Derivation of fluid dynamics from kinetic theory with the 14-moment approximation

We review the traditional derivation of the fluid-dynamical equations from kinetic theory according to Israel and Stewart. We show that their procedure to close the fluid-dynamical equations of motion is not unique. Their approach contains two approximations, the first being the so-called 14-moment approximation to truncate the single-particle distribution function. The second consists in the choice of equations of motion for the dissipative currents. Israel and Stewart used the second moment of the Boltzmann equation, but this is not the only possible choice. In fact, there are infinitely many moments of the Boltzmann equation which can serve as equations of motion for the dissipative currents. All resulting equations of motion have the same form, but the transport coefficients are different in each case.     

Local approximation of superharmonic and superparabolic functions in nonlinear potential theory

We prove that arbitrary superharmonic functions and superparabolic functions related to the p-Laplace and the p-parabolic equations are locally obtained as limits of supersolutions with desired convergence properties of the corresponding Riesz measures. As an application we show that a family of uniformly bounded supersolutions to the p-parabolic equation contains a subsequence that converges to a supersolution.     

Azafullerene C59N–Phthalocyanine Dyad: Synthesis,Characterisation and Photoinduced Electron Transfer

The synthesis of a new azafullerene C₅₉N–phthalocyanine (Pc) dyad is described. The key step for the synthesis of the C₅₉N–Pc dyad was the formation of the C₅₉N‐based carboxylic acid, which was smoothly condensed with hydroxy‐modified Pc. The structure of the C₅₉N–Pc dyad was verified by ¹H and ¹³C NMR spectroscopy, IR spectroscopy, UV/Vis spectroscopy and MS measurements. The photophysical and electrochemical properties of the C₅₉N–Pc dyad were investigated in both polar and non‐polar solvents by steady state and time‐resolved photoluminescence and absorption spectroscopy, as well as by cyclic voltammetry. Different relaxation pathways for the photoexcited C₅₉N–Pc dyad, as a result of changing the solvent polarity, were found, thus giving rise to energy‐transfer phenomena in non‐polar toluene and charge‐transfer processes in polar benzonitrile. Finally, the detailed quenching mechanisms were evaluated and compared with that of a C₆₀–Pc dyad, which revealed that the different excited‐state energies and reduction potentials of the two fullerene spheres (i.e. C₅₉N vs. C₆₀) strongly diverged in the deactivation pathways of the excited states of the corresponding phthalocyanine dyads.     

Hybrid waveguide-surface plasmon polariton modes in a guided-mode resonance grating

We analyze the coupling between surface plasmon polaritons in a metal grating and the guided modes of a dielectric waveguide. Our model structure is a gold wire grating on a slab waveguide made of silicon nitride on silica wafer. The excitation of guided-mode resonances, surface plasmon polariton modes and hybrid waveguide-plasmon modes are observed in numerical simulations. Our experiments verify the existence of the predicted modes. These hybrid modes add significant degrees of freedom in designing structures for plasmonic applications.     

Picosecond pulse laser ablation of yttria-stabilized zirconia from kilohertz to megahertz repetition rates

Thin films of yttria stabilized zirconia were deposited onto silicon substrates using high repetition rate picosecond pulse lasers. The applied lasers covered the repetition rate range from 10 kHz to 4 MHz. We found that the laser pulse overlapping which results from increased repetition rates led to considerable changes in the ablation process. Defect formation and local heating lead to lower ablation thresholds and, with sufficiently high repetition rates, to melting of the target and even to thermal evaporation. We found that yttria-stabilized zirconia (YSZ) films deposited with picosecond pulses at 1064 nm wavelength below repetition rates of 2 MHz have rough, nanostructured morphology and the same atomic ratio of yttrium and zirconium as the target. Films deposited with 2 MHz and higher repetition rates with high number of overlapping pulses are very smooth, but are yttrium deficient, providing evidence of the importance of the thermal processes.     

Numerical tests of causal relativistic dissipative fluid dynamics

We present numerical methods to solve the Israel–Stewart (IS) equations of causal relativistic dissipative fluid dynamics with bulk and shear viscosities. We then test these methods studying the Riemann problem in (1+1)- and (2+1)-dimensional geometry. The numerical schemes investigated here are applicable to realistic (3+1)-dimensional modeling of a relativistic dissipative fluid.     

Über die Bildung von Thiazolderivaten aus Harnsäure

Ohne Zusammenfassung     

A splitting method for stochastic programs

This paper derives a new splitting-based decomposition algorithm for convex stochastic programs. It combines certain attractive features of the progressive hedging algorithm of Rockafellar and Wets, the dynamic splitting algorithm of Salinger and Rockafellar and an algorithm of Korf. We give two derivations of our algorithm. The first one is very simple, and the second one yields a preconditioner that resulted in a considerable speed-up in our numerical tests. The first author was supported by the Finnish Foundation for Economic Education under grants 20728 and 21599, and by Jenny ja Antti Wihuri Foundation.     

Atomic Decomposition of a Weighted Inductive Limit in \mathbb{C}^{n}

We construct an atomic decomposition of the space H_V^∞ consisting of analytic functions on the open unit disc. The research of the second named author was supported by the Academy of Finland project “Functional Analysis and Applications”.     

A stochastic programming model for asset liability management of a Finnish pension company

This paper describes a stochastic programming model that was developed for asset liability management of a Finnish pension insurance company. In many respects the model resembles those presented in the literature, but it has some unique features stemming from the statutory restrictions for Finnish pension insurance companies. Particular attention is paid to modeling the stochastic factors, numerical solution of the resulting optimization problem and evaluation of the solution. Out-of-sample tests clearly favor the strategies suggested by our model over static fixed-mix and dynamic portfolio insurance strategies. Financial support from the Foundation for the Helsinki School of Economics under grants number 9981114 and 9981117 for P. Hilli and M. Koivu is gratefully acknowledged. The work of T. Pennanen was supported by Finnish Academy under contract no. 3385