Transformation formulae for Dirichlet polynomials

Formulae of Voronoi-Atkinson type are proved for Dirichlet polynomials related to the Dirichlet series ζ²(s) = Σd(n)n^?s or ?(s) = Σa(n)n^?s, where the a(n) are the Fourier coefficients of a cusp form, a typical example being a(n) = τ(n), the Ramanujan function. Applications are given to a formula of Atkinson (Acta Math.81 (1949), 353–376) for the mean square of $\text{|ζ(}\text{1}\text{2}\text{+ it)|}$ and to the differences between consecutive zeros of ?(s) on the critical line in the case when all the a(n) are real.     

Modelling of plasticity and damage in a polycrystalline microstructure

The mesomechanical behavior of a polycrystalline microstructure subjected to monotonic and cyclic loadings is investigated. The analysis is based on a Voronoi polygonization strategy for generation of grains embedded in a contiguous matrix. The main emphasis is to investigate the interaction between the microconstituents and the failure processes along grain boundaries. A rational interface theory based on damage development coupled to inelastic slip and dilatation is developed. The theory uses the interface width as a constitutive parameter, which regularizes the theory of LEMAITRE [1992], that is restricted to perfect bond between grain and matrix. In a series of FE-analyses parameter variations were performed: The unit cell size (as compared to the average grain diameter), the grain-matrix area ratio, the interface width and constitutive parameters. It appears that the composite behavior can be designed as brittle or ductile solely depending on the strength and rate of damage development in the interfaces. A localization band was detected, and its orientation is in the range that is predicted within continuum theory.     

Conformational analysis of hydroxymatairesinol in aqueous solution with molecular dynamics

Molecular dynamics simulations were performed on the naturally occuring lignan hydroxymatairesinol (HMR) using the GROMACS software. The aim of this study was to explore the conformational behavior of HMR in aqueous solution adopting the TIP4P model. The topology of HMR was constructed by hand and HMR was modeled with the OPLS‐AA force field implemented in GROMACS. The five torsional angles in HMR were properly analyzed during the simulations. Correlations through certain patterns were observed between the angles. The determining property for the conformation preferred in aqueous solution was found to be the dipole moment and not the lowest energy in gas phase. The solvation effects on HMR was also studied by quantum chemical calculations applying the COnductorlike Screening MOdel (COSMO), the results of which were compared with results from a previous study using the Polarized Continuum Model (PCM). In the present work, COSMO was found to give more credible relative energies than PCM. © 2009 Wiley Periodicals, Inc., J Comput Chem, 2009     

Continuous two-dimensional field-flow fractionation: a novel technique for continuous separation and collection of macromolecules and particles

Instrumental techniques to analyse macromolecular and particulate materials have undergone rapid development in response to the need for high resolution, precise identification and characterization, and enrichment and collection for further analysis. Continuous two-dimensional field-flow fractionation (2D-FFF), which is described in this article, is a novel technique for separation and collection of macromolecules and particles. 2D-FFF is based on the conventional field-flow fractionation principle but with carrier flow in two-dimensions. This overview discusses the principle of the technique, describes the instrumentation and suggests potential applications and further extensions. An overview of the basic field-flow fractionation principle is presented.     

Some inequalities for the Poincaré metric of plane domains

In this paper, the Poincaré (or hyperbolic) metric and the associated distance are investigated for a plane domain based on the detailed properties of those for the particular domain In particular, another proof of a recent result of Gardiner and Lakic [7] is given with explicit constant. This and some other constants in this paper involve particular values of complete elliptic integrals and related special functions. A concrete estimate for the hyperbolic distance near a boundary point is also given, from which refinements of Littlewood’s theorem are derived.This research was carried out during the first-named author’s visit to the University of Helsinki under the exchange programme of scientists between the Academy of Finland and the JSPS.     

On character sums and class numbers

A mean-value estimate for character sums with real characters is proved in an elementary way. The application is a proof of a conjecture on the error term in the asymptotic expression of the sum Σ_d≤xh^k(?d), where h(?d) is the class number of the quadratic field with the negative discriminant ?d, and k is an integer ≥ 2.