Leptonic ZZ decays in the littlest HiggsHiggs model with T-parity

The littlest $Higgs$ model with T-parity (called the $LHT$ model) predicts the existence of the T-odd leptons, which can generate contributions to some leptonic processes at the one-loop level. We calculate their contributions to the leptonic $Z$ decay processes $Z\to l\bar{l'}$, $Z\to l\bar{l}$, and Z\rightarro \nu\bar{\nu}. We find that the T-odd leptons can give significant contributions to the branching ratios of these decay processes in most of the parameter space. The experimental measurement values might generate constraints on the free parameters of the $LHT$ model.Comment: 16 pages, 8 figures, minor corrections; final version published in Phys.Rev.

Formation of regular spatial patterns in ratio-dependent predator-prey model driven by spatial colored-noise

Results are reported concerning the formation of spatial patterns in the two-species ratio-dependent predator-prey model driven by spatial colored-noise. The results show that there is a critical value with respect to the intensity of spatial noise for this system when the parameters are in the Turing space, above which the regular spatial patterns appear in two dimensions, but under which there are not regular spatial patterns produced. In particular, we investigate in two-dimensional space the formation of regular spatial patterns with the spatial noise added in the side and the center of the simulation domain, respectively.Comment: 4 pages and 3 figure

Hybridizing two-step growth mixture model and exploratory factor analysis to examine heterogeneity in nonlinear trajectories

Empirical researchers are usually interested in investigating the impacts of baseline covariates have when uncovering sample heterogeneity and separating samples into more homogeneous groups. However, a considerable number of studies in the structural equation modeling (SEM) framework usually start with vague hypotheses in terms of heterogeneity and possible reasons. It suggests that (1) the determination and specification of a proper model with covariates is not straightforward, and (2) the exploration process may be computational intensive given that a model in the SEM framework is usually complicated and the pool of candidate covariates is usually huge in the psychological and educational domain where the SEM framework is widely employed. Following \citet{Bakk2017two}, this article presents a two-step growth mixture model (GMM) that examines the relationship between latent classes of nonlinear trajectories and baseline characteristics. Our simulation studies demonstrate that the proposed model is capable of clustering the nonlinear change patterns, and estimating the parameters of interest unbiasedly, precisely, as well as exhibiting appropriate confidence interval coverage. Considering the pool of candidate covariates is usually huge and highly correlated, this study also proposes implementing exploratory factor analysis (EFA) to reduce the dimension of covariate space. We illustrate how to use the hybrid method, the two-step GMM and EFA, to efficiently explore the heterogeneity of nonlinear trajectories of longitudinal mathematics achievement data.Comment: Draft version 1.6, 08/08/2020. This paper has not been peer reviewed. Please do not copy or cite without author's permissio

A review of microgrid development in the United States – A decade of progress on policies, demonstrations, controls, and software tools

Microgrids have become increasingly popular in the United States. Supported by favorable federal and local policies, microgrid projects can provide greater energy stability and resilience within a project site or community. This paper reviews major federal, state, and utility-level policies driving microgrid development in the United States. Representative U.S. demonstration projects are selected and their technical characteristics and non-technical features are introduced. The paper discusses trends in the technology development of microgrid systems as well as microgrid control methods and interactions within the electricity market. Software tools for microgrid design, planning, and performance analysis are illustrated with each tool's core capability. Finally, the paper summarizes the successes and lessons learned during the recent expansion of the U.S. microgrid industry that may serve as a reference for other countries developing their own microgrid industries