Ground state at high density

Weak limits as the density tends to infinity of classical ground states of integrable pair potentials are shown to minimize the mean-field energy functional. By studying the latter we derive global properties of high-density ground state configurations in bounded domains and in infinite space. Our main result is a theorem stating that for interactions having a strictly positive Fourier transform the distribution of particles tends to be uniform as the density increases, while high-density ground states show some pattern if the Fourier transform is partially negative. The latter confirms the conclusion of earlier studies by Vlasov (1945), Kirzhnits and Nepomnyashchii (1971), and Likos et al. (2007). Other results include the proof that there is no Bravais lattice among high-density ground states of interactions whose Fourier transform has a negative part and the potential diverges or has a cusp at zero. We also show that in the ground state configurations of the penetrable sphere model particles are superposed on the sites of a close-packed lattice.Comment: Note adde

Genetic characterization of cassava (Manihot esculenta) landraces in Brazil assessed with simple sequence repeats

Based on nine microsatellite loci, the aim of this study was to appraise the genetic diversity of 42 cassava (Manihot esculenta) landraces from selected regions in Brazil, and examine how this variety is distributed according to origin in several municipalities in the states of Minas Gerais, São Paulo, Mato Grosso do Sul, Amazonas and Mato Grosso. High diversity values were found among the five above-mentioned regions, with 3.3 alleles per locus on an average, a high percentage of polymorphic loci varying from 88.8% to 100%, an average of 0.265 for observed heterozygosity and 0.570 for gene diversity. Most genetic diversity was concentrated within the regions themselves (HS = 0.52). Cluster analysis and principal component based scatter plotting showed greater similarity among landraces from São Paulo, Mato Grosso do Sul and Amazonas, whereas those from Minas Gerais were clustered into a sub-group within this group. The plants from Mato Grosso, mostly collected in the municipality of General Carneiro, provided the highest differentiation. The migration of human populations is one among the possible reasons for this closer resemblance or greater disparity among plants from the various regions