Mixed-field effect at the hyperfine level of^(127)I^(79)Br in its rovibronic ground state:Toward field manipulation of cold molecules

The mixed-field effect at the hyperfine level of the rovibronic ground state of the^(127)I^(79)Br(X^(1)Σ,v=0,J=0)molecule is computed on the J-I uncoupled basis of|JM_(J)I_(1)M_(1)I_(2)M_(2)>,where J is the molecular total angular momentum excluding nuclear spin,M_J is the projection number of J,I_(1) and I_(2) are the nuclear spins of the iodine and bromine atoms,and M_(1) and M_(2) are the projection numbers of I_(1) and I_(2),respectively.When the two applied electric and magnetic fields are parallel,the perturbations are rare and only one perturbation is observed in a relatively large field regime in our computation range.However,when the two fields are off-parallel,the perturbations increase significantly and some sublevels show the Feshbach-like resonance phenomenon.Therefore,such sublevels transit between weak-field seeking and strong-field seeking repeatedly,which can be utilized to enhance or suppress cold molecular collision and chemical reaction rates.Such behavior of the molecular hyperfine structure in the mixed off-parallel fields may also be utilized to construct an electric-field-assisted anti-Helmholtz magnetic trap for cold molecules and to realize evaporative cooling of cold molecules(sub-mK)into the ultracold regime(μK).

Competitive effect, but not competitive response, varies along a climatic gradient depending on tree species identity

Background: Understanding the role of species identity in interactions among individuals is crucial for assessing the productivity and stability of mixed forests over time. However, there is limited knowledge concerning the variation in competitive effect and response of different species along climatic gradients. In this study, we investigated the importance of climate, tree size, and competition on the growth of three tree species: spruce(Picea abies), fir(Abies alba), and beech(Fagus sylvatica), and examined their competitive response and effect along a climatic gradient.Methods: We selected 39 plots distributed across the European mountains with records of the position and growth of 5,759 individuals. For each target species, models relating tree growth to tree size, climate and competition were proposed. Competition was modelled using a neighbourhood competition index that considered the effects of inter-and intraspecific competition on target trees. Competitive responses and effects were related to climate.Likelihood methods and information theory were used to select the best model.Results: Our findings revealed that competition had a greater impact on target species growth than tree size or climate. Climate did influence the competitive effects of neighbouring species, but it did not affect the target species? response to competition. The strength of competitive effects varied along the gradient, contingent on the identity of the interacting species. When the target species exhibited an intermediate competitive effect relative to neighbouring species, both higher inter-than intraspecific competitive effects and competition reduction occurred along the gradient. Notably, species competitive effects were most pronounced when the target species' growth was at its peak and weakest when growing conditions were far from their maximum.Conclusions: Climate modulates the effects of competition from neighbouring trees on the target tree and not the susceptibility of the target tree to competition. The modelling approach should be useful in future research to expand our knowledge of how competition modulates forest communities across environmental gradients.

Mixed-Effects Parametric Proportional Hazard Model with Generalized Log-Logistic Baseline Distribution

Clustered survival data are widely observed in a variety of setting. Most survival models incorporate clustering and grouping of data accounting for between-cluster variability that creates correlation in order to prevent underestimate of the standard errors of the parameter estimators but do not include random effects. In this study, we developed a mixed-effect parametric proportional hazard (MEPPH) model with a generalized log-logistic distribution baseline. The parameters of the model were estimated by the application of the maximum likelihood estimation technique with an iterative optimization procedure (quasi-Newton Raphson). The developed MEPPH model’s performance was evaluated using Monte Carlo simulation. The Leukemia dataset with right-censored data was used to demonstrate the model’s applicability. The results revealed that all covariates, except age in PH models, were significant in all considered distributions. Age and Townsend score were significant when the GLL distribution was used in MEPPH, while sex, age and Townsend score were significant in MEPPH model when other distributions were used. Based on information criteria values, the Generalized Log-Logistic Mixed-Effects Parametric Proportional Hazard model (GLL-MEPPH) outperformed other models.

