No abstract

ABSTRACT:In operational meteorology, forecasting heavy rainfall (HRF) events has been a long-standing challenge in India. This is especially true in certain regions where the physical geography lends itself to the creation of such HRF events. Northeast India (NEI) is one such region within the Asian monsoon zone, which receive very HRF during the pre-monsoon and summer monsoon season and the summer-autumn transition month of October. These events cause flooding, damage crops and bring life to standstill. In the present work, the characteristics of HRF events in NEI are studied. The seasonal and spatial variations of HRF occurrences are analysed using 31 year of daily rainfall data from 15 rainfall stations. Using the daily data obtained from the Indian Meteorological Department, the most favorable locations were found for the stations between 27.5°N and 28.1°N. The most favorable time of occurrence of these events are between 10 June and 5 August. July records the largest number of HRF events followed by June and August. The aggregate of extreme rain events over the region has a significant decreasing trend over the region. Before the monsoon sets in, there is considerable thunderstorm (TS) activity in this region in the month of April and May that are also the cause of HRF events. While many of these HRF events occur associated with the pre-monsoon Nor'westers (tornadoes), some severe TSs may occur during the monsoon season. So, we present a climatology of severe TS days. Also we present the annual and seasonal variation of convective available potential energy (CAPE) and convective inhibition energy (CINE) at Guwahati as the index of the thermal instability. Between 1973 and 2001, CAPE shows a decreasing trend whereas CINE shows an increasing trend which seems reasonable due to the HRF events' decreasing trend.

The N = 2 supersymmetric KdV equation of Inami and Kanno is bilinearized employing the Hirota method and the existence of N soliton solutions is demonstrated. The exact form of the solutions are explicitly obtained and an interesting symmetry of the equations of motion is observed.

Two different types of N = 1 modified KdV equations are shown to possess N soliton solutions. The soliton solutions of these equations are obtained by casting the equations in the bilinear forms using the supersymmetric extension of the Hirota method. The distinguishing features of the soliton solutions of N = 1 mKdV and N = 1 mKdV B equations are discussed.

We present an axially symmetric, asymptotically flat empty space solution of the Einstein field equations containing a naked singularity. The spacetime is regular everywhere except on the symmetry axis where it possess a true curvature singularity. The spacetime is of type D in the Petrov classification scheme and is locally isometric to the metrics of case IV in the Kinnersley classification of type D vacuum metrics. Additionally, the spacetime also shows the evolution of closed timelike curves (CTCs) from an initial hypersurface free from CTCs.