Comparative analysis of variational iteration method and Haar wavelet method for the numerical solutions of Burgers–Huxley and Huxley equations

In this paper, variational iteration method is applied to compute the numerical solutions of non-linear partial differential equations like Huxley and Burgers–Huxley equation. The approximate solutions of the Huxley and Burgers–Huxley equations are compared with the Haar wavelet solution as well as with the exact solutions. The present method is very simple, effective and convenient analytical method with small computational overhead.     

Potential energy surfaces for the benzene–rare gas systems

A harmonic expansion representation of the intermolecular interaction has been exploited to obtain the potential energy surface (PES) for the C₆H₆–He, –Ne, –Ar, –Kr and –Xe systems in an analytical form. Basic data employed are binding energy, equilibrium distance and long-range attraction predicted by a semi-empirical method for selected configurations of the complexes. For those favorable cases where additional information are available the proposed PESs exhibit features in good agreement with those derived from spectroscopy and scattering experiments and/or ab initio calculations. The availability of realistic PESs expressed in an analytical form opens new perspectives of calculations in molecular dynamics and spectroscopic simulations where the benzene molecule and rare gas atoms are involved.     

Formation of the layering boundary in the water–benzene–perfluorobenzene system

The dynamics of the interface between liquid phases in the water–benzene–perfluorobenzene system was studied in a natural experiment. The interfacial tension was found to depend on the density of the organic layer. The range of interfacial tensions in which inversion of the organic and aqueous phases takes place was determined, and the working range of a separating flask as an element of the separation scheme for the mixture was revealed.     

Chemical dosimetry system for γ-ray irradiation based on the formation of phenol from aqueous benzene solutions

A chemical dosimetry system based on the radiochemical formation of phenol from aqueous benzene solutions was applied to measure the intensity of γ-ray irradiation. Using a simple and sensitive isocratic fluorometric HPLC system, radiochemically generated phenol was determined. The radiochemical formation of phenol was linear up to 100 Gy and the lower limit of detection calculated from the detection limits of phenol was estimated to be 7 mGy. The phenol formation rates were not affected by the oxygen saturation. The chemical dosimetry system investigated in this study was sensitive and was easier to use than traditional chemical dosimeters.     

Multiple Hydrogen Bonding Enables the Self-Healing of Sensors for Human–Machine Interactions

Despite its widespread use in signal collection, flexible sensors have been rarely used in human–machine interactions owing to its indistinguishable signal, poor reliability, and poor stability when inflicted with unavoidable scratches and/or mechanical cuts. A highly sensitive and self-healing sensor enabled by multiple hydrogen bonding network and nanostructured conductive network is demonstrated. The nanostructured supramolecular sensor displays extremely fast (ca. 15 s) and repeatable self-healing ability with high healing efficiency (93 % after the third healing process). It can precisely detect tiny human motions, demonstrating highly distinguishable and reliable signals even after cutting–healing and bending over 20 000 cycles. Furthermore, a human–machine interaction system is integrated to develop a facial expression control system and an electronic larynx, aiming to control the robot to assist the patient's daily life and help the mute to realize real-time speaking.     

Dispersive Liquid–Liquid Microextraction for the Preconcentration of Multiple Classes of Pesticides in Water

A simple, rapid, efficient, and environmentally friendly method was developed for the preconcentration of atrazine, simazine, diuron, bentazone, tebuconazole, and fipronil from water. Dispersive liquid–liquid microextraction was employed with determination by liquid chromatography–tandem mass spectrometry. The volumes of extraction and disperser solvents, the concentration of sodium chloride, and the pH were optimized by response surface methodology. The optimum conditions involved the use of 150 µL of 1:1 (v/v) monochlorobenzene:dichlorobenzene as the extraction solvent, 2 mL acetonitrile as the disperser solvent, and 10 mL of sample at pH 3.0. The accuracy was evaluated in terms of recovery values that were from 54 to 112%. The relative standard deviations ranged from 4 to 27%. The limits of quantification were between 0.005 and 0.05 µg L^?1. The optimized method had low matrix effects for the analytes and the results demonstrated application for the determination of pesticides in water.     

