Investigation of trajectories of inviscid fluid particles in two-dimensional rotating boxes

The particle trajectories of inviscid fluid flow within two-dimensional rotating (elliptic, triangular, and square) boxes are numerically investigated. The source panel method is employed to represent the instantaneous potential interior flow field, and the Runge–Kutta method is used to track the fluid particles. The analytic solutions for the fluid trajectories for the elliptic box are used to verify the numerical accuracy of the method. The numerical error can be reduced to the level of the round-off error if the panels are properly configured and an appropriate number of panels is used. The stagnation of the particles at the corners of the triangular box is successfully predicted with this method. The corner of the square box is found to be a singularity. A logarithmic complex potential is proposed to account for the singularity, using which the stagnation of the particles at the corner in the square box is also captured. The natural frequency of the particles in the rotating elliptic box is constant throughout the flow domain, and the fluid trajectories are epitrochoidal curves. In the triangular box and the square box, the natural frequency strongly depends on the particle position, and the particle trajectories are similar to epitrochoidal curves. In general, the trajectory patterns depend only on the box rotating frequency and the natural frequency of the fluid particle motion.      

Inequalities for two type potential operators on differential forms

The purpose of this paper is to derive some strong-type inequalities for convolution type potential operator applied on differential forms. Caccioppoli-type inequalities for integral type potential operator acting on A-harmonic tensor are also obtained.     

Potential measures for spectrally negative Markov additive processes with applications in ruin theory

The Markov additive process (MAP) has become an increasingly popular modeling tool in the applied probability literature. In many applications, quantities of interest are represented as functionals of MAPs and potential measures, also known as resolvent measures, have played a key role in the representations of explicit solutions to these functionals. In this paper, closed-form solutions to potential measures for spectrally negative MAPs are found using a novel approach based on algebraic operations of matrix operators. This approach also provides a connection between results from fluctuation theoretic techniques and those from classical differential equation techniques. In the end, the paper presents a number of applications to ruin-related quantities as well as verification of known results concerning exit problems.     

Ion-specific thermodynamic properties of colloids and proteins

Franz Hofmeister established in 1888 that different salt solutions with the same ionic charges have different efficiencies in precipitating proteins from whole egg white. We will discuss how this can be understood from the modified Poisson–Boltzmann equation that accounts for ion specificity via the ion-surface non-electrostatic potential of mean force (NE-PMF) from molecular dynamics simulations. Using this approach, it is at least in principle possible to capture the important physics of the system due to the inclusion of ion-surface van der Waals forces, short range hydration, image potential and different solvent-mediated forces. The method has been proved to be efficient and suitable for describing phenomena where the water structure close to the interface plays an essential role. As an illustrative example, we demonstrate why the double layer force between two gold electrodes coated with hydrophobic self-assembled monolayers in different electrolytes can be highly ion specific. Important thermodynamic properties related to protein aggregation, essential in biotechnology and pharmaceutical industries, can be obtained from the method shown here.     

江油市河西乡附子中药材道地产地大气降尘矿物组成及其地球化学特征分析

通过X射线衍射仪,确定了江油市河西乡附子中药材道地产地大气降尘的矿物组成为伊利石、绿泥石等,且主要来源于地面扬尘、大气光化合作用;运用富集因子法、潜在生态风险评价法对该区大气降尘中重元素的富集程度进行分析,表明其近地表大气降尘中重金属元素的污染较为严重。     

烯丙基自由基(·C3H5)与一氧化氮(NO)反应势能面的理论研究

在CCSD(T)/6-311G(d,p)//B3LYP/6-311G(d,p)+ZPE水平上对反应·CHCHCH3+NO进行了计算, 并建立了其单重态的反应势能面. 在该反应中, 分别找到生成P1(CH3CHO+HCN), P2(CH3CHO+HNC), P3(CH3CN+HCHO), P4(CH3CCH+HNO)的4条产物通道, 其中·CHCHCH3和NO中的氮原子直接连接形成m1(trans-CH3CHCHNO), m1经过顺反异构形成m2(cis-CH3CHCHNO), m2再经过CCNO四元环合, 然后发生环解离, 最后生成产物P1(CH3CHO+HCN)是最可行的产物通道, 其余三条通道为次要产物通道. 该体系中生成P1的反应路径与同类体系·C2H3+NO的主要反应路径相类似, 两者的差别是前者为动力学可行的反应, 而后者为动力学不可行反应, 这使得·CHCHCH3+NO反应比·C2H3+NO反应更具有实际意义.     

