Synthesis and Chelating Properties of Polystyrene Supported Schiff Base (N,N′-disalicylidenepropylenetriamine) Resin Toward Some Divalent Metal Ions

A new polystyrene-supported Schiff base resin, N,N-bis(salicylidenepropylenetriamine)- aminomethyl polystyrene, has been synthesized through a reaction between the commercially available 4-chloromethyl polystyrene polymer and the Schiff base, N,N′-disalicylidenepropylenetriamine. The chelation behavior of this resin toward the divalent metal ions Cu^{2 +}, Ni^{2 +}, Zn^{2 +}, and Pb^{2 +} in aqueous solutions was investigated. Batch equilibration experiments were carried out as a function of contact time, pH, amount of metal-ion, polymer mass, and temperature. The amount of metal-ion uptake of the polymers was determined by using atomic absorption spectrometry (AAS). Results of the study revealed that the resin exhibited higher capacities and a more pronounced adsorption toward Cu^{2 +} and that the metal-ion uptake follows the order: Cu^{2 +} > Zn ^{2 +} > Ni^{2 +} > Pb²⁺. The adsorption and binding capacity of the resin toward the various metal ions investigated are discussed.     

On the accurate estimation of free energies using the jarzynski equality

The Jarzynski equality is one of the most widely celebrated and scrutinized nonequilibrium work theorems, relating free energy to the external work performed in nonequilibrium transitions. In practice, the required ensemble average of the Boltzmann weights of infinite nonequilibrium transitions is estimated as a finite sample average, resulting in the so-called Jarzynski estimator, . Alternatively, the second-order approximation of the Jarzynski equality, though seldom invoked, is exact for Gaussian distributions and gives rise to the Fluctuation-Dissipation estimator . Here we derive the parametric maximum-likelihood estimator (MLE) of the free energy considering unidirectional work distributions belonging to Gaussian or Gamma families, and compare this estimator to . We further consider bidirectional work distributions belonging to the same families, and compare the corresponding bidirectional to the Bennett acceptance ratio () estimator. We show that, for Gaussian unidirectional work distributions, is in fact the parametric MLE of the free energy, and as such, the most efficient estimator for this statistical family. We observe that and perform better than and , for unidirectional and bidirectional distributions, respectively. These results illustrate that the characterization of the underlying work distribution permits an optimal use of the Jarzynski equality. © 2018 Wiley Periodicals, Inc.     

A combined mixed finite element ADI scheme for solving Richards' equation with mixed derivatives on irregular grids

We propose and analyze an efficient numerical method for solving semilinear parabolic problems with mixed derivative terms on non-rectangular domains. The spatial semidiscretization process is based on an expanded mixed finite element scheme which, combined with suitable quadrature rules, is converted into a cell-centered finite difference scheme. This choice preserves the asymptotic accuracy and local conservation of mass of the method, while substantially reducing the computational cost of the totally discrete scheme. To obtain it, an alternating direction implicit scheme is used for the integration in time. The resulting numerical algorithm involves sets of uncoupled tridiagonal systems which can be solved in parallel. We set out some theoretical results of unconditional convergence (of second order in space and first order in time) for our method. Finally, a numerical experiment is shown in order to illustrate the theoretical results.