The homotopy perturbation method applied to the nonlinear fractional Kolmogorov–Petrovskii–Piskunov equations

The fractional derivatives in the sense of Caputo, and the homotopy perturbation method are used to construct approximate solutions for nonlinear Kolmogorov–Petrovskii–Piskunov (KPP) equations with respect to time and space fractional derivatives. Also, we apply complex transformation to convert a time and space fractional nonlinear KPP equation to an ordinary differential equation and use the homotopy perturbation method to calculate the approximate solution. This method is efficient and powerful in solving wide classes of nonlinear evolution fractional order equations.     

Quantum Dynamics of a Harmonic Oscillator in a Deformed Bath

The dissipative quantum dynamics of a harmonic oscillator in the presence of a deformed bath is investigated. The deformed bath is modelled by a collection of deformed quantum harmonic oscillators as a generalization of Hopfield model. The transition probabilities between energy levels of the oscillator are obtained perturbatively and discussed.     

Modeling framework for optimal evacuation of large-scale crowded pedestrian facilities

The paper presents a simulation–optimization modeling framework for the evacuation of large-scale pedestrian facilities with multiple exit gates. The framework integrates a genetic algorithm (GA) and a microscopic pedestrian simulation–assignment model. The GA searches for the optimal evacuation plan, while the simulation model guides the search through evaluating the quality of the generated evacuation plans. Evacuees are assumed to receive evacuation instructions in terms of the optimal exit gates and evacuation start times. The framework is applied to develop an optimal evacuation plan for a hypothetical crowded exhibition hall. The obtained results show that the model converges to a superior optimal evacuation plan within an acceptable number of iterations. In addition, the obtained evacuation plan outperforms conventional plans that implement nearest-gate immediate evacuation strategies.     

Chiral Separation of 4-Iminoflavan Derivatives on Several Polysaccharide-Based Chiral Stationary Phases by HPLC

The HPLC enantiomeric separation of seven 4-iminoflavans was successfully accomplished in the normal phase mode using six polysaccharide-based chiral stationary phases namely, Chiralcel^®OD-H, Chiralcel^®OD, Chiralcel^®OJ, Chiralpak^®AD, Chiralpak^®IA and Chiralpak^®IB under normal and polar organic phase modes. The resolution depended on nature and concentration of alcoholic modifier. The results demonstrate clearly that the chromatographic system based on the coated and immobilized type Chiralpak^®IB and Chiralcel^®OD-H CSPs provide a powerful analytical tool for enantiomeric separation of all the 4-iminoflavans used in this study.

     

Corrosion protection of steel sheets by chitosan from shrimp shells at acid pH

The corrosion behavior of mild steel (MS) sheets in 0.5 M H₂SO₄ in the presence of chitosan extracted from shrimp shells (CSS) has been studied using electrochemical techniques. The optimum concentration (10 µM) of this carbohydrate polymer inhibited MS corrosion up to 85 % in the solution of the acid electrolyte. Results reveal that CSS reduced the dissolution of MS linearly with its concentration, and this reduction could be attributed to the interfacial formation of CSS film at the MS-electrolyte boundary. CSS is a mixed-type inhibitor and the shapes of Nyquist capacitive and inductive loops obtained from the impedance results could be associated with double layer reactions and relaxation of corrosive ions adsorption in the presence of CSS, respectively, at the MS/solution interface. Surface analytical studies with atomic force microscope, scanning electron microscope and Fourier transform infra-red also confirm the adsorption of CSS on MS.     

Standard molar enthalpy of formation of rubidium diphosphate

Rubidium carbonate (Rb₂CO₃) and ammonium dihydrogen phosphate (NH₄H₂PO₄) were used for synthesizing rubidium diphosphate (Rb₄P₂O₇). The purity of the latter compound was checked up by X-ray diffraction. Rb₄P₂O₇ was involved in an hypothetical reaction and dissolved together with the other components in a 3.85 % (m/m) phosphoric acid solution, using a C-80 SETARAM calorimeter. Mixing processes were also realized in the calorimeter in order to get the standard molar enthalpy of formation of rubidium diphosphate (Rb₄P₂O₇). For that a thermochemical cycle was investigated and the obtained value for the standard molar enthalpy of formation of rubidium diphosphate is (?3,183.7) kJ mol^?1. The result is about 1.8 % lower than literature value.     

