Traveling-wave solution of non-linear coupled reaction diffusion equation arising in mathematical chemistry

A simple analytical approach to find the traveling-wave solution for a set of two coupled non-linear reaction diffusion equations is reported. An exact analytical solution for traveling-waves of the Fisher equations with a general non-linearity is found. The boundary value, the boundedness and the stability of the solution are discussed. This technique is straight forward to use involving minimal algebra. Use of the method for selected case is demonstrated.     

Linear Variational Diophantine Techniques in Mass Balance of Chemical Reactions

Linear algebraic techniques based on minimization of thermodynamic functional and/or other constraints are illustrated for mass balance of chemical reactions that do not exhibit stoichiometrically unique solutions in the linear algebraic vector space. The techniques demonstrate elegant casting of chemical equations in terms of generalized linear Diophantine matrices and generalized elimination and variational schemes.     

The use of a nonlinear equation for calculation of the retention indices of polar substances in gas chromatography with linear temperature programming

New possibilities for using the equation that takes into account the nonlinear variation of parameters of the reference n-alkane scale for the calculation of retention indices of polar substances at different modes of temperature programming were considered. The advantages of this equation over the linear scale used traditionally were demonstrated in relation to C₃—C₁₁ alkan-1-ols. The equation appears to have considerable promise regarding the search for the equivalent isothermal index.     

The reactivity-selectivity principle: an imperishable myth in organic chemistry

The reactivity-selectivity principle (RSP), once a tenet of organic chemistry, eroded during the 1970s and was more or less abandoned by 1980. Although it has been clear for more than 25 years that a decrease in selectivity with increasing reactivity can only be expected with certainty if diffusion control is approached, the RSP has survived as an intuitively appealing rule. This Minireview shows why selectivity cannot generally decrease with increasing reactivity and highlights the weaknesses of the theoretical foundations of the RSP.     

Hierarchy of equations to calculate the linear spectra of molecular aggregates: Time‐dependent and frequency domain formulation

In a recent publication (Ritschel et al., J. Chem. Phys. 2015, 142, 034115) we have derived a hierarchy of coupled differential equations in time domain to calculate the linear optical properties of molecular aggregates. Here, we provide details about issues concerning the numerical implementation. In addition we present the corresponding hierarchy in frequency domain.     

Time‐dependent pair distribution functions based on Smoluchowski equation and application to an electrolyte solution

Time‐dependent pair distribution function characterizes the diffusion of pairs of molecules in liquids. In the diffusion regime, the function is described with three‐dimensional Smoluchowski equation. We propose a scheme to numerically calculate the function between polyatomic and monoatomic species based on the Smoluchowski equation. The present scheme is successfully applied to the diffusion of Ar–Ar pair in liquid Ar and ethylene carbonate (EC)‐Li⁺ pair in 1 M LiPF₆/EC electrolyte solution. © 2018 Wiley Periodicals, Inc.     

Solution of equation for a current-voltage curve describing reversible metal electrodissolution with linear boundedly semi-infinite diffusion and a linear alteration of potential in the stripping voltammetry method

An exact, sufficiently simple, explicit expression is obtained and a full contour of the stripping-voltammetry peak is calculated for a reversible process on a thin-film mercury electrode of finite thickness (linear boundedly semi-infinite diffusion is taken into account) in conditions of stripping voltammetry at a linearly altering potential. That these results were obtained at all, is due to use made of two extra boundary conditions (Nemovs and Nazarovs). The addends in the four forms of equations derived are the limiting expressions and corrections in the form of Nemovs or Nazarovs boundary conditions. It is shown that it is advisable to employ different forms of equations at large and small values of parameter H. The peaks height, full width at half-maximum, and potential are found to depend on H.Translated from Elektrokhimiya, Vol. 41, No. 1, 2005, pp. 54–68.Original Russian Text Copyright © 2005 by Nazarov, Stromberg.To the Centennial of B.N. Kabanov.Deceased.     

