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We derive and numerically implement various asymptotic approximations for the lowest or principal eigenvalue of the Laplacian with a periodic arrangement of localised traps of small \[\mathcal{O}(\varepsilon)\] spatial extent that are centred at the lattice points of an arbitrary Bravais lattice in \[{\mathbb{R}^2}\]. The expansion of this principal eigenvalue proceeds in powers of \[\nu \equiv - 1/\log (\varepsilon {d_c})\] , where dc is the logarithmic capacitance of the trap set. An explicit three-term approximation for this principal eigenvalue is derived using strong localised perturbation theory, with the coefficients in this series evaluated numerically by using an explicit formula for the source-neutral periodic Green's function and its regular part. Moreover, a transcendental equation for an improved approximation to the principal eigenvalue, which effectively sums all the logarithmic terms in powers of v, is derived in terms of the regular part of the periodic Helmholtz Green's function. By using an Ewald summation technique to first obtain a rapidly converging infinite series representation for this regular part, a simple Newton iteration scheme on the transcendental equation is implemented to numerically evaluate the improved 'log-summed' approximation to the principal eigenvalue. From a numerical computation of the PDE eigenvalue problem defined on the fundamental Wigner–Seitz (WS) cell for the lattice, it is shown that the three-term asymptotic approximation for the principal eigenvalue agrees well with the numerical result only for a rather small trap radius. In contrast, the log-summed asymptotic result provides a very close approximation to the principal eigenvalue even when the trap radius is only moderately small. For a circular trap, the first few transcendental correction terms that further improves the log-summed approximation for the principal eigenvalue are derived. Finally, it is shown numerically that, amongst all Bravais lattices with a fixed area of the primitive cell, the principal eigenvalue is maximised for a regular hexagonal arrangement of traps. [ABSTRACT FROM AUTHOR]

Surgery is considered as the primary therapeutic procedure for gliomas and several recent clinical studies have shown that total tumor resection is directly associated with longer survival when compared to subtotal resection. In order to refine the resection in the boundaries of gliomas, we are developing an intraoperative probe specifically dedicated to the localization of residual tumor labeled with positron emitters. The probe is designed to be compact and electrically safe in order to be directly coupled to the excision tool leading to simultaneous detection and removal of tumor tissues. It is built with clear and plastic scintillating fibers held in a closed packed annular arrangement ensheathing the excision tool. The annihilation [gamma] ray background is eliminated by a real-time subtraction method. Validation of the technical choice and optimization of the probe geometry were performed by preliminary measurements and Monte Carlo simulations based on the MCNP-4C code and an anthropomorphic brain phantom. The theoretical probe sensitivity was found to be 82 cps/[micro]Ci/ml with a [gamma] ray rejection efficiency of 99.6%. The expected minimum radiotracer detectable concentration for tumors labeled with [sup.18]F-FET was 0.10 [micro]Ci/ml. When compared to the 0.29 [micro]Ci/ml average concentration in the bulk of the tumor, this result demonstrate the potential ability of the probe to define more accurately the extent of brain tumor resection. Index Terms--Beta probe, fiber optics, glioma, radio-guided surgery.

We describe the measurement, at 100 K, of the SIMS relative sensitivity factors (RSFs) of the main physiological cations [Na.sup.+], [K.sup.+,] [Mg.sup.2+], and [Ca.sup.2+] in frozen--hydrated (F-H) ionic solutions. Freezing was performed by either plunge freezing or high-pressure freezing. We also report the measurement of the RSFs in flax fibers, which are a model for ions in the plant cell wall, and in F-H ionic samples, which are a model for ions in the vacuole. RSFs were determined under bombardment with neutral oxygen (FAB) for both the fibers and the F-H samples. We show that referencing to ice-characteristic secondary ions is of little value in determining RSFs and that referencing to K is preferable. The RSFs of Na relative to K and of Ca relative to Mg in F-H samples are similar to their respective values in fiber samples, whereas the RSFs of both Ca and Mg relative to K are lower in fibers than in F-H samples. Our data show that the physical factors important for the determination of the RSFs are not the same in F-H samples and in homogeneous matrixes. Our data show that it is possible to perform a SIMS relative quantification of the cations in frozen--hydrated samples with an accuracy on the order of 15%. Referencing to K permits the quantification of the ionic ratios, even when the absolute concentration of the referencing ion is unknown. This is essential for physiological studies of F-H biological samples.

A spectroscopic and nuclear magnetic resonance study of the bonding structure in amorphous carbon nitride is presented.

A study was conducted on possible applications linked to the properties of diamondlike, amorphous carbon films. The experiment presents 13C and 1H nuclear magnetic resonance investigations of selected hydrogenated amorphous carbon coatings obtained under different deposition conditions without any 13C enrichment of the precursor. The films were selected on the basis of a previous study which explored their friction behavior in high vacuum conditions.