Cluster Percolation and Explicit Symmetry Breaking in Spin Models

Many features of spin models can be interpreted in geometrical terms by means of the properties of well defined clusters of spins. In case of spontaneous symmetry breaking, the phase transition of models like the q-state Potts model, O(n), etc., can be equivalently described as a percolation transition of clusters. We study here the behaviour of such clusters when the presence of an external field H breaks explicitly the global symmetry of the Hamiltonian of the theory. We find that these clusters have still some interesting relationships with thermal features of the model.Comment: Proceedings of Lattice 2001 (Berlin), 3 pages, 3 figure

Mapping the Curricular Structure and Contents of Network Science Courses

As network science has matured as an established field of research, there are already a number of courses on this topic developed and offered at various higher education institutions, often at postgraduate levels. In those courses, instructors adopted different approaches with different focus areas and curricular designs. We collected information about 30 existing network science courses from various online sources, and analyzed the contents of their syllabi or course schedules. The topics and their curricular sequences were extracted from the course syllabi/schedules and represented as a directed weighted graph, which we call the topic network. Community detection in the topic network revealed seven topic clusters, which matched reasonably with the concept list previously generated by students and educators through the Network Literacy initiative. The minimum spanning tree of the topic network revealed typical flows of curricular contents, starting with examples of networks, moving onto random networks and small-world networks, then branching off to various subtopics from there. These results illustrate the current state of consensus formation (including variations and disagreements) among the network science community on what should be taught about networks and how, which may also be informative for K--12 education and informal education.Comment: 17 pages, 11 figures, 2 tables; to appear in Cramer, C. et al. (eds.), Network Science in Education -- Tools and Techniques for Transforming Teaching and Learning (Springer, 2017, in press

Percolation and Critical Behaviour in SU(2) Gauge Theory

The paramagnetic-ferromagnetic transition in the Ising model can be described as percolation of suitably defined clusters. We have tried to extend such picture to the confinement-deconfinement transition of SU(2) pure gauge theory, which is in the same universality class of the Ising model. The cluster definition is derived by approximating SU(2) by means of Ising-like effective theories. The geometrical transition of such clusters turns out to describe successfully the thermal counterpart for two different lattice regularizations of (3+1)-d SU(2).Comment: Lattice 2000 (Finite Temperature), 4 pages, 4 figures, 2 table

Enhanced excitation of Giant Pairing Vibrations in heavy-ion reactions induced by weakly-bound projectiles

The use of radioactive ion beams is shown to offer the possibility to study collective pairing states at high excitation energy, which are not usually accessible with stable projectiles because of large energy mismatch. In the case of two-neutron stripping reactions induced by 6He, we predict a population of the Giant Pairing Vibration in 208Pb or 116Sn with cross sections of the order of a millibarn, dominating over the mismatched transition to the ground state.Comment: 6 pages, 4 figure

Study of Giant Pairing Vibrations with neutron-rich nuclei

We investigate the possible signature of the presence of giant pairing states at excitation energy of about 10 MeV via two-particle transfer reactions induced by neutron-rich weakly-bound projectiles. Performing particle-particle RPA calculations on $^{208}$Pb and BCS+RPA calculations on $^{116}$Sn, we obtain the pairing strength distribution for two particles addition and removal modes. Estimates of two-particle transfer cross sections can be obtained in the framework of the 'macroscopic model'. The weak-binding nature of the projectile kinematically favours transitions to high-lying states. In the case of (~^6He, \~^4He) reaction we predict a population of the Giant Pairing Vibration with cross sections of the order of a millibarn, dominating over the mismatched transition to the ground state.Comment: Talk presented in occasion of the VII School-Semina r on Heavy Ion Physics hosted by the Flerov Laboratory (FLNR/JINR) Dubna, Russia from May 27 to June 2, 200

Corticomotor Excitability during Observation and Imagination of a Work of Art

We examine the effects of the artistic representation – here exemplified by Michelangelo's Expulsion from Paradise – of an action on the motor system. Using single and paired- pulse transcranial magnetic stimulation we analyze corticomotor excitability during observation of an action in the painting, during imagery of the painting, and during observation of a photograph of the same pose. We also analyze the effects of observation of two further paintings, one showing the same muscles at rest, and in the other in a more overtly emotional context. Both observation of the Expulsion and of imagery of the painting increased cortical excitability. Neither the relaxed pose of Michelangelo's Creation nor the flexed posture in the highly emotional context of Bellini's Dead Christ increased cortical excitability. Observation of a photograph of the same extended pose did not increase cortical excitability either. Moreover, intracortical inhibition was reduced during imagery of the painting. Our results offer clear motor correlates of the relationship between the esthetic quality of a work and the perception of implied movement within it

