A method for selection and use of numerical integration points for molecules with cylindrical symmetry

Boys and Handy [1] have discussed the solution of the bivariational equations with restricted numerical integration. One of the weaknesses of the method was that in the numerical summations over points, some points arose with r _ij= 0 and non-zero weights. This makes the method quite impractical for the Schrodinger Hamiltonian (because of the singularity at r _ij= 0), and it cannot be advantageous for the transcorrelated Hamiltonian C^–1HC because there will be some discontinuous higher derivatives at r _ij=0. Here it is shown how the symmetry of cylindrically symmetric molecules can be used to eliminate such points, without losing any of the advantages of the overall method, such as the convergence of the eigensolutions. It is also shown how the primary numerical integration points (z _i, r_i) may be chosen in any calculation such that each is associated with an equal amount of one-electron density. The choice of the angular coordinates are governed by the removal of the r _ij=0 points and maintaining the natural orthogonality between orbitals of different symmetry types. The method has been programmed and found to be practical, although no new molecular calculations have yet been performed. It is to be hoped that these points will give a basis for new transcorrelated calculations on diatomic molecules.This paper was presented during the session on numerical integration methods for molecules of the 1970 Quantum Theory Conference in Nottingham. It has been revised in the light of the interesting discussion which followed.     

Thermodynamic properties of organic compounds in aqueous solution. II. Apparent molal heat capacities of piperidines,morpholines, and piperazines

Apparent molal heat capacities of some piperidine, morpholine, and piperazine derivatives in aqueous solution have been determined by adiabatic calorimetry in the temperature range 20–55°C and in the molality range 0.2–1m. Comparison of experimental values with those calculated through group contributions, found for monofunctional compounds, indicates strong interactions between the hydrophilic centers. An interpretation is given of the possible mechanism of this interaction. Also, values of ΔC _p for the addition reaction of proton to nitrogen centers of mono- and bifunctional organic compounds are examined.     

Heat conductivity of three periodic Hard Disks via nonequilibrium molecular dynamics

We use a driving field, of the type first suggested by Evans, to generate a steady heat current in the simplest possible system, a two-dimensional periodic fluid of three hard disks. Hard-disk motion equations can be conveniently derived from repulsive constant-force or linear-force potentials by considering the infinitely repulsive limit of these potentials. We show that the isoenergetic and isokinetic forms of the nonequilibrium equations of motion generate steady-state heat conductivities differing by terms of order 1/N, whereN is the number of particles. The resulting conductivities appear to vary as the logarithm of the driving field strength. Even at low fields, the three-body periodic-system results lie well below Enskog's infinite-system prediction.     

The thermodynamics of proton dissociation of adenine

The thermodynamic quantities associated with ionization of the N₁ and N₉ protons of adenine have been calorimetrically determined as a function of temperature. The H values for proton dissociation of these groups, with pK values of 4.19 and 9.92, were found to be 5.1 and 9.1 kcal/mole, respectively, at 25°C, =0.025. The C _p values for proton dissociation of these groups were estimated to be –11 and –17 cal/mole-deg. These results indicate that the large heat capacity changes observed during conformational transitions of polynucleotides are not the result of ionization of the bases.     

Non isothermal heat capacities and chemical reactions using a modulated DSC

An evaluation of measurements of heat capacities by modulated differential scanning calorimetry, MDSC is presented. Heat capacities were obtained from 130 to 550 K by a non isothermal technique in which a periodic modulation was added to the linear heating rate. Effects of amplitude and period of modulation, sample weight, sample type, pan type, and cell imbalance are described. Results are compared with those obtained using the isothermal technique. Heat capacity could be measured well into the decomposition region and separated from the non reversing signal due to chemical reaction (degradation), thus allowing a precise detection of onsets of the thermal degradation. This additional information will aid in the interpretation of the degradation chemistry, a field vital for the petroleum-industry.Dedicated to Professor Bernhard Wunderlich on the occasion of his 65th birthdayPart of this paper was presented at the 23rd Conference of the North American Thermal Analysis Society, Toronto, Canada, September 25–28, 1994.The author (MVN) acknowledges the experimental assistance provided by J. Balogh of Exxon Research and Engineering Company, Linden. Helpful discussions with A. Boller of the University of Tennessee at Knoxville, Dr. Y. Jin, General Electrical, and Dr. S. Sauerbrunn formerly of TA Instruments are also acknowledged.     