TheMichaelis-Menten equation in the case of enzyme-catalyzed hydrolysis of linear homopolymer substrates with different degrees of polymerization

A novel theory has been proposed allowing the derivation of the equation ofMichaelis-Menten valid in the case of enzyme-catalyzed hydrolysis of linear homopolymer substrates with varying degrees of polymerization. This equation permits the definition of the maximal rate (V) of the enzyme reaction increasing with the molecular mass of the substrate and theMichaelis-Menten constant (Km) decreasing with the increase of the number of bonds in the substrate molecule. Two new methods have been developed permitting: 1. Determination of theMichaelis-Menten constant (Km') for a single substrate bond; and 2. Calculation of the free energy ( G) required for the formation and degradation of a single enzyme-substrate complex. The theory explains a number of experimental results published by other authors.

---

Über die Gültigkeit derMichaelis-Menten-Gleichung bei der enzymkatalysierten Hydrolyse von linearen homopolymeren Verbindungen unterschiedlichen Polymerisationsgrades

Zusammenfassung Aufgrund neuer Überlegungen ist es möglich, die Gleichung nachMichaelis-Menten auf die enzymkatalysierte Hydrolyse von homopolymeren Körpern linearer Struktur mit verschiedenem Polymerisationgrad anzuwenden. Die Gleichung erlaubt die Erfassung der maximalen Enzym-Reaktionsgeschwindigkeit (V), die sich mit dem Molekulargewicht des Substrates erhöht, sowie derMichaelis-Menten-Konstante (Km), die sich mit zunehmender Anzahl von Verknüpfungen vermindert. Es wurden zwei neue Verfahren entwickelt: Erstens die Bestimmung derMichaelis-Menten-Konstante (Km') für eine Substratbindung, zweitens die Berechnung der freien Energie ( G) für die Bildung bzw. für die Zerlegung eines Enzym-Substrat-Komplexes. Die Theorie erklärt eine Reihe von Versuchsergebnissen, die von anderer Seite bereits veröffentlicht worden sind.

     

Utilization of Rohrschneider's concept and Tekler equation in linear temperature programmed GC. Precalculation of retention data

Summary An extension of Rohrschneider's concept to the field of the linear temperature programmed gas liquid chromatography, is proposed, which is based on Antoine's equation for the temperature dependence of the reduction index of Takács et al. and Tekler. The new method presented in this paper, applied to retention data of two stationary phases of low polarity, PS-255 and OV-105, gives a new possibility of precalculating retention data.     

On the application of the modeling of the relaxation spectrum to the prediction of linear viscoelastic properties of surfactant systems

 In this work, the linear viscoelastic properties of cetyl-trimethylammonium tosilate–water system are predicted by the modeling of the relaxation spectrum. The modeled spectrum of relaxation times is of the “wedge-box” type where the “wedge” portion is located at the short-time scale of relaxation times and the “box” part covers the long-time scale. The linear viscoelastic properties are calculated through the exact relationships with the suggested spectrum. Agreement between the calculated expressions and experimental data of the moduli and the stress relaxation function is found. Comparison is also made with predictions of the empirical expressions of the Cole–Cole and the Williams–Watts models. Received: 17 December 1996 Accepted: 1 July 1997     

Numerical simulation of the kinetics of ozone decomposition in an aqueous solution

The kinetic scheme for ozone decomposition in an aqueous solution in a wide pH interval was proposed on the basis of the known literature data. The apparent first-order rate constant for ozone decomposition at pH 1–14 was calculated. Published in Russian in Izvestiya Akademii Nauk. Seriya Khimicheskaya, No. 6, pp. 1151–1156, June, 2008.     

Boundary element solution of the linear Poisson-Boltzmann equation and a multipole method for the rapid calculation of forces on macromolecules in solution

The Poisson-Boltzmann equation is widely used to describe the electrostatic potential of molecules in an ionic solution that is treated as a continuous dielectric medium. The linearized form of this equation, applicable to many biologic macromolecules, may be solved using the boundary element method. A single-layer formulation of the boundary element method, which yields simpler integral equations than the direct formulations previously discussed in the literature, is given. It is shown that the electrostatic force and torque on a molecule may be calculated using its boundary element representation and also the polarization charge for two rigid molecules may be rapidly calculated using a noniterative scheme. An algorithm based on a fast adaptive multipole method is introduced to further increase the speed of the calculation. This method is particularly suited for Brownian dynamics or molecular dynamics simulations of large molecules, in which the electrostatic forces must be calculated for many different relative positions and orientations of the molecules. It has been implemented as a set of programs in C++, which are used to study the accuracy and speed of this method for two actin monomers.     

