样条边界元法分析圆形基础板非线性非光滑接触

本文用样条边界元法分析轴对称圆形基础板的非线性非光滑接触。除事先给出外力与地基表面位移的对应关系外,地基的模型、板的厚薄(Reissner/Kirchhoff型)和外荷载沿径向的分布均可是任意的。文中将地基反力看作板的外载,对变量沿径向采用不等距祥条插值,并用无地基效应的板基本解。算例表明本文方法只要用少量自由度,便可得到令人满意的结果。     

STABILITY OF SYSTEM OF TWO-DIMENSIONAL NON-HYDROSTATIC REVOLVING FLUIDS

Applying the theory of stratification, it is proved that the system of the two-dimensional non-hydrostatic revolving fluids is unstable in the two-order continuous function class. The construction of solution space is given and the solution approach is offered. The sufficient and necessary conditions of the existence of formal solutions are expressed for some typical initial and boundary value problems and the calculating formulae to formal solutions are presented in detail.     

Anomalous rolling of spheres down an inclined plane

A sphere in air will roll down a plane that is tilted away from the vertical. The only couple acting about the point of contact between the sphere and the plane is due to the component of the weight of the sphere along the plane, provided that air friction is negligible. If on the other hand the sphere is immersed in a liquid, hydrodynamic forces will enter into the couples that turn the sphere, and the rotation of the sphere can be anomalous, i.e., as if rolling up the plane while it falls. In this paper we shall show that anomalous rolling is a characteristic phenomenon that can be observed in every viscoelastic liquid tested so far. Anomalous rolling is normal for hydrodynamically levitated spheres, both in Newtonian and viscoelastic liquids. Normal and anomalous rolling are different names for dry and hydrodynamic rolling. Spheres dropped at a vertical wall in Newtonian liquids are forced into anomalous rotation and are pushed away from the wall while in viscoelastic liquids, they are forced into anomalous rotation, but are pushed toward the wall. If the wall is inclined and the fluid is Newtonian, the spheres will rotate normally for dry rolling, but the same spheres rotate anomalously in viscoelastic liquids when the angle of inclination from the vertical is less than some critical value. The hydrodynamic mechanisms underway in the settling of circular particles in a Newtonian fluid at a vertical wall are revealed by an exact numerical simulation based on a finite-element solution of the Navier-Stokes equations and Newton's equations of motion for a rigid body.     

Electrochemical assessment of water|ionic liquid biphasic systems towards cesium extraction from nuclear waste

A room temperature ionic liquid (IL) composed of a quaternary alkylphosphonium (trihexyltetradecylphosphonium, P₆₆₆₁₄⁺) and tetrakis(pentafluorophenyl)borate anion (TB⁻) was employed within a water|P₆₆₆₁₄TB (w|P₆₆₆₁₄TB or w|IL) biphasic system to evaluate cesium ion extraction in comparison to that with a traditional water|organic solvent (w|o) combination. ¹³⁷Cs is a major contributor to the radioactivity of spent nuclear fuel as it leaves the reactor, and its extraction efficiency is therefore of considerable importance. The extraction was facilitated by the ligand octyl(phenyl)-N,N′-diisobutylcarbamoylphosphine oxide (CMPO) used in TRans-Uranium EXtraction processes and investigated through well established liquid|liquid electrochemistry. This study gave access to the metal ion to ligand (1:n) stoichiometry and overall complexation constant, β, of the interfacial complexation reaction which were determined to be 1:3 and 1.6 × 10¹¹ at the w|P₆₆₆₁₄TB interface while the study at w|o elicited an n equal to 1 with β equal to 86.5. Through a straightforward relationship, these complexation constant values were converted to distribution coefficients, δ_α, with the ligand concentrations studied for comparison to other studies present in the literature; the w|o and w|IL systems gave δ_α of 2 and 8.2 × 10⁷, respectively, indicating a higher overall extraction efficiency for the latter. For the w|o system, the metal ion-ligand stoichiometries were confirmed through isotopic distribution analysis of mass spectra obtained by the direct injection of an emulsified water–organic solvent mixture into an electron spray ionization mass spectrometer.     

