Existence and characterization of regions minimizing perimeter under a volume constraint inside Euclidean cones

We study the problem of existence of regions separating a given amount of volume with the least possible perimeter inside a Euclidean cone. Our main result shows that nonexistence for a given volume implies that the isoperimetric profile of the cone coincides with the one of the half-space. This allows us to give some criteria ensuring existence of isoperimetric regions: for instance, local convexity of the cone at some boundary point.

We also characterize which are the stable regions in a convex cone, i.e., second order minima of perimeter under a volume constraint. From this it follows that the isoperimetric regions in a convex cone are the euclidean balls centered at the vertex intersected with the cone.

     

Cold compaction of ceramic powder: Computational analysis of the effect of pressing method and die shape

This paper deals with a computational analysis of the influence of the pressing method and part geometry on the final density distribution in the cold compaction process of ceramic alumina powders. The analysis is based on the explicit finite-element model proposed and validated in a previous study. The mechanical behavior of the processing material is described using a multisurface elastoplastic model, the modified Drucker-Prager/Cap model Published in Prikladnaya Mekhanika, Vol. 43, No. 10, pp. 129–134, October 2007.     

Design and Cold Tests of Asymmetric Quasioptical Resonators

This paper presents the design and test of asymmetric quasioptical resonators for gyrotron applications, where most of the diffraction output coupling comes from the smaller of two mirrors. A computer code based on scalar diffraction theory is used to calculate the resonator losses and the electric field near the mirrors. Resonators with mirror separations approaching confocal have reduced side lobes in the diffraction patterns, which should allow for better power transmission and focusing. Cold tests have been performed at 94 and 141 GHz to measure the quality factor of the asymmetric resonators as a function of mirror separation and mirror misalignment. Typical resonator parameters include 65 cm mirror separation, 1-3% output coupling and 85% of the losses from the small mirror. A half-symmetric resonator with one flat and one curved mirror has also been investigated. The calculated values of Q are in reasonably good agreement with the cold test measurements.     

A transport model for the evolution of urban systems

When comparing an urban system to an elasto-plastic lattice, an analogy to the solid state of matter can be exploited using the concepts of the band theory similarly. Thereafter, the population dynamics – in a region of certain stability in the state space and within appropriate energy bands – can be described in terms of Cellular Automata, with two mobile agents or pseudo particles: the inhabitant (representative of an average individual) and the recurson (representative of its multidimensional resources). As in the solid state, transition rules take the form of two coupled transport equations, comprising the terms equivalent to the generation-recombination and circulation processes. The first process can be compared to a predator–prey growth model, typical of Ecology; whereas the circulation process – composed of a drift component and a diffusion component – should be compared to the concentration-sprawl demographic balance seen in urban occupation and dynamics. Thus, it needs to be defined and determined an urban potential function, an equivalent population charge, mobility and diffusion parameters, as well as net growth factors. This analogy, discussed within the context of a case study for Great Mendoza, plausibly explains the varied growth rates of the political departments, as well as the principal urban trends for spatial occupation.     

冷态德士古气化炉流场与停留时间分布的研究

测定了德士古气化炉的冷态速度分布和停留时间分布。结果表明：德士古气化炉内在轴向２．５～３．０倍直径范围内存在回流，最大回流量为射流量的３．５倍左右；在平均停留时间之前，已有５０％左右的物料逸出炉外。本文指出，德士古气化炉中存在的问题，如结渣、耐火砖寿命短、有效气体成分偏低均与炉内流场有关。     

DSC study of cold and heat denaturation processes of β-lactoglobulin A with guanidine hydrochloride

The cold and heat denaturations of bovine P-lactoglobulin A ((β-lg A) has been studied in solutions of guanidine hydrochloride (GuHCI) by differential scanning calorimetry (DSC). The experimental results are presented and discussed. It is shown that the number of protons bound by the monomeric molecules of β-lg A was unchanged before and after its heat denaturation below pH 3, and that the activation energy of the heat denaturation was depressed owing to the presence of GuHCI. In the solutions with 2.50 and 3.06 mol/L of GuHCI, both the cold and heat denaturations of P-lg A were observed. In comparison with the heat denaturation, the activation energy of cold denaturation was far lower and the number of GuHCl molecules bound by the unfolded polypeptide chains after culd denaturation increased a lot. The absolute value of the enthalpy of cold denaturation was larger than that of heat denaturation. It was found by the analysis that the contribution to the total denaturational enthalpy of conformational change itself of the monomeric molecules of β-lg A was the lowest among the globulins, according to the average of the number of heavy atoms. Project supported by the National Natural Science Foundation of China, and by the fund for excellent items under Director of the Institute of Chemistry.     