Optimal Semi-Iterative Methods for Complex SOR with Results from Potential Theory

We consider the application of semi-iterative methods (SIM) to the standard (SOR) method with complex relaxation parameter ω, under the following two assumptions: (1) the associated Jacobi matrix J is consistently ordered and weakly cyclic of index 2, and (2) the spectrum σ(J) of J belongs to a compact subset Σ of the complex plane , which is symmetric with respect to the origin. By using results from potential theory, we determine the region of optimal choice of for the combination SIM–SOR and settle, for a large class of compact sets Σ, the classical problem of characterising completely all the cases for which the use of the SIM-SOR is advantageous over the sole use of SOR, under the hypothesis that . In particular, our results show that, unless the outer boundary of Σ is an ellipse, SIM–SOR is always better and, furthermore, one of the best possible choices is an asymptotically optimal SIM applied to the Gauss–Seidel method. In addition, we derive the optimal complex SOR parameters for all ellipses which are symmetric with respect to the origin. Our work was motivated by recent results of M.Eiermann and R.S. Varga.Dedicated to Professor Richard S. Varga in recognition of his substantial contributions to the subject of the paper.     

Theoretical study of the reaction of CF3O radicals with CO

The potential energy surface for the reaction of the CF₃O radicals with CO was investigated. The geometries and vibrational frequencies of the reactants, transition states, intermediates, and products were calculated at the UB3LYP/6-311+G(2d,p), UB3LYP/6-311+G(3df,2p) and UMP2/6-311+G(2d,p) levels of theory. The energies were improved by using the G2M(CC2) and G3B3 methods. The calculation suggests the reaction proceeds via either the fluorine abstraction of CF₃O by CO to produce FCO + CF₂O with a high energy barrier or the barrierless association of the reactants to form the trans-CF₃OCO intermediate. The trans-CF₃OCO is predicted to undergo subsequent isomerization to cis-CF₃OCO or dissociate directly to the products FCO + CF₂O and CF₃ + CO₂. The collisional stabilization of trans-CF₃OCO is dominant at room temperature, while trans-CF₃OCO isomerizing to cis-CF₃OCO followed by dissociating to CF₃ + CO₂ is accessible when temperature rises. The reason for only trans-CF₃OCO without cis-CF₃OCO observable in Ashen’s experiment [S.V. Ahsen, J. Hufen, H. Willner, J.S. Francisco, Chem. Eur. J. 8 (2002) 1189] is cis-CF₃OCO can be produced only via the isomerization of trans-CF₃OCO, and its yield is inappreciable at a low experimental temperature. The enthalpies of formation for the two conformations of CF₃OCO have been deduced: (trans-CF₃OCO) = −196.25 kcal mol⁻¹, (trans-CF₃OCO) = −197.46 kcal mol⁻¹, (cis-CF₃OCO) = −193.64 kcal mol⁻¹, and (cis-CF₃OCO) = −194.90 kcal mol⁻¹.     

Computing the chemical reaction path with a ray-based fast marching technique for solving the Hamilton-Jacobi equation in a general coordinate system

This article presents a ray-based fast marching approach for solving the static Hamilton-Jacobi equation. The approach is very general and can be used for both orthogonal and non-orthogonal coordinate system. The method is unconditionally stable, algorithmatically simple and highly accurate. As an application, we use the method to compute different types of reaction path. Specifically, we consider the path for which the change in action or time is less than that of all other conceivable paths connecting two states. Such reaction paths are efficiently evaluated by back-tracing on the least-action or least-time surfaces. The method is illustrated by applying it to the collinear reactions, F + H₂ →HF + H and HF + H→H + FH.     

Computation of some thermodynamic properties of nitrogen using a new intermolecular potential from molecular dynamics simulation

A new pair-potential energy function of nitrogen has been determined via the inversion of reduced viscosity collision integrals and fitted to obtain an analytical potential form. The pair-potential reproduces the second virial coefficient, viscosity, thermal conductivity, self-diffusion coefficient, and thermal diffusion factor of nitrogen in a good accordance with experimental data over wide ranges of temperatures and densities. We have also performed the molecular dynamics simulation to obtain pressure, internal energy, heat capacity at constant volume, and self-diffusion coefficient of nitrogen at different temperatures and densities using our calculated pair-potential and some other potentials. The molecular dynamics of the nitrogen molecules has been also used to determine nitrogen equation of state in two (low and high) pressure ranges. Our results are in a good agreement with experiment and literature values.