When we calculate gravitational waveforms from extreme-mass-ratio inspirals by metric perturbation, it is a common strategy to use the adiabatic approximation. Under that approximation, we first calculate the linear metric perturbation induced by geodesics orbiting a black hole, then we calculate the adiabatic evolution of the parameters of geodesics due to the radiation reaction effect through...

Rice’s “classic” perturbation theory predicts an erroneous limit at grazing for vertically polarized plane wave scatter from an infinite perfectly conducting rough surface; likewise, the attendant result for the specularly reflected mode also fails at grazing. We show where and why in the system of perturbational equations this difficulty occurs. We then reformulate the perturbational approach ...

Solitons are ubiquitous and exist in almost every area from sky to bottom. For solitons to appear, the relevant equation of motion must be nonlinear. In the present study, we deal with the Korteweg-deVries (KdV), Modied Korteweg-de Vries (mKdV) and Regularised LongWave (RLW) equations using Homotopy Perturbation method (HPM). The algorithm makes use of the HPM to determine the initial expansion...

Rotating spiral waves are a form of self-organization observed in spatially extended systems of physical, chemical, and biological nature. In the presence of a small perturbation, the spiral wave's center of rotation and fiducial phase may change over time, i.e., the spiral wave drifts. In linear approximation, the velocity of the drift is proportional to the convolution of the perturbation wit...

High-resolution ensemble simulations (∆x = 1km) are performed with the Met Office Unified Model for the Boscastle (Cornwall, UK) flash-flooding event of 16 August 2004. Forecast uncertainties arising from imperfections in the forecast model are analysed by comparing the simulation results produced by two types of perturbation strategy. Motivated by the meteorology of the event, one type of pert...