Scaling of Hamiltonian walks on fractal lattices

We investigate asymptotical behavior of numbers of long Hamiltonian walks (HWs), i.e. self-avoiding random walks that visit every site of a lattice, on various fractal lattices. By applying an exact recursive technique we obtain scaling forms for open HWs on 3-simplex lattice, Sierpinski gasket, and their generalizations: Given-Mandelbrot (GM), modified Sierpinski gasket (MSG) and n-simplex fractal families. For GM, MSG and n-simplex lattices with odd values of n, number of open HWs $Z_N$, for the lattice with $N\gg 1$ sites, varies as $\omega^N N^\gamma$. We explicitly calculate exponent $\gamma$ for several members of GM and MSG families, as well as for n-simplices with n=3,5, and 7. For n-simplex fractals with even n we find different scaling form: $Z_N\sim \omega^N \mu^{N^{1/d_f}}$, where $d_f$ is fractal dimension of the lattice, which also differs from the formula expected for homogeneous lattices. We discuss possible implications of our results on studies of real compact polymers.Comment: 19 pages, 13 figures, RevTex4; extended Introduction, several references added; one figure added in section II; corrected typos; version accepted for publication in Phys.Rev.

Interfacial Polarization and Dielectric Properties of Epoxy/Graphite Flakes Composites

Dielectric properties of composites based on bisphenol-A-epoxy resin loaded with various content of graphite flakes (GF) have been studied. The dielectric permeability, tangent loss and ac conductivity have been examined in wide temperature (170 – 370 K) and frequency (20 Hz – 200 kHz) range. In composites loaded with GF flakes up to 10 wt.%, the dominant conduction mechanism is tunneling of electrons, while loading of 15 wt.% gives rise to electron conduction through direct contacts between fillers. Dielectric properties of composites are largely determined by the nature of the filler/matrix interface, the filler surface area and the inherent conductivity of the fillers. At low electric field frequencies, dominates socalled interfacial (or space charge) polarization due to accumulation of free charges at the interfaces between two phases (filler and matrix), which differ in electrical conductivity.Influence of the filler surface chemistry have been studied for composites loaded with 5 wt.% graphite flakes obtained: (i) under wet milling, without (GF) or with (GF-Tr100x) adding Triton-100x as a surfactant, or (ii) under dry milling in the presence of KOH (GF-KOH). The surface treatment with KOH notable increased dielectric constant of the epoxy/GF-KOH5 composite, keeping low tangent loss, comparable to the counterpart, the epoxy/GF5 composite

Morphometric and molecular analysis of a pink-berried mutant within the population of grape cultivar 'Plavac mali'

This study reports characteristics of pink-berried mutants found in the clone population of the Croatian red wine cultivar 'Plavac mali' on the basis of comparative ampelographic and DNA marker (SSR and Gret1) analysis. The pink-berried accession, also called 'Plavac mali sivi' (Croatian: sivi = English: grey or French: gris), along with the other 58 'Plavac mali' accessions of standard blue-black berry skin color, has been characterized for the first time using OIV descriptors and molecular markers. Using a set of 9 simple sequence repeat (SSR) markers, an identical SSR profile for all the analyzed accessions was revealed, indicating their monozygotic status. The analysis of Gret1 insertion within the VvMYBA1 locus revealed no DNA polymorphism responsible for the pink-berried phenotype. Surface color of the berry skin was measured with the CIELab technique using a reflectance spectrophotometer at full ripeness. The results of colorimetric variables (L*, a* and b*) suggest a significantly lower accumulation of anthocyanins in the pink-berried accession compared to the standard blue-black berries. The pink-berried accession shares all assessed morphological and genetic traits of 'Plavac mali', with the only difference being the color of the berry skin. This suggests that the pinkberried genotype is the result of a spontaneous mutation of a standard 'Plavac mali' genotype

Analysis of phyllometric parameters efficiency in discrimination of Croatian native V. vinifera cultivars