Analytic solutions to a family of Lotka–Volterra related differential equations

An initial formal analysis of the analytic solution (C.M. Evans and G.L. Findley, J. Math. Chem. 25 (1999) 105–110.) to the Lotka–Volterra (LV) dynamical system is presented. A family of firstorder autonomous ordinary differential equations related to the LV system is derived, and the analytic solutions to these systems are given. Invariants for the latter systems are introduced, and a simple transformation which allows these systems to be reduced to Hamiltonian form is provided.     

The use of the cohen–turnbull model for calculation of the self-diffusion coefficients of liquid dichloroalkanes

The paper presents the self-diffusion coefficients calculated for liquid dichloroalkanes C₆H₁₂Cl₂, C₈H₁₆Cl₂, C₁₀H₂₂Cl₂ and C₁₂H₂₄Cl₂, with the use of the Cohen and Turnbull model. Determination of self-diffusion coefficients permits a separate analysis of intra- and intermolecular motions and provides information on geometrical and dynamical properties of molecules. The self-diffusion coefficients of selected dichloroalkanes have been determined by X-ray diffraction and compared with the corresponding NMR results. The suitability of the Cohen–Turnbull model of the translating motion for prediction of self-diffusion coefficients for molecules whose shape significantly differs from the spherical symmetry is analysed. Angular distributions of X-ray scattered intensity were measured, and differential radial distribution functions of electron density (DRDFs) were calculated. The mean coordination numbers were obtained from the area delimited by the minima of the DRDFs, and their dependence on the length of the methylene chain is also presented subsequently. On the basis of the DRDFs the average free volume of the molecules and total free volume of the liquids were calculated. The activation volume of the diffusion was found to make about 0.6 of the van der Waals volume of the molecule. As expected the diffusion coefficients decrease with increasing molecular weight. The equation relating the self-diffusion coefficient with the volume of the coordination spheres in the liquid has been derived.     

Weighted pseudo almost automorphic classical solutions and optimal mild solutions for fractional differential equations and application in fractional reaction–diffusion equations

In this paper, we are concerned with a class of fractional differential equations given by $$\begin{aligned} \hbox {D}_{t}^{\alpha }x(t)=Ax(t)+f(t,x(t)). \end{aligned}$$ Our main results concern the existence, uniqueness of weighted pseudo-almost automorphic classical solutions and optimal mild solutions. Moreover, as example and applications, we study the weighted pseudo-almost automorphic classical solutions and optimal mild solutions for a fractional reaction–diffusion equation to illustrate the practical usefulness of the analytical results that we establish in the paper.     

A supramolecular polymerisation model for the structurisation of DNA–lipid complexes

Complexes formed by DNA and lipid mixtures have great interest for the assessment of self-assembling mechanisms in open biological systems. X-ray diffraction has revealed that minor alterations of the cationic/neutral lipid composition produced major alterations to the liquid crystalline structure and the hydration of the complexes. We have extended to these systems by an approach based on the identification of a fundamental repeating unit that grows according to the general principles of supramolecular polymerisation and liquid crystallinity. Structural reorganisations that optimise the electrostatic and hydrophobic compensation are enhanced by competition between the rigidity of the polyelectrolyte and the cohesion of the lipid assembly. The non-hydrated hexagonal structure revealed by X-ray examination is represented by a dendritic-type supramolecular polymerisation of DNA units decorated by the aliphatic tails of dissociated liposomes. An increase in the cationic/neutral lipid component ratio enhances the stability of planar bilayers, favouring the formation of the partly hydrated lamellar structure revealed by X-ray diffraction.     

Polymer–surfactant interaction for controlling the rheological properties of aqueous surfactant solutions

Controlling viscosity of aqueous surfactant solutions is very important for practical formulations. This can be done by having polymers interact with surfactants, thereby forming interconnected physical networks, where main ways of interaction are electrostatic and hydrophobic forces. Polymer–surfactant interactions are long established for viscosity control, but there are many ongoing activities. They are driven by wanting more biocompatible systems, which depend intricately on the choice of surfactant and polymer, and general predictions are not simple for such systems. Surfactants form spherical or wormlike micelles or vesicles. By choice of (co)polymers one can construct systems responsive to external parameters, like temperature or pH, for having tailored rheological properties. Here we describe recent developments with a focus on systems of low concentration, being interesting for applications. In summary, rheological control of polymer–surfactant systems is a versatile topic and a field of colloid science with high relevance for practical formulations.     

