On the limitation of the van der Waals-Platteeuw-based thermodynamic models for hydrates with multiple occupancy of cavities

Thermodynamic models based on the van der Waals–Platteeuw statistical theory (Adv. Chem. Phys. 2, 1 (1959)) can be very accurate in describing hydrate equilibrium conditions, even for some occasions when multiple cavity occupancy occurs. These are cases outside the range of assumptions used for the development of the original statistical theory. However, during multiple cavity occupancy such models can perform poorly when calculating the cavity occupancies. This paper reports novel Grand Canonical Monte Carlo molecular simulations for the case of pure structure II N₂ hydrate and compares the calculated cavity occupancies with experimental data and observe reasonable agreement. Also examined are the van der Waals–Platteeuw-based modifications that retained the single-occupancy assumption of the original theory and how they perform when predicting cavity occupancies and hydrate equilibrium pressures.     

On the Motion of Substance in a Channel of a Network: Extended Model and New Classes of Probability Distributions

We discuss the motion of substance in a channel containing nodes of a network. Each node of the channel can exchange substance with: (i) neighboring nodes of the channel, (ii) network nodes which do not belong to the channel, and (iii) environment of the network. The new point in this study is that we assume possibility for exchange of substance among flows of substance between nodes of the channel and: (i) nodes that belong to the network but do not belong to the channel and (ii) environment of the network. This leads to an extension of the model of motion of substance and the extended model contains previous models as particular cases. We use a discrete-time model of motion of substance and consider a stationary regime of motion of substance in a channel containing a finite number of nodes. As results of the study, we obtain a class of probability distributions connected to the amount of substance in nodes of the channel. We prove that the obtained class of distributions contains all truncated discrete probability distributions of discrete random variable ω which can take values 0,1,⋯,N. Theory for the case of a channel containing infinite number of nodes is presented in Appendix A. The continuous version of the discussed discrete probability distributions is described in Appendix B. The discussed extended model and obtained results can be used for the study of phenomena that can be modeled by flows in networks: motion of resources, traffic flows, motion of migrants, etc.     

A new approach to pointwise heat kernel upper bounds on doubling metric measure spaces

On doubling metric measure spaces endowed with a strongly local regular Dirichlet form, we show some characterisations of pointwise upper bounds of the heat kernel in terms of global scale-invariant inequalities that correspond respectively to the Nash inequality and to a Gagliardo–Nirenberg type inequality when the volume growth is polynomial. This yields a new proof and a generalisation of the well-known equivalence between classical heat kernel upper bounds and relative Faber–Krahn inequalities or localised Sobolev or Nash inequalities. We are able to treat more general pointwise estimates, where the heat kernel rate of decay is not necessarily governed by the volume growth. A crucial role is played by the finite propagation speed property for the associated wave equation, and our main result holds for an abstract semigroup of operators satisfying the Davies–Gaffney estimates.     

A new characterization of the Berger sphere in complex projective space

We give a complete classification of Lagrangian immersions of homogeneous 3-manifolds (the Berger spheres, the Heisenberg group ${\text{Nil}}_3$, the universal covering of the Lie group $\text{PSL}(2,\mathbb{R})$ and the Lie group ${\text{Sol}}_3$) in 3-dimensional complex space forms. As a corollary, we get a new characterization of the Berger sphere in complex projective space.     

Mercury forms and their transformation in pyrite under weathering

Pyrite is considered to be the major carrier of mercury in coal. Here, the chemical characteristics of two natural pyrite samples of different weathering degrees were characterized by time-of-flight secondary ion mass spectrometry (TOF-SIMS). Thermal stability of Hg was also analyzed via temperature programmed desorption experiment (TPD). Characteristic ions such as S⁻, Fe⁺, FeS⁻, and FeS₂⁻ were detected on the surface of fresh pyrite. The release temperature of Hg ranged between 180°C and 300°C, and the characteristic peak of black HgS was recorded. In addition, abundant Fe₂O₃⁻, FeSO⁻, SO₄⁻, and HSO₄⁻ were detected on the surface of weathered pyrite, and the release temperature of Hg therein was mainly distributed at 260°C to 380°C and 520°C to 600°C, corresponding to the characteristic peaks of red HgS and HgSO₄, respectively. The results show that pyrite is acidified during weathering and that Hg forms in pyrite are transformed from the original state (HgS) to HgSO₄.     

Hecke特征值相邻极大值的均值估计

取f为权为偶数k的全模群Γ = SL(2,Z)的Hecke特征型.定义Asymmf(n)为与f关联的m阶对称幂次L-函数的Dirichlet展开式的第n个正规化系数.本文中,我们给出了Σn0为一个正数.     

离子液体/H_2O_2体系脱硫实验研究

选取四种不同种类离子液体(ILs),1-丁基-3-甲基咪唑溴化物([Bmim]Br)、1-丁基-3-甲基咪唑四氟硼酸盐([Bmim]BF_4)、1-丁基-3-甲基咪唑硫酸氢盐([Bmim]HSO_4)、1-丁基-3-甲基咪唑磷酸二氢盐([Bmim]H_2PO_4)与30%H_2O_2溶液在温和条件下对两种高硫脱灰煤样(LS、QX)进行脱硫实验研究。用化学法测定脱硫前后煤样形态硫含量,并利用傅里叶变换红外光谱(FT-IR)、X射线光电子能谱(XPS)、扫描电子显微镜(SEM)及热重(TG)对脱硫前后的煤样进行表征。结果表明,离子液体的加入使H_2O_2氧化脱硫能力增强,煤中硫铁矿硫和有机硫化物硫被显著脱除;经ILs/H_2O_2体系作用后的煤样中小粒径的颗粒减少,颗粒间的缝隙增大,煤表面的凹坑明显,热重实验结果表明,ILs/H_2O_2体系作用后的煤样相对于原煤热失重增大,部分挥发性物质释放峰温提前。