Geometric properties of the complete-graph Ising model in the loop representation

The exact solution of the Ising model on the complete graph (CG) provides an important, though mean-field, insight for the theory of continuous phase transitions. Besides the original spin, the Ising model can be formulated in the Fortuin-Kasteleyn random-cluster and the loop representation, in which many geometric quantities have no correspondence in the spin representations. Using a lifted-worm irreversible algorithm, we study the CG-Ising model in the loop representation, and, based on theoretical and numerical analyses, obtain a number of exact results including volume fractal dimensions and scaling forms. Moreover, by combining with the Loop-Cluster algorithm, we demonstrate how the loop representation can provide an intuitive understanding to the recently observed rich geometric phenomena in the random-cluster representation, including the emergence of two configuration sectors, two length scales and two scaling windows.Comment: 10 pages, 10 figure

Finite-Size Scaling of the High-Dimensional Ising Model in the Loop Representation

Besides its original spin representation, the Ising model is known to have the Fortuin-Kasteleyn (FK) bond and loop representations, of which the former was recently shown to exhibit two upper critical dimensions $(d_c=4,d_p=6)$. Using a lifted worm algorithm, we determine the critical coupling as $K_c = 0.077\,708\,91(4)$ for $d=7$, which significantly improves over the previous results, and then study critical geometric properties of the loop-Ising clusters on tori for spatial dimensions $d=5$ to 7. We show that, as the spin representation, the loop Ising model has only one upper critical dimension at $d_c=4$. However, sophisticated finite-size scaling (FSS) behaviors, like two length scales, two configuration sectors and two scaling windows, still exist as the interplay effect of the Gaussian fixed point and complete-graph asymptotics. Moreover, using the Loop-Cluster algorithm, we provide an intuitive understanding of the emergence of the percolation-like upper critical dimension $d_p=6$ in the FK-Ising model. As a consequence, a unified physical picture is established for the FSS behaviors in all the three representations of the Ising model above $d_c=4$.Comment: 11 pages, 12 figure

Microsurgical and tractographic anatomical study of insular and transsylvian transinsular approach

This study is to define the operative anatomy of the insula with emphasis on the transsylvian transinsular approach. The anatomy was studied in 15 brain specimens, among five were dissected by use of fiber dissection technique; diffusion tensor imaging of 10 healthy volunteers was obtained with a 1.5-T MR system. The temporal stem consists mainly of the uncinate fasciculus, inferior occipitofrontal fasciculus, Meyer’s loop of the optic radiation and anterior commissure. The transinsular approach requires an incision of the inferior limiting sulcus. In this procedure, the fibers of the temporal stem can be interrupted to various degrees. The fiber dissection technique is a very relevant and reliable method for neurosurgeons to study the details of brain anatomic features. The DTI fiber tracking technique can identify the fiber tracts of the temporal stem. Moreover, it will also help further functional study of human insula

Assessment of the sustainability of different cropping systems under three irrigation strategies in the North China Plain under climate change

The annual double-cropping system of winter wheat and summer maize requires a large amount of irrigation which has led to the rapid depletion of groundwater resources in the North China Plain (NCP). Alternate cropping systems and limited irrigation strategies should be developed for the purposes of maintaining sustainable groundwater use now and in the future. In this study, the water use and crop production of seven cropping systems under three irrigation strategies were assessed using the Agricultural Production Systems SIMulator (APSIM) during 1987-2017 as a baseline and in 2040, 2060, and 2080 under climate change conditions at a typical site in the NCP. The APSIM was calibrated and validated using field experimental data collected during 2007-2016. The seven cropping systems included the current double annual cropping system (2C/1Y) and six other reduced cropping-intensity systems with either three crops every two years (3C/2Y) or one crop per year (1C/1Y). The three irrigation strategies were full irrigation (FI), minimum irrigation (MI, only one irrigation at sowing for seedling establishment) and critical stage irrigation (CI, adding one more irrigation at the critical stage based on MI). The results showed that under current growing conditions, sustainable groundwater use could be achieved with 2C/1Y under MI, 3C/2Y and 1C/1Y under FI. However, the annual yield production was reduced by 9-22% under 3C/2Y and 54-79% under 1C/1Y compared with that under 2C/1Y. The results indicated that 2C/1Y was a better choice for crop production under similar water use. The simulated yield for future scenarios was lower than that during the baseline period; and the reduction rate varied from 2 to 11% under FI; 6-9% under CI; and 10-21% under MI, suggesting that crop production would be more negatively affected under water-limited conditions than that under full water supply condition. The annual water use of the reduced cropping systems was projected to increase because of relative high soil evaporation during the fallow period (Ef). Water use efficiency (WUE) was reduced partly due to the increased Ef. The traditional 2C/1Y under MI had the potential to sustain the groundwater balance in the region and concurrently resulted in higher grain production and WUE than that of the systems with reduced cropping intensity, both now and under climate change, and therefore, this system should be prioritized in this region