Quadratically convergent algorithm for orbital optimization in the orbital-optimized coupled-cluster doubles method and in orbital-optimized second-order Møller-Plesset perturbation theory

Using a Lagrangian-based approach, we present a more elegant derivation of the equations necessary for the variational optimization of the molecular orbitals (MOs) for the coupled-cluster doubles (CCD) method and second-order M?ller-Plesset perturbation theory (MP2). These orbital-optimized theories are referred to as OO-CCD and OO-MP2 (or simply "OD" and "OMP2" for short), respectively. We also present an improved algorithm for orbital optimization in these methods. Explicit equations for response density matrices, the MO gradient, and the MO Hessian are reported both in spin-orbital and closed-shell spin-adapted forms. The Newton-Raphson algorithm is used for the optimization procedure using the MO gradient and Hessian. Further, orbital stability analyses are also carried out at correlated levels. The OD and OMP2 approaches are compared with the standard MP2, CCD, CCSD, and CCSD(T) methods. All these methods are applied to H(2)O, three diatomics, and the O(4)(+) molecule. Results demonstrate that the CCSD and OD methods give nearly identical results for H(2)O and diatomics; however, in symmetry-breaking problems as exemplified by O(4)(+), the OD method provides better results for vibrational frequencies. The OD method has further advantages over CCSD: its analytic gradients are easier to compute since there is no need to solve the coupled-perturbed equations for the orbital response, the computation of one-electron properties are easier because there is no response contribution to the particle density matrices, the variational optimized orbitals can be readily extended to allow inactive orbitals, it avoids spurious second-order poles in its response function, and its transition dipole moments are gauge invariant. The OMP2 has these same advantages over canonical MP2, making it promising for excited state properties via linear response theory. The quadratically convergent orbital-optimization procedure converges quickly for OMP2, and provides molecular properties that are somewhat different than those of MP2 for most of the test cases considered (although they are similar for H(2)O). Bond lengths are somewhat longer, and vibrational frequencies somewhat smaller, for OMP2 compared to MP2. In the difficult case of O(4)(+), results for several vibrational frequencies are significantly improved in going from MP2 to OMP2.     

On the predictions and limitations of the Becker-Döring model for reaction kinetics in micellar surfactant solutions

We investigate the breakdown of a system of micellar aggregates in a surfactant solution following an order-one dilution. We derive a mathematical model based on the Becker-D?ring system of equations, using realistic expressions for the reaction constants fit to results from Molecular Dynamics simulations. We exploit the largeness of typical aggregation numbers to derive a continuum model, substituting a large system of ordinary differential equations for a partial differential equation in two independent variables: time and aggregate size. Numerical solutions demonstrate that re-equilibration occurs in two distinct stages over well-separated timescales, in agreement with experiment and with previous theories. We conclude by exposing a limitation in the Becker-D?ring theory for re-equilibration of surfactant solutions.     

The variational iteration method for solving the Volterra integro-differential forms of the Lane–Emden equations of the first and the second kind

In this paper, we establish the Volterra integro-differential forms of the Lane–Emden equations. We use the variational iteration method (VIM) to effectively treat these forms. The Volterra integro-differential forms of the Lane–Emden equations overcome the singular behavior at the origin $x=0$ and do not use a variety of Lagrange multipliers. Several numerical examples are examined to show the validity of the integro-differential forms.     

Use of the three-phase model and headspace analysis for the facile determination of all partition/association constants for highly volatile solute–cyclodextrin–water systems

A versatile method for measuring the partition coefficients of volatile analytes with an aqueous pseudophase using headspace gas chromatography is reported. A “three-phase” model accounts for all equilibria present in the system, including the partitioning of the analyte in the gas and aqueous phases to the pseudophase. This method is applicable to a wide variety of volatile analytes and aqueous pseudophases, providing that sufficient pseudophase may be used to reduce the analyte partial pressure. Generally, the method offers good reproducibility and high sensitivity. The associations of five volatile analytes (hydrogen sulfide, methanethiol, dimethyl sulfide, dichloromethane, and ethyl ether) with various cyclodextrins were examined. All analytes were found to partition preferentially to the cyclodextrin pseudophase compared to the aqueous phase. In addition, several analyte–cyclodextrin combinations formed insoluble complexes in solution that enhanced the extraction of the analyte from the gas and aqueous phases. Derivatization of the cyclodextrins generally decreased the extent of analyte–cyclodextrin interaction.     

