Singular solutions top-Laplacian type equations

We construct singular solutions to equations

Modeling of three-dimensional pressure fields in sonochemical reactors with an inhomogeneous density distribution of cavitation bubbles. Comparison of theoretical and experimental results

During the last 50 years extensive experimental investigation has been carried out on the chemical effects of ultrasound, but limited work has been reported on modeling. This paper presents a new model in which a numerical calculation of the three-dimensional linear sound pressure field distribution in a commonly used sonoreactor containing three transducers is carried out. In this model the inhomogeneous three-dimensional time-dependent wave equation was solved using the finite difference approach. The modeled results are then compared with the experimentally measured values, and the agreement, in general, is found to be good. Further, our modeling studies have an advantage, since they clearly describe the continuous sound pressure field structure, unlike previously reported results in which some information is missing due to limited intermittent measured points.     

Engineering Aspects of Preparation of Nanocrystalline Particles in Microemulsions

Engineering aspects of the preparation of palladium nanoparticles in non-ionic w/o-microemulsions are examined. In order to achieve reproducible synthesis conditions a semi-batch reactor with a standardized design is used. Influences of the stirring rate and of different ways of concentration control on the product properties are observed. For reproducible synthesis it is important to establish appropriate and defined preparation conditions. Monodisperse palladium particles of around 5nm size are obtained by adding the microemulsion containing the palladium salt at a constant feed rate to the precharged microemulsion containing the reducing agent. A quantitative kinetic model is proposed to describe particle formation in microemulsions. Unknown parameters of the model have been estimated by independent examinations or can be achieved by fitting to the experimental data.     

Gravitational redshift experiments with the high-resolution Mössbauer resonance in67Zn

A gravitational tedshift (GRS) experiment using the high-resolution Mössbauer resonance in⁶⁷Zn is described. The tiny Doppler motion of the source can be checked by a dc-SQUID based displacement sensor. The results on the GRS strongly indicate that solid-state effects, which are difficult to control experimentally, finally limit the accuracy that Mössbauer measurements can provide in determining the GRS. We argue that for this reason conventional Mössbauer experiments most probably will not be able to compete with other methods in future GRS measurements of very high precision.     

Determination of the third velocity component with PTA using an intensity graded light sheet

A new method for the determination of the velocity field with all three velocity components in a light sheet was demonstrated that combines conventional particle tracking anemometry (PTA) with an intensity analysis of the particle flecks. The correlation between intensity and the dimension perpendicular to the light sheet was obtained from the monotonous variation of the laser light intensity across the width of the light sheet.     

Time of flight spectra in chemisorption

Phenomenological models based on the master equation are analyzed to calculate the temperature and angular dependence of time of flight spectra in chemisorption. Strong deviations from Knudsen's cosine law and Maxwell's velocity distribution are produced. The Gaussian model seems of little relevance for the analysis of experimental data for which, in most cases, models incorporating activation barriers are needed.     

Ethanolic fermentation of lignocellulose hydrolysates

Applied Biochemistry and Biotechnology -     

Almost sure quasilocality fails for the random-cluster model on a tree

We study the random-cluster model on a homogeneous tree, and show that the following three conditions are equivalent for a random-cluster measure: quasilocality, almost sure quasilocality, and the almost sure nonexistence of infinite clusters. As a consequence of this, we find that the plus measure for the Ising model on a tree at sufficiently low temperatures can be mapped, via a local stochastic transformation, into a measure which fails to be almost surely quasilocal.