Dynamics of the formation of two-dimensional ordered structures

The growth of ordered domains in lattice gas models, which occurs after the system is quenched from infinite temperature to a state below the critical temperatureT _c, is studied by Monte Carlo simulation. For a square lattice with repulsion between nearest and next-nearest neighbors, which in equilibrium exhibits fourfold degenerate (2×1) superstructures, the time-dependent energy E(t), domain size L(t), and structure functionS(q, t) are obtained, both for Glauber dynamics (no conservation law) and the case with conserved density (Kawasaki dynamics). At late times the energy excess and halfwidth of the structure factor decrease proportional tot ^–x, whileL(t) t ^x, where the exponent x=1/2 for Glauber dynamics and x1/3 for Kawasaki dynamics. In addition, the structure factor satisfies a scaling lawS(k,t)=t ^2xS(kt^x). The smaller exponent for the conserved density case is traced back to the excess density contained in the walls between ordered domains which must be redistributed during growth. Quenches toT>T _c, T=T_c (where we estimate dynamic critical exponents) andT=0 are also considered. In the latter case, the system becomes frozen in a glasslike domain pattern far from equilibrium when using Kawasaki dynamics. The generalization of our results to other lattices and structures also is briefly discussed.     

RELATIONSHIPS BETWEEN X—H STRETCHING OVERTONE FREQUENCIES AND BOND LENGTHS/BOND ANGLES

A relationship between the X-H (X = N, O, C, and so on) equilibrium bond length in a Morse oscillator and the X-H stretching overtone frequency shifts is obtained theoretically. We use the equation to discuss the empirical linear relationships that have been proposed for heterocyclics, alkanes and fluorinated benzenes. On the other hand, a unified relationship between the X-H bond angles and the experimental quantities (ω(?) and the coupling strength λ) is also presented for XH2, XH, and XH4 molecules or molecular fragments. Calculations of X-H bond angles for a number of molecules show that the results from our equations are in excellent agreement with the experimental values. Also we can extract the information of relative magnitude of bond coupling force field.     

Capillary electrophoresis separation of heterocyclic nitrosoamino acid-conformers at sub-ambient temperatures

The separation of a selected group of naturally occurring, heterocyclic nitrosoamino acids was achieved by capillary zone electrophoresis and the resolution of the syn and anti conformers improved as the temperature was lowered to 5 °C. The double peaks observed for each nitrosoamino acid are probably caused by the slow kinetics of conformational isomerism. The experimental setup consisted of a P/ACE 5510 electrophoresis system, a 57 cm polyacrylamidecoated capillary, and a 10 mM phosphate buffer, pH 7.2, containing 2 mM of 3-(N-N-dimethylmyristylammonio)propanesulfonate (DMMAPS) and 0.1% Tween 20. Our study shows that (a) the lower the temperature, the greater the resolution and the longer the migration times; and (b) different nitrosoamino acid conformers were resolved at different temperatures because of differences in the rate of isomerization. For example, the conformers of N-nitrosothiazolidine-4-carboxylic acid were partially resolved at 30 °C while those of N-nitrosoproline were well resolved at the same temperature.     

Functionalized naphthol[2,3-h] quinoline-7,12-diones

The addition of secondary and primary amines to ethyl (1-amino-9,10-anthraquinon-2-yl)propynoate affords an easily separable mixture of the corresponding ethyl 3-dialkylaminoor 3-alkylamino-3-(1-amino-9,10-anthraquinon-2-yl)acrylate and 3-dialkylamino- or 3-alkylaminonaphthol[2,3-h]quinoline-2(1H), 7,12-trione (in ∼4: 1 ratio). Intramolecular cyclization of the resulting substituted ethyl acrylates results in the formation of 4-dialkylaminoor 4-alkylamino-2-chlorinated pyridine rings. Subsequent nucleophilic substitution of the chlorine atom gives 2-functionalized 4-dialkylamino- or 4-alkylaminonaphtho[2,3-h]quinoline-7,12-diones. Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 11, pp. 2327–2332, November, 1998.     

Modeling and simulation of free radical polymerization of styrene under semibatch reactor conditions

The first part of this approach is concerned with the elaboration of a radical polymerization model of styrenne, based on a kinetic diagram that includes chemical and thermal initiation, propagation, termination by recombination and chain transfer to the monomer. Furthermore, volume contraction during polymerization is considered, as well as the gel and glass effects. The mathematical formalism that describes the model in terms of moments is explored in detail. The model was then used to predict the changes in monomer conversion and molecular weight after intermediate addition of initiator and monomer. The results of this operation are dependent on the conditions of the reaction mass, quantity, and moment of substance addition. Therefore, the simulations were performed at different times with respect to the gel effect; before, during and after this phenomenon, and also with respect to different temperatures and initiators. Increasing the initiator concentration before the gel effect leads to an earlier appearance of the phenomenon and to a decrease in molecular weight. The ratio reveals a polydispersity index smaller for the intermediate addition of initiator. No significant changes take place during or after the gel effect. If along with the initiator, unreacted monomver (used to dissolve the initiator) enters the reactor, a small dip in conversion is observed. The general conclusion of this paper reveals the intermediate addition of initiator as a method to control polymer properties and to prevent the “dead-end” polymerization of styrene.     

