A consistent extension of the local spin density approximation to account for quantum dot mass and dielectric mismatches

A consistent extension of local spin density approximation (LSDA) to account for mass and dielectric mismatches in nanocrystals is presented. The extension accounting for variable effective mass is exact. Illustrative comparisons with available configuration interaction calculations show that the approach is also very reliable when it comes to account for dielectric mismatches. The modified LSDA is as fast and computationally low demanding as LSDA. Therefore, it is a tool suitable to study large particle systems in inhomogeneous media without much effort.

On an asymptotic formula for the maximum voltage drop in a on-chip power distribution network

We present a new asymptotic formula for the maximum static voltage in a simplified model for on-chip power distribution networks of array bonded integrated circuits. In this model the voltage is the solution of a Poisson equation in an infinite planar domain whose boundary is an array of circular pads of radius ", and we deal with the singular limit Ɛ → 0 case. In comparison with approximations that appear in the electronic engineering literature, our formula is more complete since we have obtained terms up to order Ɛ15. A procedure will be presented to compute all the successive terms, which can be interpreted as using multipole solutions of equations involving spatial derivatives of functions. To deduce the formula we use the method of matched asymptotic expansions. Our results are completely analytical and we make an extensive use of special functions and of the Gauss constant G

Differences in phasic development rate amongst wheat cultivars independent of responses to photoperiod and vernalization. A viewpoint of the intrinsic earliness hypothesis

Differences amongst wheat cultivars in the rate of reproductive development are largely dependent on differences in their sensitivity to photoperiod and vernalization. However, when these responses are accounted for, by growing vernalized seedlings under long photoperiods, cultivars can still differ markedly in time to ear emergence. Control of rate of development by this ‘third factor’ has been poorly understood and is variously referred to as intrinsic earliness, earliness in the narrow sense, basic vegetative period, earliness per se, and basic development rate. Certain assumptions are made in the concept of intrinsic earliness. They are that differences in intrinsic earliness (i) are independent of the responses of the cultivars to photoperiod and vernalization, (ii) apply only to the length of the vegetative period up to floral initiation (as suggested by several authors), (iii) are maintained under different temperatures, measured either in days or degree days. As a consequence of this, the ranking of cultivars (from intrinsically early to intrinsically late) must be maintained at different temperatures. This paper, by the re-analysis of published data, examines the extent to which these assumptions can be supported. Although it is shown that intrinsic earliness operates independently of photoperiod and vernalization responses, the other assumptions were not supported. The differences amongst genotypes in time to ear emergence, grown under above-optimum vernalization and photoperiod (that is when the response to these factors is saturated), were not exclusively due to parallel differences in the length of the vegetative phase, and the length of the reproductive phase was independent of that of the vegetative phase. Thus, it would be possible to change the relative allocation of time to vegetative and reproductive periods with no change in the full period to ear emergence. The differences in intrinsic earliness between cultivars were modified by the temperature regime under which they were grown, i.e. the difference between cultivars (both considering the full phase to ear emergence or some sub-phases) was not a constant amount of time or thermal time at different temperatures. In addition, in some instances genotypes changed their ranking for ‘intrinsic earliness’ depending on the temperature regime. This was interpreted to mean that while all genotypes are sensitive to temperature they differ amongst themselves in the extent of that sensitivity. Therefore, ‘intrinsic earliness’ should not be considered as a static genotypic characteristic, but the result of the interaction between the genotype and temperature. Intrinsic earliness is therefore likely to be related to temperature sensitivity. Some implications of these conclusions for plant breeding and crop simulation modelling are discussed.

The univalent Bloch-Landau constant, harmonic symmetry and conformal glueing

By modifying a domain first suggested by Ruth Goodman in 1935 and by exploiting the explicit solution by Fedorov of the Polyá-Chebotarev problem in the case of four symmetrically placed points, an improved upper bound for the univalent Bloch-Landau constant is obtained. The domain that leads to this improved bound takes the form of a disk from which some arcs are removed in such a way that the resulting simply connected domain is harmonically symmetric in each arc with respect to the origin. The existence of domains of this type is established, using techniques from conformal welding, and some general properties of harmonically symmetric arcs in this setting are established.

Particle shape and orientation in laser diffraction and static image analysis size distribution analysis of micrometer sized rectangular particles

Laser diffraction (LD) and static image analysis (SIA) of rectangular particles [United States Pharmacopeia, USP30-NF25, General Chapter <776>, Optical Miroscopy.] have been systematically studied. To rule out sample dispersion and particle orientation as the root cause of differences in size distribution profiles, we immobilize powder samples on a glass plate by means of a dry disperser. For a defined region of the glass plate, we measure the diffraction pattern as induced by the dispersed particles, and the 2D dimensions of the individual particles using LD and optical microscopy, respectively. We demonstrate a correlation between LD and SIA, with the scattering intensity of the individual particles as the dominant factor. In theory, the scattering intensity is related to the square of the projected area of both spherical and rectangular particles. In traditional LD the size distribution profile is dominated by the maximum projected area of the particles (A). The diffraction diameters of a rectangular particle with length L and breadth B as measured by the LD instrument approximately correspond to spheres of diameter ØL and ØB respectively. Differences in the scattering intensity between spherical and rectangular particles suggest that the contribution made to the overall LD volume probability distribution by each rectangular particle is proportional to A2/L and A2/B. Accordingly, for rectangular particles the scattering intensity weighted diffraction diameter (SIWDD) explains an overestimation of their shortest dimension and an underestimation of their longest dimension. This study analyzes various samples of particles whose length ranges from approximately 10 to 1000 μm. The correlation we demonstrate between LD and SIA can be used to improve validation of LD methods based on SIA data for a variety of pharmaceutical powders all with a different rectangular particle size and shape.

La "imatge" de la caverna i la temptació constant de corregir Plató: Benjamin Jowett com a exemple

[cat] Les traduccions dels primers capítols del llibre VII de la República de Plató on apareix la famosa imatge de la caverna, εἰκών, presenten una sorprenent i intrigant varietat interpretativa: “al·legoria”, “mite”, “faula”, “paràbola”, “símil”, “comparació”... Aquest article, prenent com a exemple la notable fidelitat al text del traductor victorià de Plató, B. Jowett, i mitjançant una anàlisi rigorosa dels termes que acompanyen la imatge, manté la necessitat de no interpretar ni corregir en aquest cas el gran filòsof idealista o “ideocèntric”, assenyalant alhora, si el capteniment filològic és un altre, les contradiccions resultants i l’ús d’algun terme aliè al lèxic platònic com ara “al·legoria”.