Particle Size Inversion Constrained by L∞ Norm for Dynamic Light Scattering

Particle size inversion of dynamic light scattering (DLS) is a typically ill-posed problem. Regularization is an effective method to solve the problem. The regularization involves imposing constraints on the fitted autocorrelation function data by adding a norm. The classical regularization inversion for DLS data is constrained by the L2 norm. In the optimization equation, the norm determines the smoothness and stability of the inversion result, affecting the inversion accuracy. In this paper, the Lp norm regularization model is constructed. When p is 1, 2, 10, 50, 100, 1000, and ∞, respectively, the influence of their norm models on the inversion results of data with different noise levels is studied. The results prove that overall, the inversion distribution errors show a downward trend with the increase of p. When p is larger than 10, there is no significant difference in distribution error. Compared with L2, L∞ can provide better performance for unimodal particles with strong noise, although this does not occur in weak noise cases. Meanwhile, L∞ has lower sensitivity to noise and better peak resolution, and its inverse particle size distribution is closer to the true distribution for bimodal particles. Thus, L∞ is more suitable for the inversion of DLS data

Coupling effects of urea types and subsoiling on nitrogen–water use and yield ofdifferent varieties of maize in northern China

Increasing nitrogen and water use efficiencies is most important for the agricultural sustainable development in China, especially in northern China. This paper mainly studied the coupling effects of controlled-release urea and subsoiling on nitrogen and water use efficiency, and yield. The experiment adopted a split-split plot design. Main plots were varieties, including Zhengdan 958 (Z) and Denghai 3 (D). Subplots consisted of two tillage methods: rototilling for stubble breaking (R), and subsoiling after rototilling for stubble breaking (S). Sub-subplots were N regimes: conventional urea (U), controlled-release urea (C) with the amount of 225 kg N/ha, and non-N as the control. The nitrate reductase, grain quality and straw yield, soil nitrate, and nitrogen and water use efficiency were evaluated. The results showed that, the soil nitrate content of the treatment that applied the controlled-release urea at the spike formation stage is lower than the conventional urea; however, after flowering, the soil nitrate content of the treatment that applied the controlled-release urea was significantly higher than that of the conventional urea. And the treatment that applied the controlled-release urea increased the N uptake of the aboveground portion and water use efficiency of the maize. And the treatment with subsoiling maintained a high level of nitrate reductase under the same maize varieties and urea type conditions, boosted the N uptake of the aboveground portion, and increase the water use and the biomass yield. Furthermore, under the same tillage and urea type, the biomass production of Denghai 3 was higher than Zhengdan 958. The results showed that there were significant coupling effects of urea types and subsoiling on nitrogen-water use and yield of different varieties of maize. Selecting suitable varieties and using controlled-release urea combined with subsoiling can improve the efficiency of water and nitrogen use efficiency and increase the grain yield in northern China. (C) 2012 Elsevier B.V. All rights reserved

Population structure and spatial pattern of predominant tree species in a pine–oak mosaic mixed forest in the Qinling Mountains, China

This study investigated a typical pine-oak mosaic mixed forest in the Qinling Mountains, China. In the sample plot, the population structure and spatial distribution of the stems were analyzed for the predominant species, to identify the mechanisms of species coexistence and successional trends of the forest. The population structures of all species were bimodally distributed, with young trees (DBH <1 cm) more abundant than older trees. The population structures of Quercus aliena var. acuteserrata was bimodal and rather continuous. However, Pinus tabuliformis and Pinus armandii were discontinuously bimodal, with distinct size deficiencies. Q. aliena var. acuteserrata trees were clumped throughout the plot, although those of P. tabuliformis and P. armandii were clumped at small scales. Notable negative spatial associations between Q. aliena var. acuteserrata and P. tabuliformis were found at almost scales. P. armandii and Q. aliena var. acuteserrata were negatively spatially associated at small scales but positively associated at large scales. Our findings suggest that interspecific competition gradually develops among the predominant tree species. The dynamics of the pine-oak mosaic mixed forest formed a mosaic distribution of uniformly mixed types, with the slow infiltration of Q. aliena var. acuteserrata populations that would eventually establish a pure stand