Upstream proton cyclotron waves: occurrence and amplitude dependence on IMF cone angle at Mars——from MAVEN observations

Proton cyclotron waves(PCWs)can be generated by ion pickup of Martian exospheric particles in the solar wind.The solar wind ion pickup process is highly dependent on the“IMF cone angle”—the angle between the solar wind velocity and the interplanetary magnetic field(IMF),which also plays an important role in the generation of PCWs.Using data from 2.15 Martian years of magnetic field measurements collected by the Mars Atmosphere and Volatile Evolution(MAVEN)mission,we have identified 3307 upstream PCW events.Their event number distribution decreases exponentially with their duration.A statistical investigation of the effects of IMF cone angle on the amplitudes and occurrence rates of PCWs reveals a slight tendency of PCWs’amplitudes to decrease with increasing IMF cone angle.The relationship between the amplitude and IMF cone angle is weak,with a correlation coefficient r=–0.3.We also investigated the influence of IMF cone angle on the occurrence rate of PCWs and found that their occurrence rate is particularly high for intermediate IMF cone angles(~18°–42°)even though highly oblique IMF orientation occurs most frequently in the upstream region of the Martian bow shock.We also conclude that these variabilities are not artefacts of temporal coverage biases in MAVEN sampling.Our results demonstrate that whereas IMF cone angle strongly influences the occurrence of PCWs,IMF cone angle may also weakly modulate their amplitudes in the upstream region of Mars.

PATH PROBLEM SIMPLIFICATION WITH DESIRED BOUNDED LENGTHS IN ACYCLIC NETWORKS

Path determination is a fundamental problem of operations research. Current solutions mainly focus on the shortest and longest paths. We consider a more generalized problem; specifically, we consider the path problem with desired bounded lengths （DBL path problem）. This problem has extensive applications; however, this problem is much harder, especially for large-scale problems. An effective approach to this problem is equivalent simplification. We focus on simplifying the problem in acyclic networks and creating a path length model that simplifies relationships between various path lengths. Based on this model, we design polynomial algorithms to compute the shortest, longest, second shortest, and second longest paths that traverse any arc. Furthermore, we design a polynomial algorithm for the equivalent simplification of the is O（m）, where m is the number of arcs. DBL path problem. The complexity of the algorithm