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In this paper we present an extended version of Hilbert-Huang transform, namely arbitrary-order Hilbert spectral analysis, to characterize the scale-invariant properties of a time series directly in an amplitude-frequency space. We first show numerically that due to a nonlinear distortion, traditional methods require high-order harmonic components to represent nonlinear processes, except for the Hilbert-based method. This will lead to an artificial energy flux from the low-frequency (large scale) to the high-frequency (small scale) part. Thus the power law, if it exists, is contaminated. We then compare the Hilbert method with structure functions (SF), detrended fluctuation analysis (DFA), and wavelet leader (WL) by analyzing fractional Brownian motion and synthesized multifractal time series. For the former simulation, we find that all methods provide comparable results. For the latter simulation, we perform simulations with an intermittent parameter μ=0.15. We find that the SF underestimates scaling exponent when q>3. The Hilbert method provides a slight underestimation when q>5. However, both DFA and WL overestimate the scaling exponents when q>5. It seems that Hilbert and DFA methods provide better singularity spectra than SF and WL. We finally apply all methods to a passive scalar (temperature) data obtained from a jet experiment with a Taylor's microscale Reynolds number Reλ≃250. Due to the presence of strong ramp-cliff structures, the SF fails to detect the power law behavior. For the traditional method, the ramp-cliff structure causes a serious artificial energy flux from the low-frequency (large scale) to the high-frequency (small scale) part. Thus DFA and WL underestimate the scaling exponents. However, the Hilbert method provides scaling exponents ξθ(q) quite close to the one for longitudinal velocity, indicating a less intermittent passive scalar field than what was believed before. [ABSTRACT FROM AUTHOR]

We report low-energy inelastic neutron scattering data of the paramagnetic (PM) to hidden-order (HO) phase transition at T0 = 17.5 K in URu2Si2. While confirming previous results for the HO and PM phases, our data reveal a pronounced wave-vector dependence of low-energy excitations across the phase transition. To analyze the energy scans we employ a damped harmonic oscillator model containing a fit parameter 1/Τ which is expected to diverge at a second-order phase transition. Counter to expectations the excitations at Q0 ≈ (1.4,0,0) show an abrupt steplike suppression of 1/Τ below T0, whereas excitations at Q0 = (1,0,0), associated with large-moment antiferromagnetism (LMAF) under pressure, show an enhancement and a pronounced peak of 1/Τ at T0. Therefore, at the critical HO temperature T0, LMAF fluctuations become nearly critical as well. This is the behavior expected of a "supervector" order parameter with nearly degenerate components for the HO and LMAF leading to nearly isotropic fluctuations in the combined order-parameter space. [ABSTRACT FROM AUTHOR]

Recently, rhenium disulfide (ReS2) monolayers were experimentally extracted by conventional mechanical exfoliation technique from as-grown ReS2 crystals. Unlike the well-known members of transition metal dichalcogenides (TMDs), ReS2 crystallizes in a stable distorted-1T structure and lacks an indirect to direct gap crossover. Here we present an experimental and theoretical study of the formation, energetics, and stability of the most prominent lattice defects in monolayer ReS2. Experimentally, irradiation with 3-MeV He+2 ions was used to break the strong covalent bonds in ReS2 flakes. Photoluminescence measurements showed that the luminescence from monolayers is mostly unchanged after highly energetic a particle irradiation. In order to understand the energetics of possible vacancies in ReS2 we performed systematic first-principles calculations. Our calculations revealed that the formation of a single sulfur vacancy has the lowest formation energy in both Re and S rich conditions and a random distribution of such defects are energetically more preferable. Sulfur point defects do not result in any spin polarization whereas the creation of Re-containing point defects induce magnetization with a net magnetic moment of 1-3μB. Experimentally observed easy formation of sulfur vacancies is in good agreement with first-principles calculations. [ABSTRACT FROM AUTHOR]

We report that the subthreshold emission spectra of vertical-cavity surface-emitting lasers (VCSELs) can be analogously used to manifest the quantum-billiard energy spectra. The Fourier-transformed distributions of the subthreshold emission spectra are demonstrated to display various peak structures that are in good agreement with the results of the quantum-billiard model. We also verify that the statistical analyses of the nearest-neighbor eigenvalue spacing distributions obey a Poisson distribution for an equilateral-triangular device and a Wigner distribution for a stadium-shaped device. [ABSTRACT FROM AUTHOR]