Exponential Time Differencing Method for a Reaction-Diffusion System with Free Boundary

For reaction-diffusion equations in irregular domains with moving boundaries,the numerical stability constraints from the reaction and diffusion terms often require very restricted time step sizes,while complex geometries may lead to difficulties in the accuracy when discretizing the high-order derivatives on grid points near the boundary.It is very challenging to design numerical methods that can efficiently and accurately handle both difficulties.Applying an implicit scheme may be able to remove the stability constraints on the time step,however,it usually requires solving a large global system of nonlinear equations for each time step,and the computational cost could be significant.Integration factor(IF)or exponential time differencing(ETD)methods are one of the popular methods for temporal partial differential equations(PDEs)among many other methods.In our paper,we couple ETD methods with an embedded boundary method to solve a system of reaction-diffusion equations with complex geometries.In particular,we rewrite all ETD schemes into a linear combination of specificФ-functions and apply one state-of-the-art algorithm to compute the matrix-vector multiplications,which offers significant computational advantages with adaptive Krylov subspaces.In addition,we extend this method by incorporating the level set method to solve the free boundary problem.The accuracy,stability,and efficiency of the developed method are demonstrated by numerical examples.

Highly efficient synthesis of β-amino esters via Mannich-type reaction under solvent-free conditions using ZnCl_2 catalyst

β-Amino esters were synthesized via ZnCl2-catalyzed Mannich-type reaction of imines and malonate esters under solvent-free conditions in 6 min. The β-amino ester was converted into the corresponding aspartic acid derivatives.

A Rapid and Efficient Synthesis of Diaryl Thioureas via Solvent-Free Reaction Using Microwave

A rapid and efficient method for the preparation of diaryl thiourea compounds was reported for the first time. Twelve diaryl thiourea compounds that possessing biological activity have been synthesized in excellent yields (91-97%). The reaction proved to be extremely simple and highly efficient (in 1.5-4.5 min).

Efficient Solvent- and Catalyst-Free Syntheses of Imine Derivatives Applying the Pressure Reduction Technique: Remarkable Change of the Reaction Rate with the Phase Transition

Because imines could be used as convenient starting materials in various fields, the development of an easy synthetic method of imine was strongly desired. In response to this demand, we thought that it would be an effective synthesis method if an aldehyde and an amine could be reacted to give an imine in good yield under solvent- and catalyst-free conditions. In fact, we tried the reaction of benzaldehyde with various amines under solvent- and catalyst-free conditions followed by removal of water that was produced in the reaction system by a vacuum pump, and desired imines could be obtained in good yields. Observation of this reaction using a nuclear magnetic resonance spectrometer revealed that the reaction rate was extremely fast at the initial stage but slowed over time. However, the reaction of benzaldehyde with aniline differed greatly, and the reaction rate dramatically improved in 47 - 48 minutes after the start of the reaction. At this time, we found that the reaction system underwent a phase transition from the liquid phase to the solid phase.

Facile One-Pot Synthesis of Novel Hexahydro-2-quinolinecarboxylic Acids under Solvent-Free Reaction Conditions

A simple and fastthree-component synthesis of new and biologically active hexahydro-2-quinolinecarboxylic acid scaf-fold 4 was carried out using cyclocondensation reaction of arylmethylidenepyruvic acids 1, 1,3-cyclohexandiones 2 and ammonium acetate 3 under solvent-free conditions and at room temperature. This protocol has the advantages of facility, easy work-up, high yields, short reaction time and environmentally friendly character.

Oxalic acid catalyzed solvent-free one pot synthesis of coumarins

Oxalic acid was found to be an efficient catalyst for Pechmann condensation, which includes the reaction between phenols and β-keto esters leading to formation of coumarin derivatives. The advantages of present methods are the use of cheap and easy available catalyst, solvent-free reaction conditions, better yields and shorter reaction time.

BF_3·OEt_2 Promoted Solvent-free Synthesis of Benzimidazole Derivatives

Differently substituted benzimidazoles have been synthesized in very good yields in solvent-free conditions from o-phenylenediamine and aldehydes in the presence of BF3·OEt2 as a catalyst. The method is applicable to aromatic, unsaturated and aliphatic aldehydes and to substituted o-phenylenediamines without significant differences.

Silica triflate as an efficient reagent for the solvent-free synthesis of coumarins

Silica triflate, as a new silica-based reagent, can be used for the efficient synthesis of 4-substituted coumarins via a Pechmann reaction under solvent-free reaction conditions. All reactions were performed at 80 ℃ in good to high yields.

