Optimal Regularity and Long-Time Behavior of Solutions for the Westervelt Equation

We investigate an initial-boundary value problem for the quasilinear Westervelt equation which models the propagation of sound in fluidic media. We prove that, if the initial data are sufficiently small and regular, then there exists a unique global solution with optimal L _p -regularity. We show furthermore that the solution converges to zero at an exponential rate as time tends to infinity. Our techniques are based on maximal L _p -regularity for abstract quasilinear parabolic equations.     

Design,Synthesis, and Phenotypic Profiling of Pyrano‐Furo‐Pyridone Pseudo Natural Products

Natural products (NPs) inspire the design and synthesis of novel biologically relevant chemical matter, for instance through biology‐oriented synthesis (BIOS). However, BIOS is limited by the partial coverage of NP‐like chemical space by the guiding NPs. The design and synthesis of “pseudo NPs” overcomes these limitations by combining NP‐inspired strategies with fragment‐based compound design through de novo combination of NP‐derived fragments to unprecedented compound classes not accessible through biosynthesis. We describe the development and biological evaluation of pyrano‐furo‐pyridone (PFP) pseudo NPs, which combine pyridone‐ and dihydropyran NP fragments in three isomeric arrangements. Cheminformatic analysis indicates that the PFPs reside in an area of NP‐like chemical space not covered by existing NPs but rather by drugs and related compounds. Phenotypic profiling in a target‐agnostic “cell painting” assay revealed that PFPs induce formation of reactive oxygen species and are structurally novel inhibitors of mitochondrial complex I.     

The Glycosylation Mechanisms of 6,3‐Uronic Acid Lactones

Uronic acids are important constituents of polysaccharides found on the cell membranes of different organisms. To prepare uronic‐acid‐containing oligosaccharides, uronic acid 6,3‐lactones can be employed as they display a fixed conformation and a unique reactivity and stereoselectivity. Herein, we report a highly β‐selective and efficient mannosyl donor based on C‐4 acetyl mannuronic acid 6,3‐lactone donors. The mechanism of glycosylation is established using a combination of techniques, including infrared ion spectroscopy combined with quantum‐chemical calculations and variable‐temperature nuclear magnetic resonance (VT NMR) spectroscopy. The role of these intermediates in glycosylation is assayed by varying the activation protocol and acceptor nucleophilicity. The observed trends are analogous to the well‐studied 4,6‐benzylidene glycosides and may be used to guide the development of next‐generation stereoselective glycosyl donors.     

Measurement of physical properties of DyScO3 melt

Rare earth scandate crystals ReScO₃ (Re=La, Ce, Pr, Nd, Sm, Eu, Gd, Tb and Dy) can be grown from the melt at temperatures of about 2100 °C. The needs of thermal insulation of the whole system are very high in order to reach the melting point and to control the thermal gradients which are required by the Czochralski (Cz) method. The consequence is that in‐vivo system observations are practically almost impossible or very hard to perform. Therefore numerical investigations using a mathematical model of the real system can be very helpful. However, numerical models need some physical properties of the considered real system (e.g. density, viscosity, thermal expansion coefficients, thermal conductivity). Most material properties of high melting oxides are not referenced in the literature or they are incomplete and inaccurate. Because the accuracy of qualitative and quantitative results of numerical simulations depend on the used physical properties, we performed corresponding measurements in an adapted Cz configuration at a temperature around the melting point of DyScO₃ (2060 °C). The results are presented and discussed in this work. (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

On the JWKB solution of the uniformly lengthening pendulum via change of independent variable in the Bessel’s equation

Common recipe for the lengthening pendulum (LP) involves some change of variables to give a relationship with the Bessel’s equation. In this work, conventional semiclassical JWKB solution (named after Jeffreys, Wentzel, Kramers and Brillouin) of the LP is being obtained by first transforming the related Bessel’s equation into the normal form ‘via the suggested change of independent variable’. JWKB approximation of the first-order Bessel functions (ν=1) of both types along with their zeros are being obtained analytically with a very good accuracy as a result of the appropriately chosen associated initial values and they are extended to the neighbouring orders (ν=0 and 2) by the recursion relations. The required initial values are also being studied and a quantization rule regarding the experimental LP parameters is being determined. Although common numerical methods given in the literature require adiabatic LP systems where the lengthening rate is slow, JWKB solution presented here can safely be used for higher lengthening rates and a criterion for its validity is determined by the JWKB applicability criterion given in the literature. As a result, the semiclassical JWKB method which is normally used for the quantum mechanical and optical waveguide systems is applied to the classical LP system successfully.     

Influence of internal radiation on the heat transfer during growth of YAG single crystals by the Czochralski method

Heat and mass transfer taking place during growth of Y₃Al₅O₁₂ (YAG) crystals by the Czochralski method, including inner radiation, is analyzed numerically using a Finite Element Method. For inner radiative heat transfer through the crystal the band approximation model and real transmission characteristics, measured from obtained crystals, are used. The results reveal significant differences in temperature and melt flow for YAG crystals doped with different dopands influencing the optical properties of the crystals. When radiative heat transport through the crystal is taken into account the melt‐crystal interface shape is different from that when the radiative transport is not included. Its deflection remains constant over a wide range of crystal rotation rates until it finally rapidly changes in a narrow range of rotation rates. (© 2003 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)