A modal impedance-angle formalism: Rigorous proofs for optical fiber mode counting and bracketing

In a companion paper, a complex-power-flow variational scheme is applied to analyze mode propagation along open circularly cylindrical graded-index waveguides. It leads to a characteristic equation in terms of impedances rather than fields. The resulting impedance-angle formalism provides the basis for the full-wave generalization for optical fibers of the mode-counting scheme previously developed for a scalar wave propagation problem. The complex-power-flow variational scheme for bent waveguides is based on energy considerations. Hence, in its derivation, it is natural to consider a waveguide section (a volume) rather than a cross section (a surface). In the proof of the mode-counting and mode-bracketing theorems, the key issue is to show that the characteristic roots and the roots of the so-called separation function alternate. For general circularly cylindrical open waveguides, the required proofs are intricate. However, the special limiting cases in which the optical fiber is surrounded by electrically or magnetically perfectly conducting walls are tractable. To account for the general case, it appears to be necessary to regard a class of optical waveguide problems with a continuous transition from perfect electric conductor to perfect magnetic conductor boundary conditions via the situation pertaining to the actual exterior medium. Thus, a half-strip is constructed on which the so-called characteristic and separation graphs are seen to alternate. As spin-off, such a "sweep" might prove useful in the design of a fiber cladding

Succinct Dictionary Matching With No Slowdown

The problem of dictionary matching is a classical problem in string matching: given a set S of d strings of total length n characters over an (not necessarily constant) alphabet of size sigma, build a data structure so that we can match in a any text T all occurrences of strings belonging to S. The classical solution for this problem is the Aho-Corasick automaton which finds all occ occurrences in a text T in time O(|T| + occ) using a data structure that occupies O(m log m) bits of space where m <= n + 1 is the number of states in the automaton. In this paper we show that the Aho-Corasick automaton can be represented in just m(log sigma + O(1)) + O(d log(n/d)) bits of space while still maintaining the ability to answer to queries in O(|T| + occ) time. To the best of our knowledge, the currently fastest succinct data structure for the dictionary matching problem uses space O(n log sigma) while answering queries in O(|T|log log n + occ) time. In this paper we also show how the space occupancy can be reduced to m(H0 + O(1)) + O(d log(n/d)) where H0 is the empirical entropy of the characters appearing in the trie representation of the set S, provided that sigma < m^epsilon for any constant 0 < epsilon < 1. The query time remains unchanged.Comment: Corrected typos and other minor error

Observation and Numerical Simulation of Terrain-Induced Windshear at the Hong Kong International Airport in a Planetary Boundary Layer without Temperature Inversions

Terrain-induced windshear at Hong Kong International Airport (HKIA) could be hazardous to the landing and departing aircraft. Such windshear occurring in a planetary boundary layer without temperature inversions is studied in this paper by using the data from the Terminal Doppler Weather Radar and Light Detection and Ranging systems. A high resolution numerical model, called aviation model (AVM), is also employed to find out its capability to forecast the occurrence of such windshear. The model is found to have skills in capturing the terrain-induced windshear, including the terrain-induced microburst due to the mountains of Lantau Island. Moreover, the windshear detection algorithm as applied to the AVM output, called AVM-GLYGA, is able to give advance alert for the occurrence of low-level windshear. The model also offers new dataset, such as vertical velocity and vertical cross sections across the windshear feature, to study the terrain-induced windshear phenomena with new insights. The AVM is found to have good skills in depicting the terrain-disrupted airflow at the airport area, and more comprehensive study would be conducted to study the skills of AVM-GLYGA as compared with pilot windshear report as sky truth