Experimental validation of an effective carbon number-based approach for the gas chromatography–mass spectrometry quantification of ‘compounds lacking authentic standards or surrogates’

For the quantitative analysis of ‘compounds lacking authentic standards or surrogates’ (CLASS) in environmental media, we previously introduced an effective carbon number (ECN) approach to develop an empirical equation for the prediction of their response factor (RF). In this research, a series of laboratory experiments were carried out to benchmark the reliability of an ECN approach for sorbent tube/thermal desorption/gas chromatography (GC)/mass spectrometry (MS) applications. First, the ECN values were determined using external calibration data from 25 reference volatile organic compounds (VOCs) using two MS dectectors (quadrupole (Q) and time-of-flight (TOF)). Then, a certified standard mixture of 54 VOCs was analyzed by each system as a simulated unknown sample. The analytical bias, assessed in terms of percentage difference (PD) between the certified and ECN-predicted mass values, averaged 19.2 ± 16.1% (TOF-MS) and 28.2 ± 27.6% (Q-MS). The bias using a more simplified carbon number (CN)-based prediction increased considerably, yielding 53.4 ± 53.3% (TOF-MS) and 61.7 ± 81.3% (Q-MS). However, the bias obtained using the ECN-based prediction decreased significantly to yield average PD values of 9.84 ± 7.28% (TOF-MS) and 16.8 ± 8.35% (Q-MS), if the comparison was limited to 26 (out of 54) VOCs with CN ≥ 4 (i.e., 25 aromatics and hexachlorobutadiene).     

Structural diversity of organotin(IV) complexes self-assembled from hydroxamic acid and mono- or dialkyltin salts

Three hydroxamic acid ligands (HL₁ = acetohydroxamic acid; HL₂ = benzohydroxamic acid; HL₃ = N-phenylbenzohydroxamic acid), have been used to synthesize series of mono- or dialkyltin(IV) complexes, which include (i) the carboxyl acid hybrid five-coordinated dialkyltin complexes (C₄H₉)₂SnL₁L₄ (1), [(CH₃)₂SnL₂L₅]·0.5C₆H₆ (2), (HL₄ = acetic acid; HL₅ = benzoic acid); (ii) the six-coordinated mono-n-butyltin complexes (C₄H₉)SnL₁·Cl₂·H₂O (3), (C₄H₉)SnL₂·Cl₂·H₂O (4), [(C₄H₉)SnL₃·Cl₂·H₂O]·H₂O (5), [(C₄H₉Sn)₂(L₃)₂·Cl₂·(OCH₃)₂] (6); and (iii) the alkali metal-mingled seven-coordinated mono-n-butyltin complexes [(C₄H₉Sn)₃L₂Na]⁺·Cl⁻·(CH₃CH₂)₂O (7), [(C₄H₉Sn)₃L₂K]⁺·Cl⁻·CH₂Cl₂ (8). All complexes were characterized by elemental analyses, IR, ¹H, ¹³C, ¹¹⁹Sn NMR and X-ray single crystal diffraction. In these complexes, hydroxamic acids present bidentate coordination modes with the carbonyl O atom and the hydroxyl O atom binding to tin center. In complexes 1-6, each tin atom is coordinated by one hydroxamic acid ligand. However, in complexes 7 and 8, tin atom is surrounded by three hydroxamic acid ligands, and all hydroxyl O atoms of the ligands also bind to the alkali metal center (Na or K). This kind of organotin(IV) framework containing one alkali metal is found for the first time. Furthermore, the supramolecular structures of 1, 3, 4 and 6 have been found to consist of 1D linear molecular chains formed by intermolecular N-H···X or C-H···X (X = O, N or Cl) hydrogen bonds. For complex 2, an interesting macrocyclic tetramer has been built by the intermolecular N-H···O hydrogen bonds. Fascinatingly, two unique symmetric dimeric structures are recognized in complexes 7 and 8, which is individually bridged by intermolecular N-H···Cl and N-H···O hydrogen bonds. In addition, for 8, the dimeric cycles have been further connected into a 1D supramolecular chain.     