Adaptive Random Effects/Coefficients Modeling

Adaptive fractional polynomial modeling of general correlated outcomes is formulated to address nonlinearity in means, variances/dispersions, and correlations. Means and variances/dispersions are modeled using generalized linear models in fixed effects/coefficients. Correlations are modeled using random effects/coefficients. Nonlinearity is addressed using power transforms of primary (untransformed) predictors. Parameter estimation is based on extended linear mixed modeling generalizing both generalized estimating equations and linear mixed modeling. Models are evaluated using likelihood cross-validation (LCV) scores and are generated adaptively using a heuristic search controlled by LCV scores. Cases covered include linear, Poisson, logistic, exponential, and discrete regression of correlated continuous, count/rate, dichotomous, positive continuous, and discrete numeric outcomes treated as normally, Poisson, Bernoulli, exponentially, and discrete numerically distributed, respectively. Example analyses are also generated for these five cases to compare adaptive random effects/coefficients modeling of correlated outcomes to previously developed adaptive modeling based on directly specified covariance structures. Adaptive random effects/coefficients modeling substantially outperforms direct covariance modeling in the linear, exponential, and discrete regression example analyses. It generates equivalent results in the logistic regression example analyses and it is substantially outperformed in the Poisson regression case. Random effects/coefficients modeling of correlated outcomes can provide substantial improvements in model selection compared to directly specified covariance modeling. However, directly specified covariance modeling can generate competitive or substantially better results in some cases while usually requiring less computation time.

Nonlinear mixed-effects height to crown base and crown length dynamic models using the branch mortality technique for a Korean larch( Larix olgensis ) plantations in northeast China

Korean larch(Larix olgensis)is one of the main tree species for aff orestation and timber production in northeast China.However,its timber quality and growth ability are largely infl uenced by crown size,structure and shape.The majority of crown models are static models based on tree size and stand characteristics from temporary sample plots,but crown dynamic models has seldom been constructed.Therefore,this study aimed to develop height to crown base(HCB)and crown length(CL)dynamic models using the branch mortality technique for a Korean larch plantation.The nonlinear mixed-eff ects model with random eff ects,variance functions and correlation structures,was used to build HCB and CL dynamic models.The data were obtained from 95 sample trees of 19 plots in Meng JiaGang forest farm in Northeast China.The results showed that HCB progressively increases as tree age,tree height growth(HT growth)and diameter at breast height growth(DBH growth).The CL was increased with tree age in 20 years ago,and subsequently stabilized.HT growth,DBH growth stand basal area(BAS)and crown competition factor(CCF)signifi cantly infl uenced HCB and CL.The HCB was positively correlated with BAS,HT growth and DBH growth,but negatively correlated with CCF.The CL was positively correlated with BAS and CCF,but negatively correlated with DBH growth.Model fi tting and validation confi rmed that the mixed-eff ects model considering the stand and tree level random eff ects was accurate and reliable for predicting the HCB and CL dynamics.However,the models involving adding variance functions and time series correlation structure could not completely remove heterogeneity and autocorrelation,and the fi tting precision of the models was reduced.Therefore,from the point of view of application,we should take care to avoid setting up over-complex models.The HCB and CL dynamic models in our study may also be incorporated into stand growth and yield model systems in China.

Modelling tree mortality across diameter classes using mixedeffects zero-inflated models

The mortality of trees across diameter class model is a useful tool for predicting changes in stand structure.Mortality data commonly contain a large fraction of zeros and general discrete models thus show more errors.Based on the traditional Poisson model and the negative binomial model,different forms of zero-inflated and hurdle models were applied to spruce-fir mixed forests data to simulate the number of dead trees.By comparing the residuals and Vuong test statistics,the zero-inflated negative binomial model performed best.A random effect was added to improve the model accuracy;however,the mixed-effects zero-inflated model did not show increased advantages.According to the model principle,the zeroinflated negative binomial model was the most suitable,indicating that the"0"events in this study,mainly from the sample"0",i.e.,the zero mortality data,are largely due to the limitations of the experimental design and sample selection.These results also show that the number of dead trees in the diameter class is positively correlated with the number of trees in that class and the mean stand diameter,and inversely related to class size,and slope and aspect of the site.

