Drag on a metallic or nonmetallic particle exposed to a rarefied plasma flow

Drag force on a metallic or nonmetallic spherical particle exposed to a plasma flow is studied for the extreme case of a free-molecule regime. Analytical expressions are derived for the drag components due to, respectively, atoms, ions, and electrons and for the total drag on the whole sphere due to all the gas species. It has been shown that the drag is proportional to the square of the particle radius or the drag coefficient is independent of the particle radius. At low gas temperatures with a negligible degree of ionization, the drag is caused mainly by atoms and could be predicted by using the well-known drag expression given in ordinary-temperature rarefied gas dynamics. On the other hand, the drag is caused mainly by ions at high plasma temperatures with a great degree of ionization. The contribution of electrons to the total drag is always negligible. Ignoring gas ionization at high plasma temperatures would overestimate the particle drag. There is a little difference between metallic and nonmetallic spheres in their total drag forces, with a slightly higher value for a metallic sphere at high plasma temperatures, but usually such a small difference could be neglected in engineering calculations. The drag increases rapidly with increasing gas pressure or oncoming speed ratio. For a two-temperature plasma, the drag increases at low electron temperatures but decreases at high electron temperatures with the increase in the electron/heavy-particle temperature ratio.Nomenclature C _d Drag coefficient - e Elementary charge - f _D,F _D Local and total drag (N/m ² andN) - f ^– Velocity distribution function for incident gas particles - f ⁺ Velocity distribution function for reflected gas particles - k Boltzmann's constant - m Gas particle mass (kg) - n Number density of gas species (m ^–3) - P ^–,P ⁺ Surface pressure due to incident and reflected gas particles - R ₀ Sphere radius (m) - S Speed ratio,S _j=U/(2kT _j/m_j)^1/2 - T _e,T _h Electron and heavy-particle (atom, ion) temperature - T _w Wall temperature - U Oncoming plasma flow velocity - v _x, v_y, v_z Velocity components of gas particles in thex, y, andz directions (m/sec) - v Thermal motion speed of gas particles,v _j =(8kT _j /m _j )^1/2 - v _ze Smallestv _z of electrons which could reach the sphere surface,v _ze=(2e/m _e)^1/2 (m/sec) - v _zw Value ofv _z of ions or electrons as arriving at the sphere surface (m/sec) - Center angle - Gas density (kg/m³) - Shear stress (N/m²) - Absolute value of the floating potential (V) - , Local and total particle fluxes incident to the surface - a Atoms - e Electrons - h Heavy particles - i Ions - j jth gas species - m Metallic sphere - mn Nonmetallic sphere A preliminary version of this paper was presented at the Eighth International Symposium on Plasma Chemistry held in Tokyo, September 1987.     

The complete multi-ζ electric dipole moment matrix of π-(C6H6) Cr(CO)3 and tests of semi-empirical MO models

First, we evaluated the complete electric dipole moment matrixeZ using a multi- AO basis on Cr, C, and O centers fortheimportant, parent organometallic molecule -C₆H₆Cr(CO)₃. Second, we generated ground state LCAO-MO eigenvectors employing five commonly used semi-empirical procedures for molecules of this size which contain transition metals. Transformation of operator matrixeZ into the MO space of each of the five methods then leads us to conclude that the empirical input of Basch, Viste and Gray is most suitable. Finally, we compare the merits of several single- basis orbitals with the multi- metal orbitals.[/p]     

Synthesis, characterization and biological activity of some transition metals with Schiff base derived from 2-thiophene carboxaldehyde and aminobenzoic acid

Metal complexes of Schiff base derived from 2-thiophene carboxaldehyde and 2-aminobenzoic acid (HL) are reported and characterized based on elemental analyses, IR, 1H NMR, solid reflectance, magnetic moment, molar conductance and thermal analysis (TGA). The ligand dissociation as well as the metal-ligand stability constants were calculated pH metrically at 25 degrees C and ionic strength mu=0.1 (1M NaCl). The complexes are found to have the formulae [M(HL)2](X)n.yH2O (where M=Fe(III) (X=Cl, n=3, y=3), Co(II) (X=Cl, n=2, y=1.5), Ni(II) (X=Cl, n=2, y=1) and UO2(II) (X=NO3, n=2, y=0)) and [M(L)2] (where M=Cu(II) (X=Cl) and Zn(II) (X=AcO)). The molar conductance data reveal that Fe(III) and Co(II), Ni(II) and UO2(II) chelates are ionic in nature and are of the type 3:1 and 2:1 electrolytes, respectively, while Cu(II) and Zn(II) complexes are non-electrolytes. IR spectra show that HL is coordinated to the metal ions in a terdentate manner with ONS donor sites of the carboxylate O, azomethine N and thiophene S. From the magnetic and solid reflectance spectra, it is found that the geometrical structure of these complexes are octahedral. The thermal behaviour of these chelates shows that the hydrated complexes losses water molecules of hydration in the first step followed immediately by decomposition of the anions and ligand molecules in the subsequent steps. The activation thermodynamic parameters, such as, E*, DeltaH*, DeltaS* and DeltaG* are calculated from the DrTG curves using Coats-Redfern method. The synthesized ligands, in comparison to their metal complexes also were screened for their antibacterial activity against bacterial species, Escherichia coli, Pseudomonas aeruginosa, Staphylococcus pyogones and Fungi (Candida). The activity data show that the metal complexes to be more potent/antibacterial than the parent Schiff base ligand against one or more bacterial species.     