A new biosynthetic tracer for the inline measurement of virus retention in membrane processes: part II. Biochemical and physicochemical characterizations of the new tracer

In a previous work, a reproducible procedure to produce a new biosynthetic tracer was developed. This new tracer is an MS2 bacteriophage with enzymatic probes grafted on its surface, which can induce enzymatic activity of the tracer. In this paper, the biochemical and physicochemical characteristics of this new tracer are determined. A protocol was developed to determine the specific enzymatic activity kcat_TRACER of the tracer, which was found to be 2.93 ± 0.78 × 10⁴ min⁻¹ on average. Physicochemical characterizations of this new tracer showed that it is representative of viruses and may thus be used as a virus surrogate to assess the virus retention of membrane systems inline. Notably, the mean diameter and molecular weight of the tracer were found to be respectively 64.1 ± 0.3 nm and 12140 ± 3654 kDa, which are within the size and molecular weight ranges of pathogenic viruses carried by water. The tracer surface was also studied and revealed the considerable porosity of the grafted probe layer, with a mean porosity of 88%, which could explain why the zeta potential of the tracers (−14.34 ± 1.66 mV) was nearly the same as that of the native MS2 phages. Finally, a comparison between filtration of the reference microorganism used for membrane performance assessment (the MS2 phage) and the tracer suspensions showed the same filtration behaviour.     

Some generalizations of the Apostol-Genocchi polynomials and the Stirling numbers of the second kind

Recently, the authors introduced some generalizations of the Apostol-Bernoulli polynomials and the Apostol-Euler polynomials (see [Q.-M. Luo, H.M. Srivastava, J. Math. Anal. Appl. 308 (2005) 290-302] and [Q.-M. Luo, Taiwanese J. Math. 10 (2006) 917-925]). The main object of this paper is to investigate an analogous generalization of the Genocchi polynomials of higher order, that is, the so-called Apostol-Genocchi polynomials of higher order. For these generalized Apostol-Genocchi polynomials, we establish several elementary properties, provide some explicit relationships with the Apostol-Bernoulli polynomials and the Apostol-Euler polynomials, and derive various explicit series representations in terms of the Gaussian hypergeometric function and the Hurwitz (or generalized) zeta function. We also deduce their special cases and applications which are shown here to lead to the corresponding results for the Genocchi and Euler polynomials of higher order. By introducing an analogue of the Stirling numbers of the second kind, that is, the so-called λ-Stirling numbers of the second kind, we derive some basic properties and formulas and consider some interesting applications to the family of the Apostol type polynomials. Furthermore, we also correct an error in a previous paper [Q.-M. Luo, H.M. Srivastava, Comput. Math. Appl. 51 (2006) 631-642] and pose two open problems on the subject of our investigation.     

Multiple solutions for the laminar flow in a porous pipe with suction at slowly expanding or contracting wall

In this paper, the asymptotic solution for the similarity equation of the laminar flow in a porous pipe with suction at expanding and contracting wall has been obtained using the singular perturbation method. However, this solution neglects exponentially small terms in the matching process. To take into account these exponentially small terms, a method involving the inclusion of exponentially small terms in a perturbation series was used to find the two solutions analytically. The series involving the exponentially small terms and expansion ratio predicts dual solutions. Furthermore, the result indicates that the expansion ratio has much important influence on the solutions. When the expansion ratio is zero, it is a special case that Terrill has discussed.     

A reduced domain strategy for local mesh movement application in unstructured grids

Automatic control of mesh movement is mandatory in many fluid flow and fluid-solid interaction problems. This paper presents a new strategy, called reduced domain strategy (RDS), which enhances the efficiency of node connectivity-based mesh movement methods and moves the unstructured grid locally and effectively. The strategy dramatically reduces the grid computations by dividing the unstructured grid into two active and inactive zones. After any local boundary movement, the grid movement is performed only within the active zone. To enhance the efficiency of our strategy, we also develop an automatic mesh partitioning scheme. This scheme benefits from a new quasi-structured mesh data ordering, which determines the boundary of active zone in the original unstructured grid very easily. Indeed, the new partitioning scheme eliminates the need for sequential reordering of the original unstructured grid data in different mesh movement applications. We choose the spring analogy method and apply our new strategy to perform local mesh movements in two boundary movement problems including a multi-element airfoil with moving slat or deforming main body section. We show that the RDS is robust and cost effective. It can be readily employed in different node connectivity-based mesh movement methods. Indeed, the RDS provides a flexible local grid deformation tool for moving grid applications.