Additive mixed models to study the effect of tree age and climatic factors on stem radial growth of Eucalyptus trees

The effect of tree age and climatic variables on stem radial growth of two hybrid clones of Eucalyptus was determined using longitudinal data from eastern South Africa.The stem radius of was measured weekly as the response variable.In addition to tree age,average weekly temperature,solar radiation,relative humidity and wind speed were simultaneously recorded with total rainfall at the site.An additive mixed effects model that incorporates a non-parametric smooth function was used.The results of the analysis indicate that the relationship between stem radius and each of the covariates can be explained by nonlinear functions.Models that account for the effect of clone and season together with their interaction in the parametric part of the additive mixed model were also fitted.The interaction between clone and season was not significant in all cases.For analyzing the joint effect all the covariates,additive mixed models that included two or more covariates were fitted.A significant effect of tree age was found in all cases.Although tree age was the key determinant of stem radial growth,weather variables also had a significant effect that was dependent on season.

Effects of Nitrogen Addition on the Mixed Litter Decomposition in Stipa baicalensis Steppe in Inner Mongolia

During the past two centuries, global changes (i.e., enhanced nitrogen deposition) have exerted profound effects on ecological processes of steppe ecosystems. We used litterbag method and mixed litters of three different plant species tissues (Stipa baicalensis: Sb, Leymus chinensis: Lc and Artemisia frigid: Af), endemic to Stipa baicalensis Steppe, and measured the mass loss of mixtures over 417 days under the N addition treatment. We studied the effect of N addition (N0: no N addition;N15: 1.5 g N/m2·a;N30: 3.0 g N/m2·a;N50: 5.0 g N/m2·a;N100: 10.0 g N/m2·a;N150: 15.0 g N/m2·a) on the rate of mixed litter decomposition and nutrient dynamics change. The decomposition constant (k) of leaf mixtures was higher than that of root mixtures. The k values of leaf mixed combinations were 0.880 (Sb + Lc), 1.231 (Lc + Af), 1.027 (Sb + Lc + Af), respectively. The k value of stem was 0.806 (Lc + Af) and the root mixed combinations were 0.665 (Sb + Lc), 0.979 (Lc + Af) and 1.164 (Sb + Lc + Af), respectively. The results indicated that N addition had significantly effect on the mixed litter decomposition and nutrient releasing. The rate of plant tissues litter decomposition had different response to N addition. In the context of N addition, litter decomposition rate and nutrient dynamics were changed by synthetic effect of decaying time, specie types and N addition dose. Our findings suggested that prairie plants may adapt to environmental change by adjusting litter quality, thus retaining the stability of the steppe ecosystem.

Self-Mixing Interference Effects in LD Pumped Multi-Mode Solid-State Laser

Based on the effective structure of the self-mixing interference effects,a general model for the self-mixing interference effects in the LD pumped solid-state laser has been established for the first time.The numerical simulation of the self-mixing interference signal has been done,the results show that when the external cavity length is integral times of 1/2,1/3,2/3,1/4,3/4 of the effective cavity length,the intensity of the self-mixing interference signals reach maximum in value.While that of single mode laser is integral times of half of the effective cavity length,the measuring precision of displacement of single mode laser is λ/2.A conclusion can be drawn from the above results that the measuring precision of displacement of multi-mode laser is higher than that of single mode laser.

Influence of alkali mixed effect on the mixing enthalpy in 0.75B_2O_3-0.25[xNa_2O-(1-x)K_2O]glass system

The mixed alkali effect was investigated in the glass system 0.75B2O3-0.25[xNa2O-（1 -x）K20] through thermodynamic properties. The calorimetric measurements were performed in HF solution calorimetry at 298 K. The mixing enthalpy values show non-linear behaviour upon substitution of one alkali ion by another. This thermodynamic non-ideality is caused by the slight variations of distance between metallic cations, the macromolecular structure being unchanged. It can be explained, at least qualitatively, using electrolyte theory based on the Coulombic interactions of charged species originally developed by Debye and Hückel.