Influence of chemical reaction on heat and mass transfer of non-Newtonian fluid with yield stress by free convection from vertical surface in porous medium considering Soret effect

The effect of chemical reaction on free convection heat and mass transfer for a non-Newtonian power law fluid over a vertical flat plate embedded in a fluid-saturated porous medium has been studied in the presence of the yield stress and the Soret effect. The governing boundary layer equations and boundary conditions are cast into a dimen- sionless form by similarity transformations, and the resulting system of equations is solved by a finite difference method. The results are preSented and discussed for concentration profiles, as well as the Nusselt number and the Sherwood number for various values of the parameters, which govern the problem. The results obtained show that the flow field is influenced appreciably by the presence of the chemical reaction parameter γ the order of.the chemical reaction parameter m, the Soret number St, the buoyancy ratio N, the Lewis number Le, and the dimensionless rheological parameter Ω.

An efficient and green preparation of 5-aminophosphonate substituted pyrimidine nucleosides under solvent-free conditions

An environmentally benign and highly efficient one-pot preparation of α-aminophosphonates under solvent-free conditions was developed. By employing this method, 5-aminophosphonate substituted pyrimidine nucleosides were synthesized in good to excellent yields starting from 5-forrnyl-2＇-deoxyuridine, aniline and dimethylphosphite.

An efficient and solvent-free one-pot synthesis of dihydropyrimidinones under microwave irradiation

An efficient synthesis of 3,4-dihydropyrimidin-2(1H)-one derivatives using formic acid as catalyst, from aldehydes, β-ketoester and urea(thiourea) without solvent under the irradiation of microwave is described. Compared with the classical Biginelli reaction, this new method has the advantage of good yields (77–94% for aromatic aldehydes) and short reaction time (3–8 min).

Liver Nuclear Activation of Carbon Tetrachloride or Bromotrichloromethane to Trichloromethyl and Trichloromethylperoxyl Free Radicals.Their Reactions With Lipids and Proteins

The formation of·CCl3 radicals in liver nuclei was suggested by spin trapping of them with N-t-butyl-α-phenylnitrone followed by GC/MS detection of the resulting adduct. Comparison of its formation in microsomal biotransformation of CCl4 was made. In aerobic nuclear activation mixtures containing NADPH and CCl4, significant decrease in the arachidonic acid content of nuclear lipids was observed (27. 8%, compared to control), the intensity of this decrease was lower than that occurring in the corresponding microsomal incubation mixtures (29.1%). Significant decreases in arachidonic acid content of nuclear and endoplasmic reticulum lipids were also observed in animals at 6 hours of poisoning with the haloalkane. During aerobic nuclear metabolism of CCl4 or CBrCl3, cholesterol oxidation products were detected: a ketocholesterol, an epoxide like structure and 7-ketocholesterol. Nuclear protein carbonyl formation was not promoted during nuclear CCl4 biotransformation. NADPH by itself may lead to protein carbonyl formation during prolonged periods of incubation. CBrCl3 in contrast, led to decreased protein carbonyl formation. No increase in nuclear protein carbonyl formation was observed in CCl4 intoxicated animals during periods of time between 1 to 6 hours after treatment. The results indicate that during nuclear biotransformation of CCl4 or CBrCl3 reactive free radicals, PUFA degradation, reactive aldehydes and cholesterol oxidation products are formed, nearby DNA and regulatory proteins.

Mechanism and Kinetic of Free Radical Reactions for Propane Using theoretical Calculations

Quantum calculation method has been used to understand and investigate the free radical reactions of propane with hydroxyl radical in vacuum through modem quantum mechanics that is package on hyperchem 8.02 program. Optimized structures and structural reactivates have been studied through bond stability and angles using DFT calculation based on the basis set 6-31G＊. Energetic properties have been calculated like total energy, Gibbs free energy, entropy, heat of formation, and rate constant for all chemical species that＇s participate in the suggested reaction mechanism. Reaction mechanism and rate determining step had been suggested according to calculation of energy barrier values, and compares between the suggested competitive reactions for each probable reaction step. Suggested structures and the probable transition states have been studied.

