Shape Optimization for Navier–Stokes Equations with Algebraic Turbulence Model: Numerical Analysis and Computation

We study the shape optimization problem for the paper machine headbox which distributes a mixture of water and wood fibers in the paper making process. The aim is to find a shape which a priori ensures the given velocity profile on the outlet part. The mathematical formulation leads to the optimal control problem in which the control variable is the shape of the domain representing the header, the state problem is represented by the generalized Navier-Stokes system with nontrivial boundary conditions. This paper deals with numerical aspects of the problem.     

The higher-order Picone identity and comparison of half-linear differential equations of even order

An identity of the Picone type for higher-order half-linear ordinary differential operators of the form and where p_j and P_j, j=0,…,n, are continuous functions defined on [a,b] and , is derived and then the Sturmian comparison theory for the corresponding 2nth-order equations l_α[x]=0 and L_α[y]=0 based on this identity is developed.     

On an integral inequality of the Wirtinger type

In this paper, a new Picone-type identity for the quasilinear differential operator of the second order is used to establish an integral inequality involving functions and their derivatives which generalizes the classical Wirtinger inequality.     

Notes on connections attached to A-structures

The paper presents standard material on A-planar structures and their morphisms. We also introduce the general construction of connections which have the same A-planar curves and characterize some classes of connections obtained in this way. Some of the examples are studied in detail.     

Hydrophilic interaction liquid chromatography in food analysis

The use of hydrophilic interaction liquid chromatography (HILIC) in food analysis in the last decade is reviewed. The HILIC mechanism is briefly discussed, but main emphasis is put on the use of HILIC for separation of different food matrices. The food matrices are divided into food of animal origin and related products, vegetables, fruits and related compounds, and other food-related matrices. A list on important applications is provided for each category including experimental conditions and a brief summary of the results. The 100 references included will provide the reader a comprehensive overview and insight into HILIC applications to food analysis.     

Selective molecular sequestration with concurrent natural product functionalization and derivatization: from crude natural product extracts to a single natural product derivative in one step

A resin-bound nitroso compound sequestered a single unexpected component from crude plant seed extracts. Several plants, including Piper nigrum, Eugenia caryophyllata, and Pimenta dioica, were extracted with organic solvent in the presence of a nitroso-containing resin. The nitroso resin selectively sequestered a single compound, β-caryophyllene, via a chemo- and regioselective ene reaction. The ene product was released from the resin, and proper selection of the solid-phase linker and cleavage cocktail allowed concomitant further transformation of the primary ene product to a novel functionalized polycycle. Preliminary studies indicate that the new hydroxylamine-containing natural product derivatives have antibiotic activity.     

The preparation of conducting polyaniline–silver and poly(p-phenylenediamine)–silver nanocomposites in liquid and frozen reaction mixtures

The oxidation of aniline with silver nitrate in 1 mol L⁻¹ acetic acid at 20 °C yielded a composite of two conducting components, polyaniline and silver; the acceleration with 1 mol% of p-phenylenediamine is needed for efficient synthesis. The yield and molecular weight increased when aniline was copolymerized with 10 mol% p-phenylenediamine. Such product displayed metallic conductivity below 180 K and semiconductor type above this temperature. As the result, the conductivity was the same at 100 and 300 K. The oxidation of p-phenylenediamine alone with silver nitrate also produced a conducting composite having the conductivity of 1,750 S cm⁻¹ despite the assumed nonconductivity of poly(p-phenylenediamine). The present study demonstrates that all oxidations proceeded also in frozen reaction mixtures at −24 °C, i.e., in the solid state. In most cases, molecular weights of polymer component increased, the conductivity of composites with silver improved, to 2,990 S cm⁻¹ for poly(p-phenylenediamine)–silver, and remained high after deprotonation with 1 mol L⁻¹ ammonium hydroxide.

     

Dispersion interactions of carbohydrates with condensate aromatic moieties: theoretical study on the CH-π interaction additive properties

In this article we present the first systematic study of the additive properties (i.e. degree of additivity) of the carbohydrate-aromatic moiety CH-π dispersion interaction. The additive properties were studied on the β-D-glucopyranose, β-D-mannopyranose and α-L-fucopyranose complexes with the naphthalene molecule by comparing the monodentate (single CH-π) and bidentate (two CH-π) complexes. All model complexes were optimized using the DFT-D approach, at the BP/def2-TZVPP level of theory. The interaction energies were refined using single point calculations at highly correlated ab initio methods at the CCSD(T)/CBS level, calculated as E + (E(CCSD(T))-E(MP2))(Small Basis). Bidentate complexes show very strong interactions in the range from -10.79 up to -7.15 and -8.20 up to -6.14 kcal mol(-1) for the DFT-D and CCSD(T)/CBS level, respectively. These values were compared with the sum of interaction energies of the appropriate monodentate carbohydrate-naphthalene complexes. The comparison reveals that the bidentate complex interaction energy is higher (interaction is weaker) than the sum of monodentate complex interaction energies. Bidentate complex interaction energy corresponds to 2/3 of the sum of the appropriate monodentate complex interaction energies (averaging over all modeled carbohydrate complexes). The observed interaction energies were also compared with the sum of interaction energies of the corresponding previously published carbohydrate-benzene complexes. Also in this case the interaction energy of the bidentate complex was higher (i.e. weaker interaction) than the sum of interaction energies of the corresponding benzene complexes. However, the obtained difference is lower than before, while the bidentate complex interaction energy corresponds to 4/5 of the sum of interaction energy of the benzene complexes, averaged over all structures. The mentioned comparison might aid protein engineering efforts where amino acid residues phenylalanine or tyrosine are to be replaced by a tryptophan and can help to predict the changes in the interactions. The observed results also show that DFT-D correctly describes the CH-π interaction energy and their additive properties in comparison to CCSD(T)/CBS calculated interaction energies. Thus, the DFT-D approach might be used for calculation of larger complexes of biological interest, where dispersion interaction plays an important role.     

Chaos identification of a colliding constrained body on a moving belt

Nonlinear Dynamics - In this work, the combination of the 0–1 test for chaos and approximate entropy is applied to a newly established mechanical model instead of the Lyapunov exponent...