Characterization of immobilized catalases and their application in pasteurization of milk with H2O2

The catalase (fromAspergillus niger) has been immobilized by a chemical method on the pous SiO₂ modified with γ-aminopropyltrietoxysilane, followed with glutaraldehyde and by a physical method in alginate and γ-carrageenan gel. Optimum support:enzyme ratios and pH values were determined for modified SiO₂ in a series of immobilization reactions of catalase in the presence of the crosslinking agent glutaraldehyde, and for alginate and γ-carrageenan in the presence of hemoglobin and bovine serum albimine. pH and temperaturedependent activity variations and the stability properties of immobilized catalase preparations were investigated. Rate constants for H₂O₂ decomposition and catalase deactivation were determined. The decomposition rate of H₂O₂ used in the cold pasteurizatioan of milk were investigated in a discontinuous batch type reactor system. Activity half-lives of immobilized catalase were determined.     

Comparison of Pyrolysis and Microwave Acid Digestion Techniques for the Determination of Mercury in Biological and Environmental Materials

 Microwave digestion reduction-aeration and pyrolysis combined with cold vapour atomic absorption and cold vapour atomic fluorescence are compared for the determination of total mercury in several biological and environmental matrices. The biological samples were digested in a mixture of HNO₃/H₂O₂, the environmental samples in a mixture of HNO₃/HClO₄. After reduction with SnCl₂, the mercury was collected by two-stage gold amalgamation. After microwave digestion reduction-aeration, detection limits of 1.4 ng g⁻¹ and 0.6 ng g⁻¹ were obtained for cold vapour atomic absorption spectrometry (CVAAS) and cold vapour atomic fluorescence spectrometry (CVAFS), respectively, for 250 mg of environmental samples. For biological samples (500 mg) the detection limits were 0.7 ng g⁻¹ (CVAAS) and 0.4 ng g⁻¹ (CVAFS). After pyrolysis, detection limits of 3.5 ng g⁻¹ and 1.6 ng g⁻¹ for CVAAS and CVAFS, respectively, were obtained for a 10 mg sample. Pyrolysis can only be applied when the organic content of the sample is not too high. Accurate results were obtained for 8 certified reference materials of both environmental and biological origin. In addition, a real sludge sample was analysed. Author for correspondence. E-mail: richard.dams@rug.ac.be Received September 18, 2002; accepted December 3, 2002 Published online May 5, 2003     

Study of polymer treatment with tetrafluoromethane plasma: Reactivity of fluorinated species on model surfaces

Polyolefins and their model molecules, some n-alcanes, have been modified by a tetrafluoromethane microwave plasma. The chosen molecules are high-density polyethylene (HDPE) and hexatriacontane (HTC), low-density polyethylene (LDPE) and paraffin, and polycaprolactone (PCL) and octadecyl octadecanoate (ODO). It has been found, except for paraffin, that the model surfaces have the same behavior as the corresponding polymers. Plasma modification is described as the sum of two mechanisms: degradation and fluorination. These reactions seem to be competitive and parallel. Degradation and fluorination rates are dependent on treatment time and are practically independent on substrate position. A domain of fluorination exists near the edge of plasma, whatever the substrate in or outside plasma. © 1993 John Wiley & Sons, Inc.     

Sample decomposition in an electrically heated cold-trap inlet system for high speed gas chromatography

Thermal decomposition of some hydrocarbon and chlorinated hydrocarbon compounds in metal capillary tubes used in an inlet system for high speed gas chromatography has been investigated. The metal tube is cooled to about ?75°C by a flow of cold nitrogen gas in order to focus a vapor sample cryogenically. A capacitive discharge power supply is then used to heat the metal tube resistively in order to revaporize the sample and introduce it to the separation column as a plug 5-10 ms wide. The effects of tube temperature, tube material, sample vapor residence time, and type of carrier gas on thermal cracking are described. Use of a copper-nickel alloy tube resulted in less cracking than either pure platinum or pure nickel. Cracking is more significant with hydrogen as carrier gas than with helium. Cracking also increases with increasing sample residence time in the hot tube. Quantitative sample injection with minimum decomposition can be obtained for a variety of aliphatic and aromatic hydrocarbons and chlorinated hydrocarbon compounds.