Phase Field Crystal model for particles with n-fold rotational symmetry in two dimensions

We introduce a Phase Field Crystal (PFC) model for particles with n-fold rotational symmetry in two dimensions. Our approach is based on a free energy functional that depends on the reduced one-particle density, the strength of the orientation, and the direction of the orientation, where all these order parameters depend on the position. The functional is constructed such that for particles with axial symmetry (i. e. n = 2) the PFC model for liquid crystals as introduced by H. L\"owen [J. Phys.: Condens. Matter 22, 364105 (2010)] is recovered. We discuss the stability of the functional and explore phases that occur for $1 \leq n \leq 6$. In addition to isotropic, nematic, stripe, and triangular order, we also observe cluster crystals with square, rhombic, honeycomb, and even quasicrystalline symmetry. The n-fold symmetry of the particles corresponds to the one that can be realized for colloids with symmetrically arranged patches. We explain how both, repulsive as well as attractive patches, are described in our model.Comment: 20 pages, 12 figure

Cross-correlations in scaling analyses of phase transitions

Thermal or finite-size scaling analyses of importance sampling Monte Carlo time series in the vicinity of phase transition points often combine different estimates for the same quantity, such as a critical exponent, with the intent to reduce statistical fluctuations. We point out that the origin of such estimates in the same time series results in often pronounced cross-correlations which are usually ignored even in high-precision studies, generically leading to significant underestimation of statistical fluctuations. We suggest to use a simple extension of the conventional analysis taking correlation effects into account, which leads to improved estimators with often substantially reduced statistical fluctuations at almost no extra cost in terms of computation time.Comment: 4 pages, RevTEX4, 3 tables, 1 figur

Chiral Quark Model

In this talk I review studies of hadron properties in bosonized chiral quark models for the quark flavor dynamics. Mesons are constructed from Bethe--Salpeter equations and baryons emerge as chiral solitons. Such models require regularization and I show that the two--fold Pauli--Villars regularization scheme not only fully regularizes the effective action but also leads the scaling laws for structure functions. For the nucleon structure functions the present approach serves to determine the regularization prescription for structure functions whose leading moments are not given by matrix elements of local operators. Some numerical results are presented for the spin structure functions.Comment: Talk presented at the workshop QCD 2002, IIT Kanpur, Nov. 2002, 10 pages, proceedings style files include

Rapid and Inexpensive Whole-Genome Genotyping-by-Sequencing for Crossover Localization and Fine-Scale Genetic Mapping

The reshuffling of existing genetic variation during meiosis is important both during evolution and in breeding. The reassortment of genetic variants relies on the formation of crossovers (COs) between homologous chromosomes. The pattern of genome-wide CO distributions can be rapidly and precisely established by the short-read sequencing of individuals from F(2) populations, which in turn are useful for quantitative trait locus (QTL) mapping. Although sequencing costs have decreased precipitously in recent years, the costs of library preparation for hundreds of individuals have remained high. To enable rapid and inexpensive CO detection and QTL mapping using low-coverage whole-genome sequencing of large mapping populations, we have developed a new method for library preparation along with Trained Individual GenomE Reconstruction, a probabilistic method for genotype and CO predictions for recombinant individuals. In an example case with hundreds of F(2) individuals from two Arabidopsis thaliana accessions, we resolved most CO breakpoints to within 2 kb and reduced a major flowering time QTL to a 9-kb interval. In addition, an extended region of unusually low recombination revealed a 1.8-Mb inversion polymorphism on the long arm of chromosome 4. We observed no significant differences in the frequency and distribution of COs between F(2) individuals with and without a functional copy of the DNA helicase gene RECQ4A. In summary, we present a new, cost-efficient method for large-scale, high-precision genotyping-by-sequencing

Connected component identification and cluster update on GPU

Cluster identification tasks occur in a multitude of contexts in physics and engineering such as, for instance, cluster algorithms for simulating spin models, percolation simulations, segmentation problems in image processing, or network analysis. While it has been shown that graphics processing units (GPUs) can result in speedups of two to three orders of magnitude as compared to serial codes on CPUs for the case of local and thus naturally parallelized problems such as single-spin flip update simulations of spin models, the situation is considerably more complicated for the non-local problem of cluster or connected component identification. I discuss the suitability of different approaches of parallelization of cluster labeling and cluster update algorithms for calculations on GPU and compare to the performance of serial implementations.Comment: 15 pages, 14 figures, one table, submitted to PR

One-dimensional infinite component vector spin glass with long-range interactions

We investigate zero and finite temperature properties of the one-dimensional spin-glass model for vector spins in the limit of an infinite number m of spin components where the interactions decay with a power, \sigma, of the distance. A diluted version of this model is also studied, but found to deviate significantly from the fully connected model. At zero temperature, defect energies are determined from the difference in ground-state energies between systems with periodic and antiperiodic boundary conditions to determine the dependence of the defect-energy exponent \theta on \sigma. A good fit to this dependence is \theta =3/4-\sigma. This implies that the upper critical value of \sigma is 3/4, corresponding to the lower critical dimension in the d-dimensional short-range version of the model. For finite temperatures the large m saddle-point equations are solved self-consistently which gives access to the correlation function, the order parameter and the spin-glass susceptibility. Special attention is paid to the different forms of finite-size scaling effects below and above the lower critical value, \sigma =5/8, which corresponds to the upper critical dimension 8 of the hypercubic short-range model.Comment: 27 pages, 27 figures, 4 table

