New Characterizations of the Clifford Torus as a Lagrangian Self-Shrinker

In this paper, we obtain several new characterizations of the Clifford torus as a Lagrangian self-shrinker. We first show that the Clifford torus \({\mathbb {S}}^1(1)\times {\mathbb {S}}^1(1)\) is the unique compact orientable Lagrangian self-shrinker in \({\mathbb {C}}^2\) with \(|A|^2\le 2\), which gives an affirmative answer to Castro–Lerma’s conjecture in Castro and Lerma (Int Math Res Not 6:1515–1527; 2014). We also prove that the Clifford torus is the unique compact orientable embedded Lagrangian self-shrinker with nonnegative or nonpositive Gauss curvature in \({\mathbb {C}}^2\).     

Independence of alpine meadow plants from soil organic matter for nitrogen supply: evidence from stable nitrogen isotopes

Stable nitrogen isotope signatures of major sources of mineral nitrogen (mineralization of soil organic nitrogen, biological N(2) fixation by legumes, annual precipitation and plant litter decomposition) were measured to relatively define their individual contribution to grass assimilation at the Haibei Alpine Meadow Ecosystem, Qinghai, China. The results indicated that delta(15)N values (-2.40 per thousand to 0.97 per thousand) of all grasses were much lower than those of soil organic matter (3.4+/-0.18 per thousand) and mineral nitrogen (ammonium and nitrate together, 7.8+/-0.57 per thousand). Based on the patterns of stable nitrogen isotopes, soil organic matter (3.4+/-0.18 per thousand), biological N(2) fixation (0 per thousand), and precipitation (-6.34+/-0.24 per thousand) only contributed to a small fraction of nitrogen requirements of grasses, but plant litter decomposition (-1.31+/-1.01 per thousand) accounted for 67 %.     

溶剂化的热力学集团展开理论

把二元溶液的过剩内能（ｅｘｃｅｓｓ ｅｎｅｒｇｙ）分成溶剂－溶剂、溶剂－溶质及溶质－溶质相互作用部分。利用集团展开方法给出了二元溶液在正则系综的配分函数的表达式，利用该表达式得到了溶质的偏摩尔内能（ｐａｒｔｉａｌ ｍｏｌａｒ ｅｎｅｒｇｙ）和偏摩尔熵（ｐａｒｔｉａｌ ｍｏｌａｒ ｅｎｔｒｏｐｙ）的表达式。在无限稀溶液情形，过剩偏摩尔内能的溶剂－溶剂部分又称重组织内能（ｒｅｏｒｇａｎｉｚａｔｉｏｎ ｅｎｅｒｇｙ），它反映了溶质存在时对其周围溶剂分子之间的相互作用能的影响。研究表明，在溶质的粒子数密度相对较大时，溶质分子之间的相互作用将影响过过剩偏摩尔内能的溶剂－溶剂部分，对于稀溶液，过氧偏摩尔内能的溶剂－溶剂部分与溶质的摩尔分数成线性关系。对低蜜度二元溶液，溶质的过剩偏摩尔内能和过剩偏摩尔熵也与溶质的摩尔分数成线     

The temperature intervals with global exchange of replicas empirical accelerated sampling method: parameter sensitivity and extension to a complex molecular system

The recently developed "temperature intervals with global exchange of replicas" (TIGER2) algorithm is an efficient replica-exchange sampling algorithm that provides the freedom to specify the number of replicas and temperature levels independently of the size of the system and temperature range to be spanned, thus making it particularly well suited for sampling molecular systems that are considered to be too large to be sampled using conventional replica exchange methods. Although the TIGER2 method is empirical in nature, when appropriately applied it is able to provide sampling that satisfies the balance condition and closely approximates a Boltzmann-weighted ensemble of states. In this work, we evaluated the influence of factors such as temperature range, temperature spacing, replica number, and sampling cycle design on the accuracy of a TIGER2 simulation based on molecular dynamics simulations of alanine dipeptide in implicit solvent. The influence of these factors is further examined by calculating the properties of a complex system composed of the B1 immunoglobulin-binding domain of streptococcal protein G (protein G) in aqueous solution. The accuracy of a TIGER2 simulation is particularly sensitive to the maximum temperature level selected for the simulation. A method to determine the appropriate maximum temperature level to be used in a TIGER2 simulation is presented.     

