Multi-types of Skyrmions in SU(N) Quantum Hall System

The skyrmions in SU(N) quantum Hall (QH) system are discussed. By analyzing the gauge field structure and the topological properties of this QH system it is pointed out that in the SU(N) QH system there can exist (N-1) types of skyrmion structures, instead of only one type of skyrmions. In this paper, by means of the Abelian projections according to the (N-1) Cartan subalgebra local bases, we obtain the (N-1) U(1) electromagnetic field tensors in the SU(N) gauge field of the QH system, and then derive (N-1) types of skyrmion structures from these U(1) sub-field tensors. Furthermore, in light of the phi-mapping topological current method, the topological charges and the motion of these skyrmions are also discussed.

Three putative types of El Nino revealed by spatial variability in impact on Australian wheat yield

The El Nino-Southern Oscillation (ENSO) phenomenon significantly impacts rainfall and ensuing crop yields in many parts of the world. In Australia, El Nino events are often associated with severe drought conditions. However, El Nino events differ spatially and temporally in their manifestations and impacts, reducing the relevance of ENSO-based seasonal forecasts. In this analysis, three putative types of El Nino are identified among the 24 occurrences since the beginning of the twentieth century. The three types are based on coherent spatial patterns (footprints) found in the El Nino impact on Australian wheat yield. This bioindicator reveals aligned spatial patterns in rainfall anomalies, indicating linkage to atmospheric drivers. Analysis of the associated ocean-atmosphere dynamics identifies three types of El Nino differing in the timing of onset and location of major ocean temperature and atmospheric pressure anomalies. Potential causal mechanisms associated with these differences in anomaly patterns need to be investigated further using the increasing capabilities of general circulation models. Any improved predictability would be extremely valuable in forecasting effects of individual El Nino events on agricultural systems.

A time-domain test for some types of nonlinearity

The bispectrum and third-order moment can be viewed as equivalent tools for testing for the presence of nonlinearity in stationary time series. This is because the bispectrum is the Fourier transform of the third-order moment. An advantage of the bispectrum is that its estimator comprises terms that are asymptotically independent at distinct bifrequencies under the null hypothesis of linearity. An advantage of the third-order moment is that its values in any subset of joint lags can be used in the test, whereas when using the bispectrum the entire (or truncated) third-order moment is required to construct the Fourier transform. In this paper, we propose a test for nonlinearity based upon the estimated third-order moment. We use the phase scrambling bootstrap method to give a nonparametric estimate of the variance of our test statistic under the null hypothesis. Using a simulation study, we demonstrate that the test obtains its target significance level, with large power, when compared to an existing standard parametric test that uses the bispectrum. Further we show how the proposed test can be used to identify the source of nonlinearity due to interactions at specific frequencies. We also investigate implications for heuristic diagnosis of nonstationarity.