流道缩扩比对半波纹微通道流动和传热特性的影响

为探究流道缩扩比对半波纹微通道流动和传热特性的影响,设计了5种不同缩扩比的半波纹微通道模型,并对各通道内的层流流动(200＜Re＜1000,Re为雷诺数)和传热进行了数值模拟研究。结果表明,半波纹微通道的压降和努塞尔数随着流道缩扩比的减小而增大;与光滑微通道相比,半波纹微通道具有更优的传热性能但压降损失也更高;引入η作为综合性能指标,发现减小流道缩扩比是提高半波纹微通道综合换热能力的有效方式,且当Re＞490时,其综合换热能力均优于光滑微通道。     

Calibration of a multi-mobile coil magnetic manipulation system utilizing a control-oriented magnetic model

In this paper, we address the calibration of a family of magnetic manipulation systems composed of several coils that are moved around by serial robot manipulators. We show in this paper that the calibration of the whole system ultimately results in calibrating the manipulator and coil separately up to an unknown rigid transformation. For calibration of the coil, we propose to use a model that has not been used so far in the literature; a control-oriented model which is sufficiently accurate and computes the magnetic field in real time. A protocol for calibrating the magnetic manipulation system using the Nelder–Mead algorithm to estimate the model parameters is presented. Calibration was performed through simulations and validated experimentally on a physical system. It was observed that the root mean square error was reduced by 37% after calibration of the physical system, indicating an improvement in accurately estimating the magnetic model.     

Optimal error estimates of a locally one-dimensional method for the multidimensional heat equation

For the multidimensional heat equation in a parallelepiped, optimal error estimates inL ₂(Q) are derived. The error is of the order of +¦h¦² for any right-hand sidef L ₂(Q) and any initial function ; for appropriate classes of less regularf andu ₀, the error is of the order of ((+¦h¦² ), 1/2<1.Translated fromMatematicheskie Zametki, Vol. 60, No. 2, pp. 185–197, August, 1996.     

Wiener's test for space-time random walks and its applications

This paper establishes a criterion for whether a -dimensional random walk on the integer lattice visits a space-time subset infinitely often or not. It is a precise analogue of Wiener's test for regularity of a boundary point with respect to the classical Dirichlet problem. The test obtained is applied to strengthen the harder half of Kolmogorov's test for the random walk.

     

Thermodynamics of liquid mixtures containing n-alkanes and strongly polar components: VE and C P E of mixtures with either pyridine or piperidine

Excess molar volumes V _E and excess molar heat capacities C _P ^/E at constant pressure have been obtained, as a function of mole fraction x₁, for several binary liquid mixtures belonging either to series I: pyridine+n-alkane (C_lH_2l+2), with l=7, 10, 14, 16, or series II: piperidine+n-alkane, with l=7, 8, 10, 12, 14. The instruments used were a vibrating-tube densimeter and a Picker flow microcalorimeter, respectively. V ^E of pyridine+n-heptane shows a S-shaped composition dependence with a small negative part in the region rich in pyridine (x₁>0.90). All the other systems show positive V ^E only. The excess volumes increase with increasing chain length l of the n-alkane. The excess molar heat capacities of the mixtures belonging to series II are all negative, except for a small positive part for piperidine+n-heptane in the region rich in piperidine (x₁>0.87). The C _P ^/E at the respective minima, C _P ^/E (x_1,min ), become more negative with increasing l, and the x_1,min values range from about 0.26 (l=7) to 0.39 (l=14). Most interestingly, mixtures of series I exhibit curves of C _P ^/E against x₁ with two minima and one maximum, the so-called W-shape curves.Dedicated to Professor A. Néckel on the occasion of his 65^th birthday. Communicated in part at the XVII^èmes Journées de Calorimétrie, d'Analyse Thermique et de Thermodynamique Chimique, Ferrara, Italy, 27–30 October, 1986.