Free radical reaction model for n-pentane pyrolysis

A mathematical mechanism of the n-pentane pyrolysis process based on free radical reaction model was presented.The kinetic parameters of n-pentane pyrolysis are obtained by quantum chemistry and the reaction network is established. The solution of the stiff ordinary differential equations in the n-pentane pyrolysis model is completed by semi implicit Eular algorithm. Then the pyrolysis mechanism based on free radical reaction model is built,and the computational efficiency increases 10 times by algorithm optimization. The validity of this model and its solution method is confirmed by the experimental results of n-pentane pyrolysis.

Solvent-free synthesis of some ethyl arylglyoxylates

An efficient and convenient approach to synthesize of ethyl arylglyoxylates by solvent-free grinding was described. Eight ethyl arylglyoxylates had been synthesized by this method, this method provided several advantages such as little pollution, high yield, good selectivity, and simple workup procedure, their structures were confirmed by IR, ^1HNMR.

Efficient Solvent-Free Preparation of Imines, and Their Subsequent Oxidation with <i>m</i>-CPBA to Afford Oxaziridines

A simple one-pot procedure for the preparation of imines from the corresponding aldehydes and amines, and their subsequent oxidation reaction with m-CPBA to produce synthetically useful oxaziridines is reported. The method is applicable to imines derived from both aliphatic and aromatic aldehydes and diverse alkyl amines. Short reaction times, essentially quantitative yields, very mild reaction conditions, and easy purification are the main features of the procedure reported herein.

Perfect Solvent- and Catalyst-Free Syntheses of Imine Derivatives Using the Pressure Reduction Technique

In the field of organic syntheses, the development of environmentally friendly methods based on the concept of green chemistry has been always required. In response to this requirement, we reported solvent- and catalyst-free syntheses of imines using the pressure reduction technique as a key technology. We found that this reaction proceeded very rapidly in the initial stage, but its rate decreased with the passage of time. It was also found that the reaction of benzaldehyde with aniline had a specificity that the phase transition occurred. In this method, the desired imines could be obtained in good to excellent yields, but target compounds had to be given by purifications using organic solvents. Therefore, we tried to develop the perfect synthetic method of imine derivatives without organic or inorganic solvents. We selected two methods and took them into this investigation. One was exactly mixing (1:1, substance ratio) aldehydes and amines and the other was employing lower pressure (>0.1 mmHg, previous method: 1.0 mmHg) at the pressure reducing technique. When this improved synthetic method was performed, it was revealed that pure target imines were obtained in excellent yields without any purification.

Radiation-absorption,chemical reaction,Hall and ion slip impacts on magnetohydrodynamic free convective flow over semi-infinite moving absorbent surface

The investigation of radiation-absorption,chemical reaction,Hall and ion-slip impacts on unsteady MHD free convective laminar flow of an incompressible viscous,electrically conducting and heat generation/absorbing fluid enclosed with a semi-infinite porous plate within a rotating frame has been premeditated.The plate is assumed to be moving with a constant velocity in the direction of fluid movement.A uniform transverse magnetic field is applied at right angles to the porous surface,which is absorbing the fluid with a suction velocity changing with time.The non-dimensional governing equations for present investigation are solved analytically making use of two term harmonic and non-harmonic functions.The graphical results of velocity,temperature and concentration distributions on the analytical solutions are displayed and discussed with reference to pertinent parameters.It is found that the velocity profiles decreased with an increasing in Hartmann number,rotation parameter,the Schmidt number,heat source parameter,while it increased due to an increase in permeability parameter,radiation-absorption parameter,Hall and ion slip parameters.However,the temperature profile is an increasing function of radiation-absorption parameter,whereas an increase in chemical reaction parameter,the Schmidt number Sc or frequency of oscillations decrease the temperature profile on cooling.Also,it is found that the concentration profile is decreased with an escalating in the Schmidt number or the chemical reaction parameter.

Nonequilibrium Solvent Free Energy Curve from Molecular Theory in Electron Transfer Reaction

The microscopic moleeular theory for electron transfer in a model solvent ishahr developed. The nonlinear response of the solvent molecules is be computedquanitatively in a new way. Adopting computer simulation daa and choosingappropriate reaction coordinae, a reasonable free energy dinram is constructed and thercorganhaion energy for the product state is calculated.

1,3-Dicarbonyl compounds as phosphine-free ligands for Pd-catalyzed Heck and Suzuki reactions

Some 1,3-dicarbonyl compounds (such as pentane-2,4-dione and 3-oxo-N-phenylbutanamide) were found to constitute highly efficient, yet low-priced and phosphine-free ligands for the Pd-catalyzed Heck and Suzuki reactions of aryl bromides and iodides with very high turnover numbers (ca. 103–104).