Monotonicity methods in generalized Orlicz spaces for a class of non‐Newtonian fluids

The paper concerns existence of weak solutions to the equations describing a motion of some non‐Newtonian fluids with non‐standard growth conditions of the Cauchy stress tensor. Motivated by the fluids of strongly inhomogeneous behavior and having the property of rapid shear thickening, we observe that the L^p framework is not suitable to capture the described situation. We describe the growth conditions with the help of general x‐dependent convex function. This formulation yields the existence of solutions in generalized Orlicz spaces. As examples of motivation for considering non‐Newtonian fluids in such spaces, we recall the electrorheological fluids, magnetorheological fluids, and shear thickening fluids. The existence of solutions is established by the generalization of the classical Minty method to non‐reflexive spaces. The result holds under the assumption that the lowest growth of the Cauchy stress is greater than the critical exponent q=(3d+ 2)/(d+ 2), where d is for space dimension. The restriction on the exponent q is forced by the convective term. Copyright © 2009 John Wiley & Sons, Ltd.     

Maximum principles and nonexistence results for radial solutions to equations involving p‐Laplacian

We obtain the variant of maximum principle for radial solutions of, possibly singular, p‐harmonic equations of the form as well as for solutions of the related ODE. We show that for the considered class of equations local maxima of |w| form a monotone sequence in |x| and constant sign solutions are monotone. The results are applied to nonexistence and nonlinear eigenvalue problems. We generalize our previous work for the case h≡0. Copyright © 2010 John Wiley & Sons, Ltd.     

Hydrogen adsorption on Pd(133) surface

An approach based on measurements of the total energy distribution (TED) of field emitted electrons is used in order to examine properties of the Pd(133) from the aspect of hydrogen adsorption. The most favourable sites offered to a hydrogen atom to be adsorbed are indicated and an attempt to ascribe the peaks of the enhancement factor R in the TED spectrum to the specific adsorption sites is made.      

Adaptive solution of elliptic PDE-eigenvalue problems.

In this paper we introduce a new adaptive algorithm (AFEMLA) for elliptic PDE-eigenvalue problems. In contrast to other approaches the algebraic eigenvalue problem does not have to be solved to full accuracy. We incorporate the iterative solution of the resulting finite dimensional algebraic eigenvalue problems in the adaptation process in order to balance the cost with the costs for the iterative eigenvalue method. We present error estimates that incorporate the discretization errors, approximation errors in the eigenvalue solver and roundoff errors. (© 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Molecular and supramolecular helicity induction in trityl group-containing compounds: The case of chiral 3,3,3-triphenylpropionic acid derivatives

The process of dynamic chirality transmission from permanent chirality element to stereodynamic triphenylmethyl group placed in the distance of 4 bonds, has been studied for series of optically active 3,3,3-triphenylpropionic acid derivatives. Structural analysis, carried out with the use of complementary methods and supported by theoretical calculations, enabled us to determine the mechanism of chirality transmission. The observed chirality transfer phenomenon, demonstrated unequivocally as raising of non-zero Cotton effects in the region of UV absorption of trityl group, is a cascade process driven by weak intramolecular interactions. Despite the much larger inductor-effector distance, the sensitivity in chirogenesis is comparable to other stereodynamic probes reported so far. In the crystalline phase, the combination of trityl group with amino acid moiety results in the formation of helical superstructures, where individual molecules are held together by hydrogen bonding cascades. The proper combination of functionalities in the molecule skeleton allows, to some extent, the control over the association process and authorizes determination of the trityl group as the supramolecular synthon.     

Peptidomics and proteomics based on CE‐MS as a robust tool in clinical application: The past,the present,and the future

Capillary electrophoresis combined with mass spectrometry (CE‐MS) has been used for several years for the investigation of proteins and peptides as biomarkers for diagnosis and prognosis of diseases. In addition, the technology has recently been introduced to support the stratification of patients in clinical trials and in large clinical studies. In this review, we aim at presenting the development of CE‐MS over the last 20 years, by focusing on the clinical potential of proteome and peptidome analysis and highlighting some of the key technical issues and advancements that have been made in this context towards implementation. Based on the reviewed literature, it has become evident that CE‐MS is now an accepted tool in clinical application in several disease areas. Apart from a critical overview on the current state‐of‐the‐art in CE‐MS, we also indicate the expected developments for potential future use.     

Heterolepic β-Ketoiminate Zinc Phenoxide Complexes as Efficient Catalysts for the Ring Opening Polymerization of Lactide

Zinc phenoxide complexes L¹ZnOAr 1 – 4 (L¹=Me₂NC₂H₄NC(Me)CHC(Me)O) and L²ZnOAr 5 – 8 (L²=Me₂NC₃H₆NC(Me)CHC(Me)O) with donor-functionalized β-ketoiminate ligands (L^1/2) and OAr substituents (Ar=Ph 1 , 5 ; 2,6-Me₂-C₆H₃ 2 , 6 ; 3,5-Me₂-C₆H₃ 3 , 7 ; 4-Bu-C₆H₄ 4 , 8 ) with tuneable electronic and steric properties were synthesized and characterized. 1 – 8 adopt binuclear structures in the solid state except for 5 , while they are monomeric in CDCl₃ solution. 1 – 8 are active catalysts for the ring opening polymerization (ROP) of lactide (LA) in CH₂Cl₂ at ambient temperature and the catalytic activity is controlled by the electronic and steric properties of the OAr substituent, yielding polymers with high average molecular weight (M_n) and moderately controlled molecular weight distribution (MWDs). 1 and 5 showed a living polymerization character and kinetic studies on the ROP of L–LA with 1 and 5 proved first order dependencies on the monomer concentration. Homonuclear decoupled ¹H-NMR analyses of polylactic acid (PLA) formed with rac-LA proved isotactic enrichment of the PLA microstructure.     

Amplification of changes of a thin film's macromolecular structure into macroscopic reaction-diffusion patterns

A reaction-diffusion process induced from a micronetwork geometry amplifies changes in the molecular structure of a thin gel film into macroscopic readout patterns. When the gel undergoes a helix-to-coil phase transition, the patterns formed by RD switch from symmetry-broken to symmetric ones. Theoretical analysis explains how the system reconfigures internally in response to mass transfer between the applied network and the probed film.