Dynamical versus variational symmetries: understanding Noether's first theorem

It is argued that awareness of the distinction between dynamical and variational symmetries is crucial to understanding the significance of Noether's 1918 work. Special attention is paid, by way of a number of striking examples, to Noether's first theorem, which establishes a correlation between dynamical symmetries and conservation principles.     

Photoinduced dynamics of a cyanine dye: parallel pathways of non-radiative deactivation involving multiple excited-state twisted transients

Cyanine dyes are broadly used for fluorescence imaging and other photonic applications. 3,3′-Diethylthiacyanine (THIA) is a cyanine dye composed of two identical aromatic heterocyclic moieties linked with a single methine, –CH. The torsional degrees of freedom around the methine bonds provide routes for non-radiative decay, responsible for the inherently low fluorescence quantum yields. Using transient absorption spectroscopy, we determined that upon photoexcitation, the excited state relaxes along two parallel pathways producing three excited-state transients that undergo internal conversion to the ground state. The media viscosity impedes the molecular modes of ring rotation and preferentially affects one of the pathways of non-radiative decay, exerting a dominant effect on the emission properties of THIA. Concurrently, the polarity affects the energy of the transients involved in the decay pathways and further modulates the kinetics of non-radiative deactivation.     

The novel application of Fourier thermal analysis in foundry technologies

The process of casting in sand moulds is used for a large volume of castings manufactured in the world. Internal channels and complex geometries of these products are formed by the placement of cores within the mould cavity. Resin-bound sand mixtures are essential ingredients in engine component manufacturing. In this study, a state-of-the-art application of Fourier thermal analysis in foundry technologies is presented. Investigation of decomposition phenomena of resin-bound moulding materials during casting production is a brand new area to use the potential of thermal sciences. Temperature measurements in test samples of standard types of moulding mixtures were performed. The registered cooling curves were processed by a numerical iteration algorithm to determine the amount of heat absorbed during degradation of the moulding material. Thermogravimetric analysis (TG) and differential thermal analysis (DTA) of sand mixtures were carried out to compare the results of the Fourier thermal analysis with TG and DTA curves.     

Model study on steady heat capacity in driven stochastic systems

We explore two- and three-state Markov models driven out of thermal equilibrium by non-potential forces, to demonstrate basic properties of the steady heat capacity based on the concept of quasistatic excess heat. It is shown that large enough driving forces can make the steady heat capacity negative. For both the low- and high-temperature regimes we propose an approximative thermodynamic scheme in terms of “dynamically renormalized” effective energy levels.     

Gold-surface binding of molecular switches studied by M?ssbauer spectroscopy

The nonanuclear coordination compound [Mo^IV{(CN)Fe^III(3-methyl-saldptn)}₈]Cl₄ exhibits multiple spin transitions (3-methyl-saldptn = N,N′-bis(3′′-methyl-2′′-hydroxy-benzyliden)-1,7-diamino-4-azaheptane). This spin crossover cluster is bound via a self-assembled monolayer onto a two dimensional array gold surface. M?ssbauer spectroscopy indicates that the thermally and optically induced spin crossover of the compound is maintained. Thereby, the foundation for its potential practical application (e.g. in the field of information storage) was laid.     

Stochastic programs without duality gaps

This paper studies dynamic stochastic optimization problems parameterized by a random variable. Such problems arise in many applications in operations research and mathematical finance. We give sufficient conditions for the existence of solutions and the absence of a duality gap. Our proof uses extended dynamic programming equations, whose validity is established under new relaxed conditions that generalize certain no-arbitrage conditions from mathematical finance.     

Electrochemical characterisation of a Zn/(PEO)4ZnCl2/Nb2O5 solid-state cell

The (PEO)₄ZnCl₂ electrolyte (PEO, polyethylene oxide) was studied in view of its potential application in a solid-state rechargeable zinc cell. The electrochemical stability window was established, and decomposition voltage values between 3.19 (20 °C) and 1.44 V (150 °C) were estimated. Cyclic voltammetry studies using a Pt/(PEO)₄ZnCl₂/Pt cell indicated reversibility of the Zn²⁺/Zn couple at the electrode/electrolyte interface. Laboratory cells Zn(−)/(PEO)₄ZnCl₂/Nb₂O₅(+) were assembled and studied at 55 °C, under various discharge current densities. Results of cell discharge profiles, capacity values, charge–discharge cycles and cell stabilities are reported.     

On Barycentric Interpolation. II (Grünwald–Marcinkiewicz type Theorems)

Grünwald–Marcinkiewicz type theorems with respect to barycentric Lagrange interpolation based on equidistant and Chebyshev node-sytems in [–1, 1] are proved. It turns out that the results are very similar to the ones known for the classical Lagrange interpolation.