Numerical approximation of a nonisothermal two-dimensional general rate model of reactive liquid chromatography

A nonlinear and nonisothermal two-dimensional general rate model is formulated and approximated numerically to allow quantitatively analyzing the effects of temperature variations on the separations and reactions in liquid chromatographic reactors of cylindrical geometry. The model equations form a nonlinear system of convection-diffusion-reaction partial differential equations coupled with algebraic equations for isotherms and reactions. A semidiscrete high-resolution finite volume method is modified to approximate the system of partial differential equations. The coupling between the thermal waves and concentration fronts is demonstrated through numerical simulations, and important parameters are pointed out that influence the reactor performance. To evaluate the precision of the model predictions, consistency checks are successfully carried out proving the accuracy of the predictions. The results allow to quantify the influence of thermal effects on the performance of the fixed beds for different typical values of enthalpies of adsorption and reaction and axial and radial Peclet numbers for mass and heat transfer. Furthermore, they provide useful insight into the sensitivity of nonisothermal chromatographic reactor operation.     

On the convergence of the midpoint method

The midpoint method is an iterative method for the solution of nonlinear equations in a Banach space. Convergence results for this method have been studied in [3, 4, 9, 12]. Here we show how to improve and extend these results. In particular, we use hypotheses on the second Fréchet derivative of the nonlinear operator instead of the third-derivative hypotheses employed in the previous results and we obtain Banach space versions of some results that were derived in [9, 12] only in the real or complex space. We also provide various examples that validate our results.      

Remarks on the generalized Newton method

We give some convergence results for the generalized Newton method for the computation of zeros of nondifferentiable functions which we proposed in an earlier work. Our results show that the generalized method can converge quadratically when used to compute the zeros of the sum of a differentiable function and the (multivalued) subgradient of a lower semicontinuous proper convex function. The method is therefore effective for variational inequalities and can be used to find the minimum of a function which is the sum of a twice-differentiable convex function and a lower semicontinuous proper convex function. A numerical example is given.     

Density,viscosity, and N2O solubility of aqueous amino acid salt and amine amino acid salt solutions

Physicochemical properties of aqueous amino acid salt (AAS), potassium salt of sarcosine (KSAR) and aqueous amine amino acid salt (AAAS), 3-(methylamino)propylamine/sarcosine (SARMAPA) have been studied. Densities of KSAR were measured for sarcosine mole fraction 0.02 to 0.25 for temperature range 298.15 K to 353.15 K, the viscosities were measured for 0.02 to 0.10 mole fraction sarcosine (293.15 K to 343.15 K) while the N₂O solubilities were measured from 0.02 to 0.10 mole fraction sarcosine solutions (298.15 K to 363.15 K). Densities of SARMAPA were measured for sarcosine mole fraction 0.02 to 0.23 for temperature range (298.15 K to 353.15 K), viscosities were measured for 0.02 to 0.16 mole fraction sarcosine (293.15 K to 343.15 K) while the N₂O solubilities were measured from 0.02 to 0.16 mole fraction sarcosine solutions (298.15 K to 343.15 K). Experimental results were correlated well with empirical correlations and N₂O solubility results for KSAR were predicted adequately by a Schumpe model. The solubilities of N₂O in AAS and AAAS are significantly lower than values for amines. The solubilities vary as: amine > AAAS > AAS.     

The tensor Golub–Kahan–Tikhonov method applied to the solution of ill-posed problems with a t-product structure

This paper discusses an application of partial tensor Golub–Kahan bidiagonalization to the solution of large-scale linear discrete ill-posed problems based on the t-product formalism for third-order tensors proposed by Kilmer and Martin (M. E. Kilmer and C. D. Martin, Factorization strategies for third order tensors, Linear Algebra Appl., 435 (2011), pp. 641-658). The solution methods presented first reduce a given (large-scale) problem to a problem of small size by application of a few steps of tensor Golub–Kahan bidiagonalization and then regularize the reduced problem by Tikhonov's method. The regularization operator is a third-order tensor, and the data may be represented by a matrix, that is, a tensor slice, or by a general third-order tensor. A regularization parameter is determined by the discrepancy principle. This results in fully automatic solution methods that neither require a user to choose the number of bidiagonalization steps nor the regularization parameter. The methods presented extend available methods for the solution for linear discrete ill-posed problems defined by a matrix operator to linear discrete ill-posed problems defined by a third-order tensor operator. An interlacing property of singular tubes for third-order tensors is shown and applied. Several algorithms are presented. Computed examples illustrate the advantage of the tensor t-product approach, in comparison with solution methods that are based on matricization of the tensor equation.     

Analysis of two-dimensional models for liquid chromatographic reactors of cylindrical geometry

This work presents the analytical solutions of two-dimensional isothermal reactive general rate models for liquid chromatographic reactors of cylindrical geometry. Both irreversible and reversible reactions are considered. The model equations form a linear system of convection-diffusion-reaction partial differential equations coupled with algebraic equations for isotherms. Analytical solutions are derived by integrated implementation of finite Hankel transform, Laplace transform, eigen-decomposition technique, and conventional ordinary differential equations solution technique. To verify the analytical results, a high-resolution finite volume scheme is also applied to numerically approximate the model equations. The current results can be very useful to optimize and upgrade the liquid chromatographic reactors.     

QSAR modeling and chemical space analysis of antimalarial compounds

Generative topographic mapping (GTM) has been used to visualize and analyze the chemical space of antimalarial compounds as well as to build predictive models linking structure of molecules with their antimalarial activity. For this, a database, including ~3000 molecules tested in one or several of 17 anti-Plasmodium activity assessment protocols, has been compiled by assembling experimental data from in-house and ChEMBL databases. GTM classification models built on subsets corresponding to individual bioassays perform similarly to the earlier reported SVM models. Zones preferentially populated by active and inactive molecules, respectively, clearly emerge in the class landscapes supported by the GTM model. Their analysis resulted in identification of privileged structural motifs of potential antimalarial compounds. Projection of marketed antimalarial drugs on this map allowed us to delineate several areas in the chemical space corresponding to different mechanisms of antimalarial activity. This helped us to make a suggestion about the mode of action of the molecules populating these zones.     

Design of multi-binding-site inhibitors, ligand efficiency, and consensus screening of avian influenza H5N1 wild-type neuraminidase and of the oseltamivir-resistant H274Y variant

The binding sites of wild-type avian influenza A H5N1 neuraminidase, as well as those of the Tamiflu (oseltamivir)-resistant H274Y variant, were explored computationally to design inhibitors that target simultaneously several adjacent binding sites of the open conformation of the virus protein. The compounds with the best computed free energies of binding, in agreement by two docking methods, consensus scoring, and ligand efficiency values, suggest that mimicking a polysaccharide, beta-lactam, and other structures, including known drugs, could be routes for multibinding site inhibitor design. This new virtual screening method based on consensus scoring and ligand efficiency indices is introduced, which allows the combination of pharmacodynamic and pharmacokinetic properties into unique measures.