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.     

CH4/空气简化动力学机理数值验证

选择绕圆柱预混燃烧算例，验证CH₄/空气三种简化动力学机理（16s41r、15s19r和53s325r）.考虑均匀来流，忽略湍流和湍流与燃烧相互作用以及燃料扩散效应，假设层流有限反应速率，采用保自由流5阶WENO格式求解多组分Euler方程组，得到CH₄/空气预混燃烧流场温度等值线、沿驻点线压力和温度及其CH₄、CO和CO₂质量百分数分布.结果表明：三种简化动力学机理给出的流场均出现弓形激波和火焰面，弓形激波和火焰驻点距离及其形状、诱导区宽度和简化动力学机理相关.当圆柱直径增大，弓形激波和火焰向圆柱上游移动，对应的驻点距离均增大，诱导区宽度变短，点火延时变小，但火焰和弓形激波位置次序未变化.53s325r模型要比16s41r模型和15s19r模型精度要高，点火延时覆盖的压力和温度范围也较宽，所有简化机理均未完全反应，在较大圆柱直径下游达到化学平衡.     

The contact Yamabe flow on K-contact manifolds

We use the contact Yamabe flow to find solutions of the contact Yamabe problem on K-contact manifolds.     

Heavy-Ion Collisions: Experimental Highlights

Lattice QCD predicts a phase transition between hadronic matter and a system of deconfined quarks and gluons (the Quark Gluon Plasma) at high energy densities. Our current understanding of this new state of matter will be discussed with two key results from the Relativistic Heavy Ion Collider (RHIC).     

Determination of nicotinamide by stopped-flow injection method in pharmaceutical formulations

A simple stopped-flow injection system with spectrophotometric detection was proposed for the determination of nicotinamide (NAM) in pharmaceutical formulations. In this system cyanogen chloride formed from the combination of an acidic KSCN with the NaClO streams reacts with injected NAM to form glutaconic aldehyde. Then the product of these three components was coupled with another buffered (pH 3.5) stream of barbituric acid and directed towards the detector. A 45 s after sample injection the pump was stopped for 130 s. During this time the reactants in the flow cell were provided with the required temperature (40 °C) by placing the cell in a home made cell jacket to increase the yield of the polymethine dye product. Eventually, the absorbance of the formed pink color dye was monitored spectrophotometrically at 560 nm and NAM in the concentration range of 1.0–25.0 μg/mL (R = 0.9974 and D.L = 0.5 μg/mL) was determined. The results obtained by this method were compared statistically and agree with those obtained by the method described in the British Pharmacopoeia.     

Investigation Micellar Catalysis of p-Nitrophenyl Acetate Hydrolysis with Mn(Niten)2H2O Complex

In this article, a mononuclear Mn(Niten)2H₂O complex was prepared to catalyze hydrolysis of p-nitrophenyl acetate (PNPA) in presence of Cetyltrimethylammonium bromide (CTAB) micellar system in different pH range from 6.5–10 at 25°C. These results obtained indicate that the complex exhibits good catalytic function. It also appears the complex accelerates the hydrolytic cleavage of PNPA in cationic CTAB micellar solution which may be due to coordinating ability of substrate to complex, electrostatic interaction between micelles and complex and due to electrostatic interaction between micelles with reactant.     

The first stereoselective synthesis of dendrodolide A

The first stereoselective total synthesis of natural product, dendrodolide A (1) is described from readily available (R)-propylene oxide and 3-buten-1-ol as starting materials. The synthesis was achieved in 10 steps with an overall yield of 19.1%. The key steps involved in the synthesis are Jacobsen hydrolytic kinetic resolution, epoxide ring opening with 2-allyl-1, 3-dithiane, Yamaguchi esterification, and ring-closing metathesis (RCM).     

Thermal Stability of Amorphous Solid Dispersions

Amorphous solid dispersion drug delivery systems (ASD DDS) were proved to be efficient for the enhancement of solubility and bioavailability of poorly water-soluble drugs. One of the major keys for successful preparation of ASD is the selection of appropriate excipients, mostly polymers, which have a crucial role in improving drug solubility and its physical stability. Even though, excipients should be chemically inert, there is some evidence that polymers can affect the thermal stability of active pharmaceutical ingredients (API). The thermal stability of a drug is closely related to the shelf-life of pharmaceutical products and therefore it is a matter of high pharmaceutical relevance. An overview of thermal stability of amorphous solids is provided in this paper. Evaluation of thermal stability of amorphous solid dispersion is perceived from the physicochemical perspective, from a kinetic (motions) and thermodynamic (energy) point of view, focusing on activation energy and fragility, as well all other relevant parameters for ASD design, with a glance on computational kinetic analysis of solid-state decomposition.     

Aeolian transport of sand

The airborne transport of particles on a granular surface by the saltation mechanism is studied through numerical simulation of particles dragged by turbulent air flow. We calculate the saturated flux q_s and show that its dependence on the wind strength u_* is consistent with several empirical relations obtained from experimental measurements. We propose and explain a new relation for fluxes close to the threshold velocity u_t, namely, q_s=a(u_*-u_t)^α with α≈2. We also obtain the distortion of the velocity profile of the wind due to the drag of the particles and find a novel dynamical scaling relation. We also obtain a new expression for the dependence of the height of the saltation layer as function of the strength of the wind.