Evaluation of unconstrained and constrained mathematical functions to model girth growth of rubber trees (Hevea brasiliensis) using young agemeasurements

No attempt has been made to date to model growth in girth of rubber tree （Hevea brasiliansis）. We evaluated the few widely used growth functions to identify the most parsimonious and biologically reasonable model for describing the girth growth of young rubber trees based on an incomplete set of young age measurements. Monthly data for girth of immature trees （age 2 to 12 yearsi from two locations were sub- jected to modelling. Re-parameterized, unconstrained and constrained growth functions,of Richards （RM）, Gompertz （GM） and the monomo- lecular ＇model ^（MM） were fitted to data. Duration of growth was the firsf constraint introduced. In the stagel We attempted a population aver- age （PA） model to capture the trend in growth. The best PA model was fitted as a subject specific （SS） model. We used appropriate error vari- ance-covariance structure to account for correlation due to repeated measurements over time. Unconstrainecl functions underestimated the asymptotic maximum that did not reflective carrying capacity of the locations. Underestimafions were attributed to the partial set＇ of meas- urements made during the early growth phase of the trees. MM proved superior to RM and GM. In the randomcoefficient models, both Gf and Go appeared to be influenced by tree level effects. Inclusion of diagonal definite positive matrix removed the correlation between random effects. The results were similar at both locations. In the overall assessment MM appeared as the candidate model for studying the girth-age relationships in Hevea trees. Based on the fitted model we conclude that, in Hevea trees, growth rate is maintained at maximum value at to, then decreases until the final state at dG/dt 〉 0, resulting in yield curve with no period of accelerating growth. One physiological explanation is that photosynthetic activity in Hevea trees decreases as girth increases and constructive metabolism is larger than destructive metabolism.

Theoretical Investigation on Triplet Excitation Energy Transfer in Fluorene Dimer

Triplet-triplet energy transfer in fluorene dimer with electronic structure calculations. The two is investigated by combining rate theories key parameters for the control of energy transfer, electronic coupling and reorganization energy, are calculated based on the diabatic states constructed by the constrained density functional theory. The fluctuation of the electronic coupling is further revealed by molecular dynamics simulation. Succeedingly, the diagonal and off-diagonal fluctuations of the Hamiltonian are mapped from the correlation functions of those parameters, and the rate is then estimated both from the perturbation theory and wavepacket diffusion method. The results manifest that both the static and dynamic fluctuations enhance the rate significantly, but the rate from the dynamic fluctuation is smaller than that from the static fluctuation.

First application of large reactivity measurement through rod drop based on three-dimensional space–time dynamics

Abstract Reactivity measurement is an essential part of a zero-power physics test,which is critical to reactor design and development.The rod drop experimental technique is used to measure the control rod worth in a zero-power physics test.The conventional rod drop experimental technique is limited by the spatial effect and the difference between the calculated static reactivity and measured dynamic reactivity;thus,the method must be improved.In this study,a modified rod drop experimental technique that constrains the detector neutron flux shape function based on three-dimensional space–time dynamics to reduce the reactivity perturbation and a new method for calculating the detector neutron flux shape function are proposed.Correction factors were determined using Monte Carlo N-particle transport code and transient analysis code for a pressurized water reactor at the Ulsan National Institute of Science and Technology and Xi’an Jiaotong University,and a large reactivity of over 2000 pcm was measured using the modified technique.This research evaluated the modified technique accuracy,studied the influence of the correction factors on the modification,and investigated the effect of constraining the shape function on the reactivity perturbation reduction caused by the difference between the calculated neutron flux and true value,using the new method to calculate the shape function of the detector neutron flux and avoiding the neutron detector response function(weighting factor)calculation.

Constrained lattice density functional theory and its applications on vapor–liquid nucleations

Vapor-liquid phase transition occurs via a nucleation process, and depending on the role of foreign objects, nucleation can be either homogeneous or heterogeneous. In this review, we focus on the recently developed constrained lattice density functional theory （CLDFT） and its applications on vapor-liquid nucleation. We also review the recent theoretical advance on the stability of nanobubbles. Based on CLDFT, a pinning and supersaturation mechanism has proposed to interpret the surprising stability of surface nanobubbles. The mechanism can interpret most characteristics of nanobubbles. More importantly, the mechanism suggests that the critical nucleus can be stabilized under the condition of contact line pinning. Thus, CLDFT studies provide an alternative way to measure the critical nucleus that is difficult to measure experimentally in the bulk solution, through stabilizing it with surface roughness or heterogeneities.

Analysis on a Superlinearly Convergent Augmented Lagrangian Method

The augmented Lagrangian method is a classical method for solving constrained optimization.Recently,the augmented Lagrangian method attracts much attention due to its applications to sparse optimization in compressive sensing and low rank matrix optimization problems.However,most Lagrangian methods use first order information to update the Lagrange multipliers,which lead to only linear convergence.In this paper,we study an update technique based on second order information and prove that superlinear convergence can be obtained.Theoretical properties of the update formula are given and some implementation issues regarding the new update are also discussed.