The aims of this study were to achieve correct cultivar classification of leaf samples by using phyllometric parameters to determine the performance of parameters applied as the discriminant criteria and to determine the minimal number of leaf parameters needed to accurately classify leaf samples within cultivars. Seventy-nine phyllometric parameters were measured/calculated on 360 leaf samples from eleven grapevine cultivars, gathered during several years, from different growing conditions and with some differences in the sampling methods applied. Stepwise discriminant analysis was used to rank the phyllometric parameters according to their efficiency in the discrimination of cultivars. A series of discriminant analyses was performed with successive introduction of new parameters as discriminatory elements until 100 % correct classification of leaf samples into the correct cultivar was achieved. This was achieved using only the seven highest ranking phyllometric parameters from the stepwise discriminant analysis. Additionally, canonical discriminant analysis was performed to evaluate the differences between cultivars in the same parameters. This study represents a model for analysis of the efficiency of different ampelometric parameters for discrimination of V. vinifera cultivars.

Differences in chemical composition of 'Plavac mali' grape berries

Evaluation of differences in yield and quality of grapevine is often based on the random samples of berries harvested on the same date. Due to differences in ripeness of berries from the same cluster, and among berries from different clusters of the same vine, the determined differences among examined treatments (clones, agricultural practices etc.) based on random berry samples may be over- or underestimated. The aims of this study were to determine: (1) differences among three 'Plavac mali' clones in the proportion of berries of different density classes (sugar concentration level) using the flotation method; (2) differences in berry weight and chemical composition among density classes of the same clone, and (3) differences between clones of the same density class. Significant differences were determined for all observed characteristics, among different berries density classes and clones. The results obtained indicate that berry samples used to compare different clones should be, to the greatest possible extent, at the same level of ripeness, as this significantly effects chemical composition. This can be achieved using the density separation of berries with the simple flotation method presented in this study. The presented results could be useful in the future improvement of clonal selection methodology as well as in improvement of sampling strategy for other types of researches

Cryopreservation and cryotherapy of grapevine (Vitis vinifera L.)

This study aimed at testing the efficiency of a droplet-vitrification cryopreservation protocol in eliminating selected grapevine viruses. The cryopreservation protocol led to approximately 50 % recovery with cultivar 'Portan' and five international cultivars tested, but very low recovery was noted with Croatian cultivars. GFLV and GLRaV-3, two (economically important grapevine) viruses were eliminated in a high percentage (up to 100 %) of plants regenerated from cryopreserved shoot tips. Virus sanitation was observed as well in samples before liquid nitrogen exposure. Genetic stability of plants regenerated after cryopreservation was studied using AFLP markers. Polymorphic fragments were observed in non-cryopreserved and cryopreserved samples treated with PVS2 solution, the number of which increased with increasing durations of exposure to PVS2 solution

Reproductive potential of the functionally female native Croatian grapevine 'Grk bijeli'

A native Croatian grapevine 'Grk bijeli', sharing a parent-offspring relationships with 'Tribidrag' (aka 'Zinfandel'), is grown exclusively on the Adriatic island of Korčula. It is one of the grape cultivars with female-only functional flowers, causing reduced fertilisation and leads to problems in grape production and wine quality. A typical cluster of 'Grk bijeli' at maturity contains fully developed seeded berries, in addition to a highly variable proportion of undersized seedless berries. The aim of this study was to identify the cause of the reduced reproduction potential of 'Grk bijeli' in order to establish a better growing environment for improved yield and grape quality. 'Grk bijeli' female gametophyte develops normaly and at maturity contains both egg and central cell, together with two synergid cells and three antipodal cells. On the other hand, 'Grk bijeli' pollen grains show developmental deviations. Specifically, most of the pollen grains undergo the first pollen mitosis and contain one vegetative cell and one generative cell, while 20 % of ungerminating grains also accomplish the second pollen mitosis, giving rise to two sperm cells and one vegetative cell. Morover, 'Grk bijeli' pollen has acolporate morphology, which prevents germination and contributes to reduced reproduction. Furthermore, fertilisation after pollination with other varieties results in various degrees of ovule abortion depending on the pollinator, revealing Croatian cultivars 'Plavac mali crni' and 'Pošip bijeli' as favourable varieties. Although this study describes a highly valuable cultivar of local importance, it also contributes to fundamental knowledge of grapevine reproductive biology and offers a strategy for improvement of wine production and oenological performance of semi-fertile varieties in general