Fast simplicial quadrature-based finite element operators using Bernstein polynomials

We derive low-complexity matrix-free finite element algorithms for simplicial Bernstein polynomials on simplices. Our techniques, based on a sparse representation of differentiation and special block structure in the matrices evaluating B-form polynomials at warped Gauss points, apply to variable coefficient problems as well as constant coefficient ones, thus extending our results in Kirby (Numer Math, 2011, in press).     

Optimal pairwise and non-pairwise alchemical pathways for free energy calculations of molecular transformation in solution phase

We estimate the global minimum variance path for computing the free energy insertion into or deletion of small molecules from a dense fluid. We perform this optimization over all pair potentials, irrespective of functional form, using functional optimization with a two-body approximation for the radial distribution function. Surprisingly, the optimal pairwise path obtained via this method is almost identical to the path obtained using a optimized generalized "soft core" potential reported by Pham and Shirts [J. Chem. Phys. 135, 034114 (2011)]. We also derive the lowest variance non-pairwise potential path for molecular insertion or deletion and compare its efficiency to the pairwise path. Under certain conditions, non-pairwise pathways can reduce the total variance by up to 60% compared to optimal pairwise pathways. However, optimal non-pairwise pathways do not appear generally feasible for practical free energy calculations because an accurate estimate of the free energy, the parameter that is itself is desired, is required for constructing this non-pairwise path. Additionally, simulations at most intermediate states of these non-pairwise paths have significantly longer correlation times, often exceeding standard simulation lengths for solvation of bulky molecules. The findings suggest that the previously obtained soft core pathway is the lowest variance pathway for molecular insertion or deletion in practice. The findings also demonstrate the utility of functional optimization for determining the efficiency of thermodynamic processes performed with molecular simulation.     

On the derivation of the entropy of ideal quantum gases confined in a three-dimensional harmonic potential

In this work,the entropy functions of ideal quantum gases in a three-dimensional harmonic trap are analytically calculated using temperature as an explicit variable.Afterward,the applicability of the analytical formulas is validated by comparison with the numerical calculation.The results illustrate that the obtained functions could be applied for the whole temperature regime with a maximum relative deviation of less than 7.5%in the vicinity of the critical temperature Tcin the case of Bose gases.Meanwhile,for Fermi gases,although the analytical formula fits well at very low-and high-temperature regimes,it cannot be applied at temperature in the range[0.3-0.5]T_F,where T_F is the Fermi temperature.In addition,the consistency between our formulas and classical ones at significantly high temperatures is also discussed.     

On Grushin’s equation

The paper deals with nonlinear problems for equations of Grushin type. We prove some nonexistence results via Pokhozhaev’s identity. In the rest of the paper we prove some results on smoothness near the boundary of eigenfunctions by using an explicit formula for fundamental solutions and the Kelvin transform for the operator.     

Low-dimensional compounds containing cyano groups. III: a structural,spectral and thermal study of dicyanoargentates containing 4-methylpyridine

The complexes Cu^II(4-Mepy)₂Ag₂(CN)₄ (1) and Cu^II(4-Mepy)₃Ag_2–x Cu^I _x (CN)₄ (2) (4-Mepy = 4-methylpyridine, x = 0.07) were isolated from a reaction mixture containing 4-Mepy, K[Ag(CN)₂] and CuSO₄. I.r. spectra indicated the presence of both monodentate and bridging cyano groups in (1) and (2), confirmed by their known structures, both consisting of neutral zigzag chains. Two neighbouring chains in (2) are linked by argentophilic interactions between Ag atoms of bridging dicyanoargentate anions, whose positions are partly occupied by Cu^I ions to the extent of 7 at.%, with an unusually short Ag...Ag distance of 2.9264(5) Å, to form a ladder. Individual ladders are tied together as sheets by weaker argentophilic interactions between silver atoms of interdigitated monodentate dicyanoargentate anions of two different ladders. Thermal decomposition of (2) occurs in two separated stages. In the first stage, three 4-Mepy molecules are liberated from the formula unit and, in the second stage, redox decomposition of the cyano groups occurs. The thermal decomposition of (1) is more complicated as the release of two 4-Mepy molecules is overlapped by decomposition of one cyano group followed by further redox decomposition of the remaining cyano groups.     

Validation of an in-house measurement procedure for determination of selected priority hazardous substances in water and estimation of measurement uncertainty

Accreditation and Quality Assurance - This study investigates measurement procedure validation for the determination of hexachlorobenzene, pentachlorobenzene and trifluralin as priority hazardous...     

Bifurcation indicator based on meshless and asymptotic numerical methods for nonlinear poisson problems

We propose in this work new algorithms associating asymptotic numerical method and meshless discretization (MFS‐MPS: Method of fundamental solutions‐Method of particular solutions) to compute branch solutions of nonlinear Poisson problems. To detect singular points on these branches, geometrical indicator, Padé approximants, and analytical bifurcation indicator are proposed. Numerical applications show the robustness and the effectiveness of the proposed algorithms. © 2014 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 30: 978–993, 2014     

Antioxidant activity of two wild edible mushrooms (Morchella vulgaris and Morchella esculanta) from North Turkey

The ethanol extracts of Morchella vulgaris (EEMV) and Morchella esculanta (EEME) were analysed for their antioxidant activities in different systems including reducing power, free radical scavenging, superoxide anion radical scavenging, total antioxidant activity, and metal chelating activity. EEMV and EEME had similar reducing power, free radical scavenging, superoxide anion radical scavenging, hydrogen peroxide scavenging, and metal chelating activity at concentrations of 50, 100, and 150 microg/mL. These various antioxidant activities were compared to standard antioxidants such as butylated hydroxyanisole (BHA), butylated hydroxytoluene (BHT), and alpha-tocopherol. The percent inhibition of different concentrations of EEMV on peroxidation in the linoleic acid system was 85 and 87 % respectively, which was greater than that of 100 and 250 microg/mL of alpha-tocopherol (50 and 77%, respectively) and similar to 250 microg/mL of BHA (85, 87%, respectively). The percent inhibition of different concentrations of EEME on peroxidation in the linoleic acid system was 80 and 87 % respectively, which was greater than that of 100 and 250 microg/mL of alpha-tocopherol (50, 77%) and similar to 250 microg/mL BHA (87%). On the other hand, the percent inhibition of 100 and 250 microg/mL of BHT was 97 and 99%, respectively. In addition, the total phenolic compounds in EEMV and EEME were determined as gallic acid equivalents.     

On the energy landscapes of 3-indole acetic acid and 3-indole propionic acid. A study of side chain flexibilities in their S(0) and S(1) electronic states

The tandem of 3-indole acetic acid (IAA) and 3-indole propionic acid (IPA) is ideally suited for a detailed study of the intramolecular forces responsible for the conformational properties of species containing side chains. Toward this end, high resolution S(1)<-- S(0) excitation spectra of the three origin bands in IAA and the two origin bands in IPA were recorded and analyzed. Each origin is assigned to a unique conformer. A discussion of the resulting energy landscape is given.