The Hagedorn Temperature and Partition Thermodynamics

We review the resonance gas formalism of hadron thermodynamics and recall that an exponential increase of the resonance spectrum leads to a limiting temperature of hadronic matter. We then show that the number p(n) of ordered partitions of an integer n grows exponentially with n and satisfies the integer counterpart of the statistical bootstrap equation. Considering the set of all partitions as a Gibbs ensemble provides a partition thermodynamics which is also governed by a limiting temperature, determined by the combinatorial structure of the problem. Further associating intrinsic quantum numbers to integers results in a phase diagram equivalent to that found in QCD for hadronic matter as function of temperature and baryochemical potential.Comment: Dedicated to Rolf Hagedorn, 1919-2003. 11 pages, 3 figures. Final version accepted for publication in the European Physical Journal

Benchmarks for testing community detection algorithms on directed and weighted graphs with overlapping communities

Many complex networks display a mesoscopic structure with groups of nodes sharing many links with the other nodes in their group and comparatively few with nodes of different groups. This feature is known as community structure and encodes precious information about the organization and the function of the nodes. Many algorithms have been proposed but it is not yet clear how they should be tested. Recently we have proposed a general class of undirected and unweighted benchmark graphs, with heterogenous distributions of node degree and community size. An increasing attention has been recently devoted to develop algorithms able to consider the direction and the weight of the links, which require suitable benchmark graphs for testing. In this paper we extend the basic ideas behind our previous benchmark to generate directed and weighted networks with built-in community structure. We also consider the possibility that nodes belong to more communities, a feature occurring in real systems, like, e. g., social networks. As a practical application, we show how modularity optimization performs on our new benchmark.Comment: 9 pages, 13 figures. Final version published in Physical Review E. The code to create the benchmark graphs can be freely downloaded from http://santo.fortunato.googlepages.com/inthepress

Efficient operator-coarsening multigrid schemes for local discontinuous Galerkin methods

An efficient $hp$-multigrid scheme is presented for local discontinuous Galerkin (LDG) discretizations of elliptic problems, formulated around the idea of separately coarsening the underlying discrete gradient and divergence operators. We show that traditional multigrid coarsening of the primal formulation leads to poor and suboptimal multigrid performance, whereas coarsening of the flux formulation leads to optimal convergence and is equivalent to a purely geometric multigrid method. The resulting operator-coarsening schemes do not require the entire mesh hierarchy to be explicitly built, thereby obviating the need to compute quadrature rules, lifting operators, and other mesh-related quantities on coarse meshes. We show that good multigrid convergence rates are achieved in a variety of numerical tests on 2D and 3D uniform and adaptive Cartesian grids, as well as for curved domains using implicitly defined meshes and for multi-phase elliptic interface problems with complex geometry. Extension to non-LDG discretizations is briefly discussed

Alkaline static feed electrolyzer based oxygen generation system

In preparation for the future deployment of the Space Station, an R and D program was established to demonstrate integrated operation of an alkaline Water Electrolysis System and a fuel cell as an energy storage device. The program's scope was revised when the Space Station Control Board changed the energy storage baseline for the Space Station. The new scope was aimed at the development of an alkaline Static Feed Electrolyzer for use in an Environmental Control/Life Support System as an oxygen generation system. As a result, the program was divided into two phases. The phase 1 effort was directed at the development of the Static Feed Electrolyzer for application in a Regenerative Fuel Cell System. During this phase, the program emphasized incorporation of the Regenerative Fuel Cell System design requirements into the Static Feed Electrolyzer electrochemical module design and the mechanical components design. The mechanical components included a Pressure Control Assembly, a Water Supply Assembly and a Thermal Control Assembly. These designs were completed through manufacturing drawing during Phase 1. The Phase 2 effort was directed at advancing the Alkaline Static Feed Electrolyzer database for an oxygen generation system. This development was aimed at extending the Static Feed Electrolyzer database in areas which may be encountered from initial fabrication through transportation, storage, launch and eventual Space Station startup. During this Phase, the Program emphasized three major areas: materials evaluation, electrochemical module scaling and performance repeatability and Static Feed Electrolyzer operational definition and characterization