Large-scale fabrication of two-dimensional spider-web-like gelatin nano-nets via electro-netting

For the first time, two-dimensional (2D) gelatin nano-nets are fabricated by regulating the solution properties and several process parameters during electrospinning/electro-netting. The spider-web-like nano-nets that comprise interlinked one-dimensional (1D) ultrathin nanowires (10-35 nm) are stacked layer-by-layer and widely distributed in the three-dimensional (3D) porous membranes. The final morphology of the gelatin nano-nets, including nanowire diameter, area density and pore-width of the nano-nets, is highly dependent on the solution concentration, salt concentration, kinds of solvents, applied voltage, ambient temperature and relative humidity (RH). The occurrence of rapid phase separation on the splitting-film and the formation of hydrogen bond among gelatin molecules during electro-netting are proposed as the possible mechanisms for the formation of these spider-web-like nano-nets.     

State-dependent photoionization cross-sections of 3d transition metal atoms

Using the saturation method, we measured the absolute photoionization cross-sections of several excited states of titanium, vanadium, chromium, iron, and cobalt. These results are reported for the first time in this paper. The measured values range from 0.4 ± 0.1 Mb to 6.9 ± 2.0 Mb. The results show that the photoionization cross-section depends on the atomic state and not just on the electronic configuration.     

Characterization of microdroplets using optofluidic signals

We develop a simple method to determine the microdroplet features in a microfluidic chip fabricated by conventional soft lithography. Different sizes of microdroplets are generated through a typical microfluidic T-junction by adjusting the flow rates of the two immiscible liquids. Droplet size and content can be determined by monitoring the optofluidic signals reflected at the fluid-polydimethylsiloxane (PDMS) interface. The demonstrated droplet characterization system can be readily integrated with other microfluidic networks, making it promising for biochemical and biosensing applications.     

Synthesis of high‐aspect‐ratio,top‐open and ultraflat‐surface TiO2 nanotubes through double‐layered configuration

In this Letter, a novel modified anodization was utilized to synthesize high‐aspect‐ratio, top‐open and ultraflat‐surface TiO₂ nanotubes. The interruption of voltage during anodization leads to the formation of a double‐layered structure. Due to the weak mechanical connection between the upper and the underlying layer, the two parts can be easily detached. Compared with the conventional ultrasonication method to remove the clusters of nanotubes where rough surfaces resulted, this efficient and reliable strategy may facilitate further applications of TiO₂ nanotubes in diverse conditions.

     

Computing quasiconformal maps using an auxiliary metric and discrete curvature flow

Surface mapping plays an important role in geometric processing, which induces both area and angular distortions. If the angular distortion is bounded, the mapping is called a quasiconformal mapping (QC-Mapping). Many surface mappings in our physical world are quasiconformal. The angular distortion of a QC mapping can be represented by the Beltrami differentials. According to QC Teichmüller theory, there is a one-to-one correspondence between the set of Beltrami differentials and the set of QC surface mappings under normalization conditions. Therefore, every QC surface mapping can be fully determined by the Beltrami differential and reconstructed by solving the so-called Beltrami equation. In this work, we propose an effective method to solve the Beltrami equation on general Riemann surfaces. The solution is a QC mapping associated with the prescribed Beltrami differential. The main strategy is to define an auxiliary metric (AM) on the domain surface, such that the original QC mapping becomes conformal under the auxiliary metric. The desired QC-mapping can then be obtained by using the conventional conformal mapping method. In this paper, we first formulate a discrete analogue of QC mappings on triangular meshes. Then, we propose an algorithm to compute discrete QC mappings using the discrete Yamabe flow method. To the best of our knowledge, it is the first work to compute the discrete QC mappings for general Riemann surfaces, especially with different topologies. Numerically, the discrete QC mapping converges to the continuous solution as the mesh grid size approaches to 0. We tested our algorithm on surfaces scanned from real life with different topologies. Experimental results demonstrate the generality and accuracy of our auxiliary metric method.     

宽带准连续光纤激光在周期极化铌酸锂中倍频特性的研究

双包层光纤激光器和非线性光学材料(如周期性极化的铌酸锂晶体,PPLN)相结合,开辟了实用性非线性光学器件的一个新领域。研究了准相位匹配周期性极化反转铌酸锂晶体对宽带准连续光纤激光倍频的温度特性和频谱特性。在理论上,从准相位匹配相位失配关系出发,推导了晶体温度与抽运源中心波长的关系以及温度响应带宽,并和已报道实验结果进行了比较,二者符合得很好。此外,还推导了倍频周期极化铌酸锂晶体对抽运基频光源的响应谱线带宽。在实验上,采用长度20mm,极化周期6．5μm,厚度0．5mm的周期极化铌酸锂晶体光纤激光器准连续宽带输出进行了倍频,获得了在不同控制温度下的倍频光光谱,并对此进行了详细分析。