Rate of convergence of a particle method to the solution of the Mc Kean-Vlasov's equation

This paper studies the rate of convergence of an appropriatediscretization scheme of the solution of the Mc Kean-Vlasovequation introduced by Bossy and Talay. More specifically,we consider approximations of the distribution and of thedensity of the solution of the stochastic differentialequation associated to the Mc Kean - Vlasov equation. Thescheme adopted here is a mixed one: Euler/weakly interactingparticle system. If $n$ is the number of weakly interactingparticles and $h$ is the uniform step in the timediscretization, we prove that the rate of convergence of thedistribution functions of the approximating sequence in the $L^1(\Omega\times \Bbb R)$ norm and in the sup norm is of theorder of $\frac 1{\sqrt n} + h $, while for the densities is ofthe order $ h +\frac 1 {\sqrt {nh}}$. This result is obtainedby carefully employing techniques of Malliavin Calculus.

Size - compositions of net plankton samples taken off northern Peru

Analiza las estadisticas recolectadas del plancton a 1/2 metro vertical y a un metro oblicuo en una cuadricula de 10 x 15 millas nauticas

A recent change in size distribution of blue mussels (Mytilus edulis) in the western part of the Gulf of Finland

Markus Öst & Mikael Kilpi

The ontogeny of sexual size dimorphism of a moth: when do males and females grow apart?

Sexual dimorphism in body size (sexual size dimorphism) is common in many species. The sources of selection that generate the independent evolution of adult male and female size have been investigated extensively by evolutionary biologists, but how and when females and males grow apart during ontogeny is poorly understood. Here we use the hawkmoth, Manduca sexta, to examine when sexual size dimorphism arises by measuring body mass every day during development. We further investigated whether environmental variables influence the ontogeny of sexual size dimorphism by raising moths on three different diet qualities (poor, medium and high). We found that size dimorphism arose during early larval development on the highest quality food treatment but it arose late in larval development when raised on the medium quality food. This female-biased dimorphism (females larger) increased substantially from the pupal-to-adult stage in both treatments, a pattern that appears to be common in Lepidopterans. Although dimorphism appeared in a few stages when individuals were raised on the poorest quality diet, it did not persist such that male and female adults were the same size. This demonstrates that the environmental conditions that insects are raised in can affect the growth trajectories of males and females differently and thus when dimorphism arises or disappears during development. We conclude that the development of sexual size dimorphism in M. sexta occurs during larval development and continues to accumulate during the pupal/adult stages, and that environmental variables such as diet quality can influence patterns of dimorphism in adults.

Size dependence of refractive index of Si nanoclusters embedded in SiO2

he complex refractive index of SiO2 layers containing Si nanoclusters (Si-nc) has been measured by spectroscopic ellipsometry in the range from 1.5 to 5.0 eV. It has been correlated with the amount of Si excess accurately measured by x-ray photoelectron spectroscopy and the nanocluster size determined by energy-filtered transmission electron microscopy. The Si-nc embedded in SiO2 have been produced by a fourfold Si+ ion implantation, providing uniform Si excess aimed at a reliable ellipsometric modeling. The complex refractive index of the Si-nc phase has been calculated by the application of the Bruggeman effective-medium approximation to the composite media. The characteristic resonances of the refractive index and extinction coefficient of bulk Si vanish out in Si-nc. In agreement with theoretical simulations, a significant reduction of the refractive index of Si-nc is observed, in comparison with bulk and amorphous silicon. The knowledge of the optical properties of these composite layers is crucial for the realization of Si-based waveguides and light-emitting devices.

Generic finite-size enhancement of pairing in mesoscopic Fermi systems

The finite-size-dependent enhancement of pairing in mesoscopic Fermi systems is studied under the assumption that the BCS approach is valid and that the two-body force is size independent. Different systems are investigated such as superconducting metallic grains and films as well as atomic nuclei. It is shown that the finite size enhancement of pairing in these systems is in part due to the presence of a surface which accounts quite well for the data of nuclei and explains a good fraction of the enhancement in Al grains.

Distribution of single-particle strength due to short-range and tensor correlations

The distribution of single-particle strength in nuclear matter is calculated for a realistic nucleon-nucleon interaction. The influence of the short-range repulsion and the tensor component of the nuclear force on the spectral functions is to move approximately 13% of the total strength for all single-particle states beyond 100 MeV into the particle domain. This result is related to the abundantly observed quenching phenomena in nuclei which include the reduction of spectroscopic factors observed in (e,ep) reactions and the missing strength in low energy response functions.

Sequential partitioning: an alternative to understanding size distributions of avalanches in first-order phase transitions

We study the problem of the partition of a system of initial size V into a sequence of fragments s1,s2,s3 . . . . By assuming a scaling hypothesis for the probability p(s;V) of obtaining a fragment of a given size, we deduce that the final distribution of fragment sizes exhibits power-law behavior. This minimal model is useful to understanding the distribution of avalanche sizes in first-order phase transitions at low temperatures.

