost curve. For a given time bucket length, a cost difference with a variable number of subbatches per operation of only 2.1% can be obtained if an appropriate, equal number of subbatches for each product can be found. Other equal subbatching strategies show much larger cost differences on average, ranging from 4-11%. In order to obtain these results, a new variable subbatch heuristic has been designed.

Aharonov-Bohm Exciton Absorption Splitting in Chiral Specific Single-Walled Carbon Nanotubes in Magnetic Fields of up to 78 T

The Ajiki-Ando (A-A) splitting of single-walled carbon nanotubes(SWNT) originating from the Aharanov-Bohm effect was observed in chiral specific SWNTs by the magneto-absorption measurements conducted at magnetic fields of up to 78 T. The absorption spectra from each chirality showed clear A-A splitting of the $E_{11}$ optical excitonic transitions. The parameters of both the dark-bright exciton energy splitting and the rate of A-A splitting in a magnetic field were determined for the first time from the well-resolved absorption spectra.Comment: 5 pages, 3 figure

Splitting of Andreev levels in a Josephson junction by spin-orbit coupling

We consider the effect of spin-orbit coupling on the energy levels of a single-channel Josephson junction below the superconducting gap. We investigate quantitatively the level splitting arising from the combined effect of spin-orbit coupling and the time-reversal symmetry breaking by the phase difference between the superconductors. Using the scattering matrix approach we establish a simple connection between the quantum mechanical time delay matrix and the effective Hamiltonian for the level splitting. As an application we calculate the distribution of level splittings for an ensemble of chaotic Josephson junctions. The distribution falls off as a power law for large splittings, unlike the exponentially decaying splitting distribution given by the Wigner surmise -- which applies for normal chaotic quantum dots with spin-orbit coupling in the case that the time-reversal symmetry breaking is due to a magnetic field.Comment: 6 pages, 3 figure