Initial blow-up rates and universal bounds for nonlinear heat equations

We establish a universal upper bound on the initial blow-up rate for all positive classical solutions of the Dirichlet problem for the nonlinear heat equation

     

Relationship between local structure and relaxor behavior in perovskite oxides

Despite intensive investigations over the past five decades, the microscopic origins of the fascinating dielectric properties of ABO3 relaxor ferroelectrics are currently poorly understood. Here, we show that the frequency dispersion that is the hallmark of relaxor behavior is quantitatively related to the crystal chemical characteristics of the solid solution. Density functional theory is used in conjunction with experimental determination of cation arrangement to identify the 0 K structural motifs. These are then used to parametrize a simple phenomenological Landau theory that predicts the universal dependence of frequency dispersion on the solid solution cation arrangement and off-center cation displacements.     

Calculation of the mean first passage time tested on simple two-dimensional models

A particle diffusing in a two-dimensional (2D) container, shaped as a simplified configuration space of two passing 2D circular particles in a flat channel, is considered. The mean first passage time through one absorbing boundary is calculated using the one-dimensional Fick-Jacobs equation and its modification; both derived by mapping the 2D diffusion equation onto the longitudinal ("reaction") coordinate. The obtained results are compared with the hopping time, defined as the inverted lowest eigenvalue of the full 2D problem. The comparison shows that the mapped equations give reliable results, in contrast to predictions of the simplest concept of the transition state theory.     

Synchrotron SAX and WAX diffraction study of a hydrated very long-chain, dendritic amphiphile + DPPC mixture

The tri-headed anionic dendritic amphiphile, 4-(2-carboxyethyl)-4-[(icosyloxycarbonyl)amino]heptanedioic acid (3CCb20), forms mixed aggregates with dipalmitoylphosphatidylcholine (DPPC) in excess water at 3CCb20:DPPC = 0.91:1 molar ratio. On heating, these mixed aggregates transform into fluid bilayers stacked in the liquid crystalline lamellar L phase at about 40 °C. This phase transition and the microstructure of 3CCb20 + DPPC aggregates were studied with small- and wide-angle synchrotron X-ray diffraction. The ability of 3CCb20 to solubilize solidlike lipid bilayers could contribute to the antimicrobial activities of 3CCb20, including its anti-HIV activity.     

Aqueous phase size exclusion chromatography of polyvinylalcohols of different degrees of hydrolysis

The aqueous-phase size exclusion chromatography (SEC) represents a suitable method for the analysis of molecular weight distribution (MWD) of polyvinylalcohols (PVOHs) of different degree of hydrolysis ranging from 72 to 98 mol-% applying the Suprema columns. Eluents of different composition were used consisting of either a mixture of water and acetonitrile for the lower degrees of hydrolysis (72 - 88 mol-%) or 0.1 M LiNO₃ solution for the higher degrees of hydrolysis (88 - 98 mol-%). By knowing the M̄_w̄ values of commercially available PVOHs samples of a given degree of hydrolysis and using the commercial water soluble narrow distribution standards, a principle of the constant hydrodynamic equivalence ratios was applied to obtain the absolute values of the molecular weights of PVOHs of different degree of hydrolysis. The effect of a various number of extrusion cycles on MWD of different PVOHs was used to demonstrate the sensitivity of the selected SEC conditions.     

Investigating the interaction of x-ray free electron laser radiation with grating structure

The interaction of free electron laser pulses with grating structure is investigated using 4.6±0.1 nm radiation at the FLASH facility in Hamburg. For fluences above 63.7±8.7 mJ/cm², the interaction triggers a damage process starting at the edge of the grating structure as evidenced by optical and atomic force microscopy. Simulations based on solution of the Helmholtz equation demonstrate an enhancement of the electric field intensity distribution at the edge of the grating structure. A procedure is finally deduced to evaluate damage threshold.     

Spectral Properties of Y-Shaped Donor-Acceptor Push-Pull Imidazole-based Fluorophores: Comparison between Solution and Polymer Matrices

The spectral properties of a novel type of Y-shaped fluorophores consisting of an imidazole ring end-capped with two electron-donating N,N-dimethylaminophenyl groups at positions C4 and C5 and one electron-withdrawing cyano group on the imidazole moiety at position C2 were examined. The π-linker separating the 4,5-bis[4-(N,N-dimethylamino)phenyl]-1H-imidazole donor moiety and the cyano group comprises 1,4-phenylene (1), (E)-phenylethenyl (2), (E)-phenylbuta-1,3-dienyl (3), biphenyl (4), (E)-phenylethenylphenyl (5) and phenylethynylphenyl (6) conjugated paths. The absorption and fluorescence spectra were obtained in toluene, dichloromethane, acetonitrile and methanol and in polymer matrices such as polystyrene (PS), poly(methyl methacrylate) (PMMA) and poly(vinylchloride) (PVC). The most intense absorption bands of fluorophores 1-6 were observed within the range of 283 to 330?nm. Less intense but longer-wavelength absorption bands designated as charge-transfer bands were observed at approximately 380-430?nm depending on the medium. The fluorophores exhibited strong fluorescence in the visible region with a Stokes shift of approximately 4300-5800?cm(-1) in non-polar toluene and polystyrene, whereas very low intensity of fluorescence was observed with a Stokes shift in the 6500-7800?cm(-1) region in polar methanol and acetonitrile. The large Stokes shift indicates a large difference in the spatial arrangement of the chromophore in the absorbing and emitting states. A relatively intense fluorescence (quantum yields of 0.12-0.69) was observed only for derivative 1 in all media except methanol. The fluorophores doped in matrices yielded more intense fluorescence compared with the fluorescence in liquid media. The use of solid polymer matrices lowers the probability of forming non-emissive excited states. The fluorescence lifetimes were short (1-4?ns) for all of the fluorophores in solvents and in polymer matrices.     

Preparation and Spectral Characterization of Fluorescence Probes Based on 4-N,N-Dimethylamino Benzoic Acid and Sterically Hindered Amines

The adducts of simple chromophore 4-N,N-dimethylamino benzoic acid with 2,2,6,6-tetrametyl-4-hydroxy- or 4-amino-piperidine were examined as fluorescence probes (spin double sensors) to monitor radical processes. The links in the adducts were either an ester or amide group, and the sterically hindered amines were in the form of -NH, -NO? and -NOR. The spectral properties of the three related derivatives (esters or amides) were quite similar. The maxima of the absorption spectra were in the range of 295-315?nm, and the maximum of fluorescence was located in the range of 330-360?nm, depending on the polarity of the solvent. In polar solvents, a red-shifted fluorescence band at 460-475?nm was observed. The fluorescence of these derivatives was rather weak as compared to anthracene under the same conditions. The Stokes shift was large, as high as 6,000?cm(-1), indicating the formation of a twisted intra-molecular charge transfer (TICT) state. No large differences in Stokes shifts were observed in polymer matrices of poly(methyl methacrylate), polystyrene and poly(vinyl chloride). The extent of intramolecular quenching was expressed as Φ(NX)/Φ(NO) (X?=?H, NOR) and was in the range of 1-3 in solution and as high as 8 in polymer matrices. The low efficiency of intramolecular quenching limits the application of these new adducts as fluorescence probes for the monitoring of radical processes in solution but favors their application in polymer matrices.