On the many-time formulation of classical particle dynamics

Starting from the standard one-time dynamics of n nonrelativistic particles, the n-time equations of motion are inferred, and a variational principle is formulated. A suitable generalization of the classical LieKnig theorem is demonstrated, which allows the determination of all the associated presymplectic structures. The conditions under which the action of an invariance group is canonical are studied, and a corresponding Noether theorem is deduced. A formulation of the theory in terms of n first-class constraints is recovered by means of coisotropic imbeddings. The proposed approach also provides for a better understanding of the relativistic particle dynamics, since it shows that the different roles of the physical positions and the canonical variables is not peculiar to special relativity, but rather to any n-time approach: indeed a nonrelativistic no-interaction theorem is deduced.

Normalization factors for magnetic relaxation of small particle systems in non-zero magnetic field.

We critically discuss relaxation experiments in magnetic systems that can be characterized in terms of an energy barrier distribution, showing that proper normalization of the relaxation data is needed whenever curves corresponding to different temperatures are to be compared. We show how these normalization factors can be obtained from experimental data by using the Tln (t/t0) scaling method without making any assumptions about the nature of the energy barrier distribution. The validity of the procedure is tested using a ferrofluid of Fe3O4 particles.

Age and size structure of gap-dynamic, old-growth boreal forest stands in Newfoundland

[Abstract]

Crystal size distribution of periclase in contact metamorphic dolomite marbles from the southern Adamello Massif, Italy

Crystal size distributions (CSD) of periclase in contact metamorphic dolomite marbles are presented for two profiles near the Cima Uzza summit in the southern Adamello Massif (Italy). The database was combined with geochemical and petrological information to deduce the controls on the periclase-forming reaction. The contact metamorphic dolomite marbles are exposed at the contact of mafic intrusive rocks and are partially surrounded by them. Brucite is retrograde and pseudomorphs spherical periclase crystals. Prograde periclase growth is the consequence of limited infiltration of water-rich fluid at T near 605C. Stable isotope data show depletion in (13)C and (18)O over a narrow region (40 cm) near the magmatic contact, whereas the periclase-forming reaction front extends up to 4 m from the contact. CSD analyses along the two profiles show that the median grain size of the periclase crystals does not change, but that there is a progressively greater distribution of grain sizes, including a greater proportion of larger grains, with increasing distance from the contact. A qualitative model, based on the textural and geochemical data, attributes these variations in grain size to changing reaction affinities along a kinetically dispersed infiltration front. This study highlights the need to invoke disequilibrium processes for metamorphic mineral growth and expands the use of CSDs to systems of mineral formation driven by fluid infiltration.

Radial dose function of a 90Sr 90Y seed in water and A150: Comment on Calibration and characterization of beta-particle sources for intravascular brachytherapy

Intravascular brachytherapy with beta sources has become a useful technique to prevent restenosis after cardiovascular intervention. In particular, the Beta-Cath high-dose-rate system, manufactured by Novoste Corporation, is a commercially available 90Sr 90Y source for intravascular brachytherapy that is achieving widespread use. Its dosimetric characterization has attracted considerable attention in recent years. Unfortunately, the short ranges of the emitted beta particles and the associated large dose gradients make experimental measurements particularly difficult. This circumstance has motivated the appearance of a number of papers addressing the characterization of this source by means of Monte Carlo simulation techniques.

Size distribution of atmospheric particulate ionic species at a coastal site in Portugal

A Berner impactor was used to collect size-differentiated aerosol samples from March to August 2003 in the city of Aveiro, on the Portuguese west coast. The samples were analysed for the main water-soluble ion species. The average concentration of sulphate, nitrate, chloride and ammonium was 6.38, 3.09, 1.67 and 1.27 µg m-3, respectively. The results show that SO4(2-) and NH4+ were consistently present in the fine fraction < 1 µm, which represents, on average, 72 and 89% of their total atmospheric concentrations, respectively. The NO3-particles were concentrated in the coarse size. Chloride presented the characteristic coarse mode for marine aerosols. During some spring/summer events, an ammonium surplus was observed (NH4+/SO4(2-) molar ratios > 2), possibly due to greater availability of ammonia coming from agricultural activities or from the neighbouring chemical industrial complex. During the remaining periods, the aerosol was found to be somewhat acidic and predominantly in the form of ammonium bisulphate (NH4+/SO4(2-) molar ratios = 0.5-1.25). Samples collected under a major or exclusive influence of maritime air masses were essentially constituted by coarse particles with enrichment in sea salt, while for air masses of continental origin the contribution of water-soluble ionic species in the fine mode was more pronounced.