Nonlinear perturbation of a high-order exceptional point:Skin discrete breathers and the hierarchical power-law scaling

We study the nonlinear perturbation of a high-order exceptional point(EP)of the order equal to the system site number L in a Hatano-Nelson model with unidirectional hopping and Kerr nonlinearity.Notably,we find a class of discrete breathers that aggregate to one boundary,here named as skin discrete breathers(SDBs).The nonlinear spectrum of these SDBs shows a hierarchical power-law scaling near the EP.Specifically,the response of nonlinear energy to the perturbation is given by E_(m)∝Γ~(α_(m)),whereα_(m)=3^(m-1)is the power with m=1,...,L labeling the nonlinear energy bands.This is in sharp contrast to the L-th root of a linear perturbation in general.These SDBs decay in a double-exponential manner,unlike the edge states or skin modes in linear systems,which decay exponentially.Furthermore,these SDBs can survive over the full range of nonlinearity strength and are continuously connected to the self-trapped states in the limit of large nonlinearity.They are also stable,as confirmed by a defined nonlinear fidelity of an adiabatic evolution from the stability analysis.As nonreciprocal nonlinear models may be experimentally realized in various platforms,such as the classical platform of optical waveguides,where Kerr nonlinearity is naturally present,and the quantum platform of optical lattices with Bose-Einstein condensates,our analytical results may inspire further exploration of the interplay between nonlinearity and non-Hermiticity,particularly on high-order EPs,and benchmark the relevant simulations.

Seasonal Variation of Carbon and Nitrogen Emissions from Turfgrass

The role of turfgrasses in C and N cycling in the southeastern U.S. has not been well documented. The objectives of this research were to determine the characterization of chemical quality, clipping decomposition rates, and C and N release from warm- and cool-season turfgrasses. The study was conducted for 46 weeks in 2012 in Auburn, AL. Four warm season turfgrasses were used included (bermudagrass [Cynodon dactylon (L.) Pers. × C. transvaalensis Burtt Davy], centipedegrass (Eremochloa ophiuroides (Munro) Hack), St. Augustinegrass (Stenotaphrum secundatum (Walter) Kuntze), zoysiagrass (Zoysia japonica Steud.), and one cool season turfgrass (tall fescue (Festuca arundinacea Schreb)). Litter was placed into nylon bags at an oven dry rate of 3.6 Mg?ha?1. Litter bags were retrieved after 0, 1, 2, 4, 8, 16, 24, 32, and 46 weeks, and analyzed for total C and N. A double exponential decay model was used to describe mass, C, and N loss. Results indicated that tall fescue decomposition occurred rapidly compared to warm season turfgrasses. Litter mass loss measured after 46 weeks was determined to be 61.7%, 73.7%, 72.2%, 86.8%, and 45.4% in bermudagrass, centipedegrass, St. Augustinegrass, tall fescue, and zoysiagrass respectively. Zoysiagrass litter had a higher lignin concentration, while tall fescue had the lowest lignin. Over 46 weeks’ release of C was in the order: zoysiagrass > bermudagrass = centipedegrass = St. Augustinegrass > tall fescue, and release of N was in the order zoysiagrass > centipedegrass > bermudagrass = St. Augustinegrass > tall fescue. Our study concluded that, zosiagrass is a better choice for home lawns.

On-the-fly Doppler broadening method based on optimal doubleexponential formula

As temperature changes constantly in nuclear reactor operation, on-the-fly Doppler broadening methods are commonly adopted for generating nuclear cross sections at various temperatures in neutron transport simulation. Among the existing methods, the widely used SIGMA1 approach is inefficient because it involves error function and Taylor series expansion. In this paper, we present a new on-the-fly Doppler broadening with optimal double-exponential formula based on SuperMC to improve efficiency with given accuracy. In this method, doubleexponential formula in 1/16 steps is used for broadening cross section at low energy, with both accuracy and efficiency. Meanwhile, the Gauss–Hermite quadrature of different orders is used for broadening cross section at resonance energy. The method can generate neutron cross section rapidly and precisely at the desired temperature.Typical nuclide cross sections and benchmarking tests are presented in detail.

Synthesis and Fluorescence Property of A New Subphthalocyanine

A new soluble subphthalocyanine was first prepared and its fluorescence property was investigated. It exhibited both S-1 and S-2 emissions, of which the quantum yields and the lifetimes were measured.

Enhancement of red to orange emission ratio of YPO_4:Eu^(3+),Ce^(3+) and its dependence on Ce^(3+) concentration

Eu3＋ and Ce3＋ co-doped YPO4 microspheres were synthesized by hydrothermal method without template. The emission spectra showed that the red emission centered at 618nm could be readily increased relatively to the orange emission centered at 590nm by controlling the doping concentration of Ce3＋ ion. The investigation based on excitation spectra and decay curves demonstrated that the doped Ce3＋ ions took two efficient energy transfers to Eu3＋ ions and affected the lifetime of the emission states of Eu3＋ ions so that the emission spectra of Eu3＋ ion were accordingly tuned with the Ce3＋ content increasing. This controllable red （5D0→7F2） to orange （ 5D0→7F1） emission ratio of YPO4：Eu3＋,Ce3＋ made it very promising for encoded anti-fake labels and bio-labels.

Modeling detector response function of alpha particles for neutron depth profiling

The energy spreading of recorded ions is influenced by straggling,geometrical acceptance angles and detector energy resolution effects in neutron depth profiling(NDP)and a symmetric Gaussian function model was customarily applied before.In addition,the spectra of mono-energetic alpha particles show a well known asymmetric shape as well when measured by silicon detectors.This article presents a physical model predicting the observed energy spectrum of a sample ion with target nuclides in prearranged depths.It is expressed as the convolution of a Gaussian function with a left-hand double-exponential function.Experiment showed that the predicted ions spectrum derived from the asymmetric model matches the observed energy spectrum.Therefore,the model can be applied to produce matrix for inversion of NDP spectrum.