Preparation and characterization of Mg(II)-, Ca(II) and Cd(II) complexes of 1,2-ethanediol and water

Mixed ligand complexes of different compositions were prepared with water, sulfate ion and 1,2-ethanediol as ligand. IR spectra and the thermoanalytical curves of the complexes were recorded. Oxygen atoms bound by one or two coordinate bonds to the metal ion, or by hydrogen-bonds in the crystal, were observed. As for the water molecule, 1,2-ethanediol molecules of crystal and monohydrate type were found, depending on the type of binding of the oxygen atoms.This revised version was published online in November 2005 with corrections to the Cover Date.     

Cost operator algorithms for the transportation problem

A primal transportation algorithm is devised via post-optimization on the costs of a modified problem. The procedure involves altering the costs corresponding to the basic cells of the initial (primal feasible) solution so that it is dual feasible as well. The altered costs are then successively restored to their true values with appropriate changes in the optimal solution by the application of cell or area cost operators discussed elsewhere. The cell cost operator algorithm converges to optimum within (2T – 1) steps for primal nondegenerate transportation problems and [(2T + 1) min (m, n)] – 1 steps for primal degenerate transportation problems, whereT is the sum of the (integer) warehouse availabilities (also the sum of the (integer) market requirements) andm andn denote the number of warehouses and markets respectively. For the area cost operator algorithm the corresponding bounds on the number of steps areT and (T + 1) min (m, n) respectively.This report was prepared as part of the activities of the Management Sciences Research Group, Carnegie—Mellon University, under Contract N00014-67-A-0314-0007 NR 047-048 with the U.S. Office of Naval Research.     

A central limit theorem for age- and density-dependent population processes

Consider a population consisting of one type of individual living in a fixed region with area A. In [8], we constructed a stochastic population model in which the death rate is affected by the age of the individual and the birth rate is affected by the population density P_A(t), i.e., the population size divided by the area A of the given region. In [8], we proposed a continuous deterministic model which in general is a nonlinear Volterra type integral equation and proved that under appropriate conditions the sequence P_A(t) would converge to the solution P(t) of our integral equation in the sense that

$\text{lim}\text{→∞}\text{P}\text{sup}\text{0?s?t}\text{|P}{}_{\mathrm{A}}\text{(s) ? P(s)|>ε}\text{=0}\text{for every}\text{ε > 0}$

.In this paper, we obtain a “central limit theorem” for the random element √A(P_A(t)?P(t)). We prove that under appropriate conditions √A(P_A(t)?P(t)) will converge to a Gaussian process. (See Theorem 3.4 for the explicit formula of this Gaussian process.)     

Optimization of an electrolytic conductivity detector for determination of toxic nitrogen-containing food contaminants separated by open tubular column gas chromatography

The combination of open tubular column gas chromatography with electrolytic conductivity detection has been evaluated for the determination of nitrogen-containing pesticide residues in food extracts. Optimization of the column position at the column-detector interface was crucial to the successful operation of the detector. The signal-to-noise ratio and response stability of the detector are greatly influenced by the composition of the electrolyte solvent. Large volume splitless injections using retention gaps and optimized detector operating conditions enabled pesticide residues in food extracts to be determined at sub parts-per-million levels. Although the electrolytic conductivity detector is less sensitive than the thermionic ionization detector, its greater nitrogen selectivity can he crucial to the determination of nitrogen-containing contaminants in food extracts, particularly in complex mixtures where phosphorus-containing contaminants or matrix compounds are also present.     

A study of the polarographic behaviour of meso-tetra(4-trimethylammoniumphenyl)porphine and its copper and magnesium complexes and its analytical applications

The investigation of the electrochemical reduction and the adsorption of meso-tetra(4-trimethylammoniumphenyl)porphine (T(4-TMAP)P) at a mercury electrode in alkaline solution shows that the overall reduction involves three two-electron steps, of which the first step is reversible and the latter two are irreversible. In addition, T(4-TMAP)P and its metal complexes of Cu(II) and Mg(II) can be strongly adsorbed on the surface of a mercury electrode. The adsorption phenomena have been utilized as a preconcentration step for the determination of trace amounts of the two ions by single sweep polarography. For copper, the detection limit is 1 × 10^–8 mol dm^–3, for magnesium, 1 × 10^–7 mol dm^–3, the latter being limited by the reagent blank. The proposed method was applied to the determination of Cu and Mg in various types of samples (chemicals, hair and liver tissues) with satisfactory results.