Saint-Venant's principle in nonlinear plane elasticity with sufficiently small strains

A homogeneous, isotropic cylinder in an equilibrium state of plane strain, whose cross-section is a rectangle R : [0 < y ₁ < 2L; 0 < y ₂ < h] with h/L 1, is considered. There are no body forces and the long sides are stress free. At y ₁ = 0 and y ₁ = 2L, there are arbitrary loadings, each statically equivalent to a uniformly distributed tensile or compressive stress c. Within the theory of nonlinear elasticity and with the strains and strain gradients assumed to be sufficiently small (but with no such assumptions on the displacement gradients), it is proved that if (,=1,2) represents the Cauchy stress tensor and the Kronecker delta, then |–c₁₁| decays exponentially to zero in R with distance from the nearer end, and the decay constant depends only upon the material but is independent of L.     

Synthesis and characterization of ferromagnetic Fe3C/C composite nanoparticles as a catalyst for carbon nanotube growth

Polystyrene template microspheres of narrow size distribution were prepared by dispersion polymerization of styrene in a mixture of ethanol and 2-methoxy ethanol. These template particles dispersed in aqueous solution have been used for the entrapment of ferrocene by a swelling process of methylene chloride emulsion droplets containing ferrocene within these particles, followed by evaporation of methylene chloride. The effects of CH₂Cl₂ volume and the [CH₂Cl₂]/[FeC₁₀H₁₀] (w/w) ratio on the size and size distribution of the swollen template particles were elucidated. Air-stable Fe₃C nanoparticles embedded in amorphous carbon matrix (Fe₃C/C) have been prepared by thermal decomposition of the ferrocene-swollen template polystyrene particles at 500 °C for 2 h in a sealed cell. Decomposition of these swollen template particles for 2 h at higher temperatures led to the formation of carbon nanotubes (CNTs) in addition to the Fe₃C/C composite nanoparticles. The yield of the CNTs increased as the annealing temperature was raised. An opposite behavior was observed for the diameter of the formed CNTs. The size and size distribution, crystallinity, and magnetic properties of the different Fe₃C/C composite nanoparticles have also been controlled by the annealing temperature.     

Analysis of thermal phases in calcareous Iron Age pottery using FT-IR and Raman spectroscopy

The work deals with the FT-IR and micro-Raman spectroscopy study of the pseudo-amorphous and crystalline thermal phases in the composition of calcareous Iron Age pottery from the Galilee. The application of second-derivative and curve-fitting techniques improves the identification of the thermal phases in the composition of the pottery and makes it possible to analyze the pseudo-amorphous phases which are formed during the firing of the clayey raw material to pottery. This technique makes it possible to distinguish between meta-smectite and meta-kaolinite and to estimate the firing temperature of the pottery. The Micro-Raman spectroscopy is sensitive to the structural degree of ordering of the thermal phases and enables point analysis of peculiar components in the composition of the pottery. Based on the spectroscopic study, it is concluded that the calcareous pottery contained large amounts of microcrystalline-recarbonated calcite mixed with the meta-clay. The large amount of recarbonated calcite in the pottery material and the relatively low firing temperature indicates that instead of sintering the clay, lime technology was used for the cementation of the calcareous vessels. This process took place after the firing by recarbonation of the decomposed calcite which leads to cementation of the vessels with microcrystalline calcite.     

Surface properties of plasma membrane vesicles isolated from melon (Cucumus melo L.) root cells differing in salinity tolerance

The hypotheses that genotypic differences in salinity tolerance may result from (i) differences in global surface charge density or (ii) from differences in global Ca²⁺ binding were tested. An attempt was made to correlate the differing salinity tolerance of four melon cultivars with surface properties of vesicles extracted from the plasma membrane (PM) of their root cells. Surface characterization involved measurements of electrophoretic mobility and sorption of ⁴⁵Ca²⁺ to the vesicles in the presence of varying concentrations of Ca²⁺, Na⁺ and Mg²⁺. Irrespective of salinity tolerance, vesicles from the four cultivars yielded similar ζ potentials under similar conditions, indicating similar global surface charge densities. Sorption studies with vesicles from two cultivars differing in salinity tolerance predicted independently this result of equal surface charge density. The estimated global binding affinities of Ca²⁺, Na⁺ and Mg²⁺ to the PM of both cultivars were the same with binding coefficients of 50, 0.8 and 9 M⁻¹, respectively. Consequently, the hypotheses enumerated above to interpret genotypic differences in salinity toxicity are rejected. However, vesicles from the salt-resistant strain sorbed 19% more Ca²⁺ per given amount of protein in the membrane, indicating the existence of a larger number of negatively charged surface sites per given amount of protein and a smaller amount of protein per given area of membrane. Genotypic differences in site-specific Ca²⁺-binding affinity (e.g. at ion channels) remain a viable hypothesis for genotypic differences in salinity tolerance.     

Optimization of Fabry-Perot ring resonator embedding a grating based mirror

We study a triangular arrangement of two flat mirrors and a grating mirror for coupling a \(-1{\mathrm{st}}\) diffracted order light beam into a traveling-wave intra-cavity light recirculation and out-of-cavity output, combining the \(0\,{\mathrm{th}}\) and the repeatedly diffracted secondary \(+1{\mathrm{st}}\) order beams. The thus designed and then optimized grating Fabry-Perot ring cavity demonstrates high output contrast and detection resolution for wavelength, cavity length and incidence angle.     

Response times in gated M/G/1 queues: The processor-sharing case

A class of single server queues with Poisson arrivals and a gated server is considered. Whenever the server becomes idle the gate separating it from the waiting line opens, admitting all the waiting customers into service, and then closes again. The batch admitted into service may be served according to some arbitrary scheme. The equilibrium waiting time distribution is provided for the subclass of conservative schemes with arbitrary service times and the processor-sharing case is treated in some detail to produce the equilibrium time-in-service and response time distributions, conditional on the length of required service. The LIFO and random order of service schemes and the case of compound Poisson arrivals are treated briefly as examples of the effectiveness of the proposed method of analysis. All distributions are provided in terms of their Laplace transforms except for the case of exponential service times where the L.T. of the waiting time distribution is inverted. The first two moments of the equilibrium waiting and response times are provided for most treated cases and in the exponential service times case the batch size distribution is also presented.     

Nilpotent fusion categories

In this paper we extend categorically the notion of a finite nilpotent group to fusion categories. To this end, we first analyze the trivial component of the universal grading of a fusion category C, and then introduce the upper central series of C. For fusion categories with commutative Grothendieck rings (e.g., braided fusion categories) we also introduce the lower central series. We study arithmetic and structural properties of nilpotent fusion categories, and apply our theory to modular categories and to semisimple Hopf algebras. In particular, we show that in the modular case the two central series are centralizers of each other in the sense of M. Müger.