Column properties and flow profiles of a flat, wide column for high-pressure liquid chromatography

The design and the construction of a pressurized, flat, wide column for high-performance liquid chromatography (HPLC) are described. This apparatus, which is derived from instruments that implement over-pressured thin layer chromatography, can carry out only uni-dimensional chromatographic separations. However, it is intended to be the first step in the development of more powerful instruments that will be able to carry out two-dimensional chromatographic separations, in which case, the first separation would be a space-based separation, LC(x), taking place along one side of the bed and the second separation would be a time-based separation, LC(t), as in classical HPLC but proceeding along the flat column, not along a tube. The apparatus described consists of a pressurization chamber made of a Plexiglas block and a column chamber made of stainless steel. These two chambers are separated by a thin Mylar membrane. The column chamber is a cavity which is filled with a thick layer (ca. 1mm) of the stationary phase. Suitable solvent inlet and outlet ports are located on two opposite sides of the sorbent layer. The design allows the preparation of a homogenous sorbent layer suitable to be used as a chromatographic column, the achievement of effective seals of the stationary phase layer against the chamber edges, and the homogenous flow of the mobile phase along the chamber. The entire width of the sorbent layer area can be used to develop separations or elute samples. The reproducible performance of the apparatus is demonstrated by the chromatographic separations of different dyes. This instrument is essentially designed for testing detector arrays to be used in a two-dimensional LC(x) x LC(t) instrument. The further development of two-dimension separation chromatographs based on the apparatus described is sketched.     

6-Endo-dig versus 5-exo-dig: Exploring Radical Cyclization Preference with First-, Second-, and Third-row Linkers using High-level Quantum Chemical Methods

As an expansion upon Baldwin rules, the cyclization reactions of hex-5-yn-1-yl radical systems with different first-, second-, and third-row linkers are explored at the CCSD(T) level via means of the SMD(benzene)-G4(MP2) thermochemical protocol. Unlike C, O, and N linkers, systems with B, Si, P, S, Ge, As, and Se linkers are shown to favor 6-endo-dig cyclization. This offers fundamental insights into the rational synthetic design of cyclic compounds. A thorough analysis of stereoelectronic effects, cyclization barriers, and intrinsic barriers illustrates that structural changes alter the cyclization preference by mainly impacting 5-exo-dig reaction barriers. Based on the high-level computational modeling, we proceed to develop a new tool for cyclization preference prediction from the correlation between cyclization barriers and radical structural parameters (e. g., linker bond length and bond angle). A strong correlation is found between the radical attack trajectory angle and the reaction barrier heights, i. e., cyclization preference. Finally, the influence of stereoelectronic effects on the two radical cyclization pathways is further investigated in stereoisomers of hypervalent silicon system, which provides novel insight into cyclization control.     

Numerical and theoretical study of weak Galerkin finite element solutions of Turing patterns in reaction–diffusion systems

In this paper, we introduce numerical schemes and their analysis based on weak Galerkin finite element framework for solving 2‐D reaction–diffusion systems. Weak Galerkin finite element method (WGFEM) for partial differential equations relies on the concept of weak functions and weak gradients, in which differential operators are approximated by weak forms through the Green's theorem. This method allows the use of totally discontinuous functions in the approximation space. In the current work, the WGFEM solves reaction–diffusion systems to find unknown concentrations (u, v) in element interiors and boundaries in the weak Galerkin finite element space WG(P₀, P₀, RT₀) . The WGFEM is used to approximate the spatial variables and the time discretization is made by the backward Euler method. For reaction–diffusion systems, stability analysis and error bounds for semi‐discrete and fully discrete schemes are proved. Accuracy and efficiency of the proposed method successfully tested on several numerical examples and obtained results satisfy the well‐known result that for small values of diffusion coefficient, the steady state solution converges to equilibrium point. Acquired numerical results asserted the efficiency of the proposed scheme.