Incorporating topographic factors in nonlinear mixed-effects models for aboveground biomass of natural Simao pine in Yunnan,China

A total of 128 Simao pine trees （Pinus kesiya var. langbianensis） from three regions of Pu＇er City, Yunnan Province, People＇s Republic of China, were destructively sampled to obtain tree aboveground biomass （AGB）. Tree variables such as diameter at breast height and total height, and topographical factors such as altitude, aspect of slope, and degree of slope were recorded. We considered the region and site quality classes as the ran- dom-effects, and the topographic variables as the fixed- effects. We fitted a total of eight models as follows： least- squares nonlinear models （BM）, least-squares nonlinear models with the topographic factors （BMT）, nonlinear mixed-effects models with region as single random-effects （NLME-RE）, nonlinear mixed-effects models with site as single random-effects （NLME-SE）, nonlinear mixed-ef- fects models with the two-level nested region and site random-effects （TLNLME）, NLME-RE with the fixed-ef- fects of topographic factors （NLMET-RE）, NLME-SE with the fixed-effects of topographic factors （NLMET-SE）, and TLNLME with the fixed-effects of topographic factors （TLNLMET）. The eight models were compared by modelfitting and prediction statistics. The results showed： model fitting was improved by considering random-effects of region or site, or both. The models with the fixed-effects of topographic factors had better model fitting. According to AIC and BIC, the model fitting was ranked as TLNLME 〉 NLMET-RE 〉 NLME-RE.〉 NLMET-SE 〉 TLNLMET 〉 NLME-SE 〉 BMT 〉 BM. The differences among these models for model prediction were small. The model pre- diction was ranked as TLNLME 〉 NLME-RE 〉 NLME- SE 〉 NLMET-RE 〉 NLMET-SE 〉 TLNLMET 〉 BMT 〉 BM. However, all eight models had relatively high prediction precision （〉90 %）. Thus, the best model should be chosen based on the available data when using the model to predict individual tree AGB.

Covalent bonding and J–J mixing effects on the EPR parameters of Er^(3+) ions in GaN crystal

The EPR parameters of trivalent Er（3＋） ions doped in hexagonal Ga N crystal have been studied by diagonalizing the 364×364 complete energy matrices. The results indicate that the resonance ground states may be derived from the Kramers doublet Γ6. The EPR g-factors may be ascribed to the stronger covalent bonding and nephelauxetic effects compared with other rare-earth doped complexes, as a result of the mismatch of ionic radii of the impurity Er（3＋）ion and the replaced Ga（3＋） ion apart from the intrinsic covalency of host Ga N. Furthermore, the J–J mixing effects on the EPR parameters from the high-lying manifolds have been evaluated. It is found that the dominant J–J mixing contribution is from the manifold 2K（15/2）, which accounts for about 2.5%. The next important J–J contribution arises from the crystal–field mixture between the ground state 4I（15/2） and the first excited state4I（13/2）, and is usually less than 0.2%. The contributions from the rest states may be ignored.

Nonlinear Mixed-Effects Models for Repairable Systems Reliability

Mixed-effects models,also called random-effects models,are a regression type of analysis which enables the analyst to not only describe the trend over time within each subject,but also to describe the variation among different subjects.Nonlinear mixed-effects models provide a powerful and flexible tool for handling the unbalanced count data.In this paper,nonlinear mixed-effects models are used to analyze the failure data from a repairable system with multiple copies.By using this type of models,statistical inferences about the population and all copies can be made when accounting for copy-to-copy variance.Results of fitting nonlinear mixed-effects models to nine failure-data sets show that the nonlinear mixed-effects models provide a useful tool for analyzing the failure data from multi-copy repairable systems.

J-mixing Effect of the Crystal-field on the Spectroscopic Characteristics of Rare-earth Doped Laser Crystals

By using the re-derived formulae for both line-strength of electricdipole transition and simple J-mixing coefficients within the 4f shell in a rare-earthion, the spectroscopic properties of the luminescent material Eu3+ =Y2O3 and laser crystals Tb3+:=YAlO3 and Nd3+:YVO4, are investigated in detail. On the basis of three fitting Ω parameters and the effective reduced matrix elements, the spectral linestrengths, spontaneous emission probabilities, fluorescent branching ratios and lifetimeare calculated. The better agreement between theoretical results and experimental dataindicates the importance of J-mixing in the spectroscopic study of laser crystals.