Study of phase behaviour for the aqueous two-phase polymer–polymer systems using the modified UNIQUAC-NRF model

A modified form of the UNIQUAC-NRF activity coefficient model was used to study the phase behaviour of the aqueous two-phase systems (ATPSs) of polyethylene glycol (PEG) and dextran (DEX) with different molecular weights at various temperatures. In the proposed model, a ternary interaction parameter was added to the expression for the excess Gibbs free energy and, in turn, to the corresponding activity coefficient rendered by the UNIQUAC-NRF model. The combinatorial part of the new model takes the same form as that of the original UNIQUAC model and the residual part considers the nonrandomness and also the binary and the ternary interactions among the molecules in mixtures of PEG, DEX, and water. The results show that the new model can more accurately correlate the experimental data for the systems studied in this work than those obtained from the original UNIQUAC and the UNIQUAC-NRF activity coefficient models. In order to favourably compare the results the same minimisation procedure and the same experimental data were used for the models studied in this work. The results for the Root Mean Square Deviations (RMSD) produced by the three UNIQUAC-based models are also reported.     

Preparation of thorium oxalate–silica sorbent and its application for the sorption of americium from aqueous solutions

A new sorbent, thorium oxalate incorporated in silica gel matrix was prepared. This material was characterized by X-ray, Thermo-gravimetric Analysis, surface area and porosity analysis. The material was obtained in the form of granular particles in the mesh size range of 80–150 American Standard of Testing Materials, yielding good liquid flow, when packed in ion exchange column. This sorbent was investigated for the sorption of americium from various aqueous media such as nitric acid, oxalic acid and sulphuric acid by distribution coefficient studies. Column experiments were carried out to study the practical application of this sorbent for removal of americium from oxalic acid-nitric acid solutions. Elution studies were also carried out for the recovery of americium.     

Fluorescence enhancement of the protein–curcumin–sodium dodecyl benzene sulfonate system and protein determination

Protein can greatly enhance the fluorescence of curcumin (CU) in the presence of sodium dodecyl benzene sulfonate (SDBS). Experiments indicate that under the optimum conditions, the enhanced intensity of fluorescence is proportional to the concentration of proteins in the range of 0.0050–20.0 μg mL⁻¹ for bovine serum albumin (BSA), 0.080–20.0 μg mL⁻¹ for human serum albumin (HSA), and 0.040–28.0 μg mL⁻¹ for egg albumin (EA). Their detection limits (S/N=3) are 1.4 ng mL⁻¹, 20 ng mL⁻¹, and 16 ng mL⁻¹, respectively. The method has been satisfactorily used for the determination of proteins in actual samples. In comparison with most of fluorimetric methods, this method is quick and simple, has high sensitivity and good stability. The interaction mechanism is also studied.     

Extending the kinetic solution of the classic Michaelis–Menten model of enzyme action

The principal aim of studies of enzyme-mediated reactions has been to provide comparative and quantitative information on enzyme-catalyzed reactions under distinct conditions. The classic Michaelis–Menten model (Biochem Zeit 49:333, 1913) for enzyme kinetic has been widely used to determine important parameters involved in enzyme catalysis, particularly the Michaelis–Menten constant (K _M ) and the maximum velocity of reaction (V _max ). Subsequently, a detailed treatment of the mechanisms of enzyme catalysis was undertaken by Briggs–Haldane (Biochem J 19:338, 1925). These authors proposed the steady-state treatment, since its applicability was constrained to this condition. The present work describes an extending solution of the Michaelis–Menten model without the need for such a steady-state restriction. We provide the first analysis of all of the individual reaction constants calculated analytically. Using this approach, it is possible to accurately predict the results under new experimental conditions and to characterize and optimize industrial processes in the fields of chemical and food engineering, pharmaceuticals and biotechnology.