Quantitative Correlations for the Estimation of Thermodynamic and Molecular Properties of Pyridines and 2,2′-Bipyridyines

Standard heats of formation, entropies, ionization potentials, and molecular dipole moments of a series of pyridines have been calculated by MNDO, AM1 and PM3 methods. Linear relationship have been established which permit a priori estimation of thermodynamic and molecular characteristics of pyridines. Correlation have been found between the values of pK_a for 2,2′-bipyridines for aqueous solutions and their gas phase proton affinities.__________Translated from Khimiya Geterotsiklicheskikh Soedinenii, No. 3, 391–402, March, 2005.     

Bonferroni-type inequalities; Chebyshev-type inequalities for the distributions on [0, n]

An elementary majorant-minorant method to construct the most stringent Bonferroni-type inequalities is presented. These are essentially Chebyshev-type inequalities for discrete probability distributions on the set {0, 1,..., n}, where n is the number of concerned events, and polynomials with specific properties on the set lead to the inequalities. All the known results are proved easily by this method. Further, the inequalities in terms of all the lower moments are completely solved by the method. As examples, the most stringent new inequalities of degrees three and four are obtained. Simpler expressions of Mrgritescu's inequality (1987, Stud. Cerc. Mat., 39, 246–251), improving Galambos' inequality, are given.     

An open optimization problem in statistical quality control

We ask the experts in global optimization if there is an efficient solution to an optimization problem in acceptance sampling: Here, one often has incomplete prior information about the quality of incoming lots. Given a cost model, a decision rule for the inspection of a lot may then be designed that minimizes the maximum loss compatible with the available information. The resulting minimax problem is sometimes hard to solve, as the loss functions may have several local maxima which vary in an unpredictable way with the parameters of the decision rule.     

Some exact expressions for the mean and higher moments of functions of sample moments

Examples of exact expressions for the moments (mainly of the mean) of functions of sample moments are given. These provide checks on alternative developments such as asymptotic series for n, and simulation processes. Exact expressions are given for the mean of the square of the sample coefficient of variation, particularly in uniform sampling; Frullani integrals studied by G. H. Hardy arise. It should be kept in mind that exact results for (joint) moment generating functions (mgfs) are of interest as they produce a means of obtaining exact results for (cross) moments—including moments with negative indices. Thus an exact expression for the joint mgf of the 1st two noncentral moments can be used to obtain the mean of the (c.v.)² (but not for the mean of the c..). A general expression is given for the moment generating function of the sample variance. The limitations of Fisher's symbolic formula for the characteristic function of sample moments (or more general statistics) are noted.This research was sponsored by the Applied Mathematical Sciences Research program, Office of Energy Research, U. S. Department of Energy under contract DE-AC0584OR21400 with the Martin Marietta Energy Systems. Inc.     

Comparative Characteristics of Some Physicochemical Properties of Azoles

We have carried out a correlation analysis of some physicochemical characteristics of pyrrole, pyrazole, imidazole, triazole, and tetrazole, calculated by the semiempirical quantum-chemical AM1 method. We have found the linear dependences of the ionization potential, the dipole moment, and the acidity on the -electron excess, and also the dependence of the ionization potential on the enthalpy of formation of the studied azoles.     

Solvatochromism of 3-[2-(aryl)benzoxazol-5-yl]alanine derivatives

The photophysical properties of N-Boc-3-[2-(9-anthryl)benzoxazol-5-yl]-l-alanine methyl ester (BoxAnt) and N-Boc-3-[2-[4-(9′-(10′-butyl)anthryl)phenyl]benzoxazol-5-yl]-l-alanine methyl ester (BoxPhAnt) were studied in a series of solvents. Their absorption spectra are less sensitive to the solvent polarity than the corresponding fluorescence spectra which show a pronounced solvatochromic effect leading to large Stokes shifts. Using an efficient solvatochromic method, based on the empirical solvent polarity parameter , a large change of the dipole moment on excitation for BoxPhAnt has been found. From an analysis of the solvatochromic behaviour of the absorption and fluorescence spectra in terms of bulk solvent polarity functions, f(_r, n) and g(n), a larger excited-state dipole moment (about 8 D, ψ = 56) was obtained for BoxPhAnt than for BoxAnt (about 3 D, ψ = 0). Both applied methods gave similar values of the excited-state dipole moments for both compounds studied.     

测量圆盘转动惯量产生误差的曲线研究

结合三线摆实验的基本过程,进行实验数据的采集。利用投影法来测量圆盘的转角大小,借助于matlab的cftool工具箱,对数据进行曲线拟合,对测出来的二组数据拟合,得到转角与百分差曲线图。通过误差的大小比较,得出圆盘转动惯量测量值与理论值的百分差随转角变化最接近于三次曲线。