Retrospective analysis of chronic hepatitis C in untreated patients with nonlinear mixed effects model

It is well known that viral load of the hepatitis C virus (HCV) is related to the efficacy of interferon therapy. The complex biological parameters that impact on viral load are essentially unknown. The current knowledge of the hepatitis C virus does not provide a mathematical model for viral load dynamics within untreated patients. We car-ried out an empirical modelling to investigate whether different fluctuation patterns exist and how these patterns (if exist) are related to host-specific factors. Data was prospectively col-lected from 147 untreated patients chronically infected with hepatitis C, each contributing be-tween 2 to 10 years of measurements. We pro-pose to use a three parameter logistic model to describe the overall pattern of viral load fluctua-tion based on an exploratory analysis of the data. To incorporate the correlation feature of longitu-dinal data and patient to patient variation, we introduced random effects components into the model. On the basis of this nonlinear mixed ef-fects modelling, we investigated effects of host-specific factors on viral load fluctuation by in-corporating covariates into the model. The pro-posed model provided a good fit for describing fluctuations of viral load measured with varying frequency over different time intervals. The aver-age viral load growth time was significantly dif-ferent between infection sources. There was a large patient to patient variation in viral load as-ymptote.

Study on Removal Effect of Ammonia Nitrogen in Sewage by the Mixed Substrate

Red brick,cement brick and ceramsite were taken as the substrate of constructed wetland,and removal effect of ammonia nitrogen by the mixed substrate under different combination manners and aeration condition was explored. Research results showed that cement brick had the best removal effect on ammonia nitrogen,followed by red brick and ceramsite; aeration was favorable for the removal of ammonia nitrogen by each substrate and the mixed substrate; removal rate sequence of ammonia nitrogen by each mixed substrate was red brick + cement brick > red brick + cement brick + ceramsite > cement brick + ceramsite > red brick + ceramsite; the combination of red brick + cement brick had the best removal effect on ammonia nitrogen in domestic sewage. Comprehensively considering,the mixed substrate of red brick + cement brick has better stability and higher ammonia nitrogen removal rate,and it is suitable as the mixed adsorption substrate of constructed wetland.

Transverse effects in photorefractive two-wave mixing

In a biased photorefractive crystal, the process of two one-dimensional waves mixing, i.e., the dynamical evolution of both pump beam and signal beam, is traced by numerically solving the coupled-wave equation. Direct simulations show that the propagation and stability of the two beams are completely determined by the system parameters, such as the external bias field, the intensity and the beam waist of the pump beam. By adjusting these parameters, one can control the state of two Gaussian waves mixing. The numerical results are helpful for performing a two-wave mixing experiment.

Sensitizing Effect of Mixed Surfactants on the Colouration of Scandium(Ⅲ)with Phenylfluorone or Its Derivatives

In the presence of mixed micelle of a cationic and a nonionic surfactants,the reaction of scandium(Ⅲ) with phenylfluorone or its derivatives results in a very sensitive colouration:furthermore this chromophoric system tolerates the existence of a considerable amount of masking agents,so that many interfering ions can be masked and its selectivity would be further improved.After studying the optimum conditions and main charac- ters of some similar systems,the system of Sc(Ⅲ)—Orthonitrophenyuorone—Cetyltrimethylammonium Bromide(CTMAB)—Triton X-200 is chosen for the spectrophotometric determination of microamount of scandium.The proposed method shows not only high sensitivity(with a molar absorptivity of 2.12×1~sL mol^(-1)·cm^(-1))and selectivity,but also high tolerance of chromophoric conditions.Beer's law is obeyed over a range of 0～6.0 μg Sc/25ml.If the dual-wavelength method is applied,a much higher molar absorptivity o|' 3.04×10~5L·mol^(-1)·cm^(-1)than those of other systems ever reported in the literatures can be attained:more- over.its linear range is extended to 0～8.0 μg Sc/25ml and its reproducibility is also improved.

Numerical investigation of variable viscosities and thermal stratification effects on MHD mixed convective heat and mass transfer past a porous wedge in the presence of a chemical reaction

An analysis is presented to investigate the effects of variable viscosities and thermal stratification on the MHD mixed convective heat and mass transfer of a viscous, incompressible, and electrically conducting fluid past a porous wedge in the presence of a chemical reaction. The wall of the wedge is embedded in a uniform nonDarcian porous medium in order to allow for possible fluid wall suction or injection. The governing boundary layer equations are written into a dimensionless form by similarity transformations. The transformed coupled nonlinear ordinary differential equations are solved numerically with finite difference methods. Numerical calculations up to the thirdorder level of truncation are carried out for different values of dimensionless parameters. The results are presented graphically, and show that the flow field and other quantities of physical interest are significantly influenced by these parameters. The results are compared with those available in literature, and show excellent agreement.