Effect of solution chemistry on the fouling potential of dissolved organic matter in membrane bioreactor systems

Dissolved organic matter (DOM) as a potent foulant in membrane bioreactor (MBR) systems has attracted great attention in recent years. This paper attempts to elucidate the effect of solution chemistry (i.e. solution pH, ionic strength, and calcium concentration) on the fouling potential of DOM with different characteristics. Results of microfiltration experiments showed that the fouling potential of DOM having higher hydrophobic content increased more markedly at low pH due to the reduced ionization of carboxylic and phenolic functional groups of aquatic humic substances. In contrast, the fouling potential of hydrophilic DOM components and the molecular size of DOM appeared to be less affected by solution pH. The more compact molecular configuration of DOM at high ionic strength contributed to form a denser fouling layer, and limited the amount of foulants retained by the membranes on the other hand. DOM fouling potential greatly increased with increasing calcium concentration. The magnitude of the increase, however, was independent of the hydrophobicity of DOM, suggesting strong interactions exist between calcium ions and hydrophilic DOM components. Moreover, it was observed that the main mechanism governing the effect of calcium ions on the molecular size of DOM transited from charge shielding to complex formation as calcium concentration increased.     

An equation for the calculation of retention indices in temperature-programmed gas chromatography with allowance for the nonlinear variation of the retention parameters ofn-alkanes

In view of the nonlinear variation of the temperature increments ofn-alkanes found previously, the accuracy of the calculations of the retention indices (I _pr) of substances in temperature-programmed capillary gas chromatography carried out in terms of six known equations was verified. A new four-parameter equation was proposed, and a general method for the calculation of its coefficients, suitable for all stationary phases, based on the adjusted retention times ofn-alkanes was suggested. The coefficients of the equation for 12 temperature variation programs were determined. Using the homologous series of methyl esters of fatty acids as an example, it was shown that the proposed equation ensures the minimum error of determination ofI _pr under various conditions. The equation also makes it possible to carry out interpolation and extrapolation calculations. The coefficients of the equation are found using the least-squares method based on data for any 4–5 referencen-alkanes. Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 2, pp. 323–327, February, 1997.     

Use of cluster expansion techniques in quantum chemistry. A linear response model for calculating energy differences

In this paper we have reviewed the theoretical framework of the coupled-cluster (cc) based linear response model as a tool for directly calculating energy differences of spectroscopic interest like excitation energy (ee), ionisation potential (ip) or electron affinity (ea). In this model, the ground state of a many-electron system is described as in a coupled cluster theory for closed shells. The electronic ground state is supposed to interact with an external photon field of frequencyw, and the poles of the linear response function as a function ofw furnish with the elementary excitations of the system. Depending on the general form of the coupling term chosen, appropriate difference energies like ee, ip or EA may be generated. Pertinent derivations of the general working equations are reviewed, and specific details as well as approximations for ee, ip or ea are indicated. It is shown that the theory bears a close resemblance to the equation of motion (eom) method but is superior to the latter in that the ground state correlation is taken to all orders and may be looked upon as essentially a variant of renormalisedtda. A perturbative analysis elucidating the underlying perturbative structure of the formulation is also given which reveals that the theory has a hybrid structure: the correlation terms are treated akin to an open shellmbpt, while the relaxation terms are treated akin to a Green function theory. A critique of the methodvis-a-vis other cc-based approaches for difference energies forms the concluding part of our review.     

Concerning the existence of linear carbon molecules in soot obtained in an electric arc

The presence of soluble linear carbon molecules in fullerene-containing soot obtained by arc spraying of graphite was confirmed by Fourier IR spectroscopy, electron diffraction, mass spectrometry, and NMR spectrometry data. Carbon chains are oriented in the layer perpendicular to the support surface and are packed in a hexagonal crystal lattice with d₁₁₀ = 4.35 Å.Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 7, pp. 1387–1390, July, 1995.The present work was supported by the Russian Foundation for Basic Research (Project Nos. 93-03-4492 and 93-03-18705).