Nucleon Structure Functions from a Chiral Soliton in the Infinite Momentum Frame

We study the frame dependence of nucleon structure functions obtained within a chiral soliton model for the nucleon. Employing light cone coordinates and introducing collective coordinates together with their conjugate momenta, translational invariance of the solitonic quark fields (which describe the nucleon as a localized object) is restored. This formulation allows us to perform a Lorentz boost to the infinite momentum frame of the nucleon. The major result is that the Lorentz contraction associated with this boost causes the leading twist contribution to the structure functions to properly vanish when the Bjorken variable $x$ exceeds unity. Furthermore we demonstrate that for structure functions calculated in the valence quark approximation to the Nambu--Jona--Lasinio chiral soliton model the Lorentz contraction also has significant effects on the structure functions for moderate values of the Bjorken variable $x$.Comment: 16 pages, 1 figure, revised version to be published in Int. J. Mod. Phys.

Governance of marine protected areas in the least-developed countries : case studies from West Africa

ISSN 2070-7010International audienceThe need for effective governance of the marine protected areas (MPAs) in least developed countries (LDCs) is commensurate with the significant territorial stakes raised by their extensive maritime domain. Another significant challenge is the conservation of biodiversity and of ecosystems whose level of productivity is similar to that of coral reefs (e.g. in East Africa and Madagascar, the Red Sea, Maldives, Cambodia, and South Pacific islands), upwelling systems (e.g. in West Africa and Angola) and estuarine and delta ecosystems (e.g. in West and East Africa, Bangladesh and Myanmar). However, the overriding issue is to reconcile conservation and human presence as, in LDCs, human activities are tolerated in almost all MPAs covered by International Union for Conservation of Nature categories II-VI. Finally, issues related to identity claims and to the process of establishment of property and other legal entitlements on nature are gaining importance. A review of the literature on fisheries and MPAs governance showed how polysemous and vague the notion of governance was until very recently and how few or oversimplified were the analyses of MPA governance in the LDCs. However, only detailed analyses would allow the characterization of governance systems and identification of their weaknesses with the view to suggesting new governance arrangements and appropriate public policy options. Such analytical deficiencies may be explained by the lack of analytical frameworks capable of taking into account the plurality and intricacy of socio-economic organizations and institutions, the sociocultural features and the role of new mediators and "development brokers" that shape MPA governance in the LDCs. The deficiencies may also be explained by the fact that the dominating hierarchical governancesystems tend to underestimate the complexity of MPA governance systems. Therefore, it has been necessary to develop an analytical framework to study the governance of MPAs in the LDCs, drawing on four sources of inspiration: (i) the interactive fisheries governance approach; (ii) the risk governance approach; (iii) the socioanthropology of mediations and brokerage; and (iv) the governance analytical framework. The framework indicates the five issues that must be addressed in order to operationalize the concept of governance in LDC MPAs: (i) definition of the problem or the issue at stake; (ii) identification of the set of relevant governance norms; (iii) presentation of the actors involved in the governance process; (iv) highlighting the nodes around which actors' strategies converge; and (v) recalling the processes that have led to the current state of governance. This analytical framework makes it possible to characterize the governance system of each of the MPAs considered and to develop a typology of these systems. The characterization of different governance systems highlights their weaknessesand paves the way for new public policy options and, more generally, for the restructuring of governance to correct these weaknesses. However, prior to the development of the analytical framework and the characterization of governance systems, the main MPA governance principles and constraints, as well their legal context, must be clarified. The whole methodology was tested on three West African coastal and marine protected areas, which seemed to provide textbook cases illustrating the difficulties of governance in LDCs: the Banc d'Arguin National Park in Mauritania, the Saloum Delta Biosphere Reserve in Senegal, and the Bolama Bijagos Archipelago Biosphere Reserve in Guinea-Bissau. The analysis of demographic and economic constraints in these West African MPAs showed the importance of: (i) increasing population density and mobility; (ii) the intensification of resource exploitation; and (iii) and the openingof the MPA economy. The analysis of the legal and institutional contexts showed the international inspiration of the MPA objectives and conservation arrangements,and the syncretism of the legal system

Parton distributions in the chiral quark model: a continuum computation

We compute the parton distributions for the chiral quark model. We present a new technique for performing such computations based on Green functions. This approach avoids a discretization of the spectrum. It therefore does not need any smoothing procedures. The results are similar to those of other groups, however the distributions peak at smaller $x$.Comment: 19 pages, 8 Figures, LaTeX, some typos corrected, some additional comments in the conclusion