Entanglement in a simple quantum phase transition

What entanglement is present in naturally occurring physical systems at thermal equilibrium? Most such systems are intractable and it is desirable to study simple but realistic systems that can be solved. An example of such a system is the one-dimensional infinite-lattice anisotropic XY model. This model is exactly solvable using the Jordan-Wigner transform, and it is possible to calculate the two-site reduced density matrix for all pairs of sites. Using the two-site density matrix, the entanglement of formation between any two sites is calculated for all parameter values and temperatures. We also study the entanglement in the transverse Ising model, a special case of the XY model, which exhibits a quantum phase transition. It is found that the next-nearest-neighbor entanglement (though not the nearest-neighbor entanglement) is a maximum at the critical point. Furthermore, we show that the critical point in the transverse Ising model corresponds to a transition in the behavior of the entanglement between a single site and the remainder of the lattice.

The sit-up: complex kinematics and muscle activity in voluntary axial movement

This paper describes the kinematics and muscle activity associated with the standard sit-up, as a first step in the investigation of complex motor coordination. Eight normal human subjects lay on a force table and performed at least 15 sit-ups, with the arms across the chest and the legs straight and unconstrained. Several subjects also performed sit-ups with an additional weight added to the head. Support surface forces were recorded to calculate the location of the center of pressure and center of gravity; conventional motion analysis was used to measure segmental positions; and surface EMG was recorded from eight muscles. While the sit-up consists of two serial components, 'trunk curling' and 'footward pelvic rotation', it can be further subdivided into five phases, based on the kinematics. Phases I and II comprise trunk curling. Phase I consists of neck and upper trunk flexion, and phase II consists of lumbar trunk lifting. Phase II corresponds to the point of peak muscle contraction and maximum postural instability, the 'critical point' of the sit-up. Phases III-V comprise footward pelvic rotation. Phase III begins with pelvic rotation towards the feet. phase W with leg lowering, and phase V with contact between the legs and the support surface. The overall pattern of muscle activity was complex with times of EMG onset, peak activity, offset, and duration differing for different muscles. This complex pattern changed qualitatively from one phase to the next, suggesting that the roles of different muscles and, as a consequence, the overall form of coordination, change during the sit-up. (C) 2003 Elsevier Science Ltd. All rights reserved.

Simulations of thermal Bose fields in the classical limit

We demonstrate that the time-dependent projected Gross-Pitaevskii equation (GPE) derived earlier [M. J. Davis, R. J. Ballagh, and K. Burnett, J. Phys. B 34, 4487 (2001)] can represent the highly occupied modes of a homogeneous, partially-condensed Bose gas. Contrary to the often held belief that the GPE is valid only at zero temperature, we find that this equation will evolve randomized initial wave functions to a state describing thermal equilibrium. In the case of small interaction strengths or low temperatures, our numerical results can be compared to the predictions of Bogoliubov theory and its perturbative extensions. This demonstrates the validity of the GPE in these limits and allows us to assign a temperature to the simulations unambiguously. However, the GPE method is nonperturbative, and we believe it can be used to describe the thermal properties of a Bose gas even when Bogoliubov theory fails. We suggest a different technique to measure the temperature of our simulations in these circumstances. Using this approach we determine the dependence of the condensate fraction and specific heat on temperature for several interaction strengths, and observe the appearance of vortex networks. Interesting behavior near the critical point is observed and discussed.

A evasão discente no contexto da reestruturação universitária : o caso dos cursos de Administração e Ciências Contábeis da Universidade Federal do Espírito Santo

O objetivo desta pesquisa foi levantar os motivos que influenciam a evasão discente em quatro cursos de graduação da Universidade Federal do Espírito Santo. A reestruturação universitária proposta pelo REUNI - Programa de Apoio a Planos de Expansão das Universidades Federais serviu como contexto ao estudo, pois instituiu diretrizes para o combate à evasão no ensino superior. O modelo de evasão de cunho sociológico proposto por Tinto (1997) baseou as análises realizadas nesta pesquisa porque toma a instituição como responsável por ações capazes de criar um ambiente de aprendizado necessário à permanência do estudante. A pesquisa de campo quali-quantitativa foi realizada com os alunos evadidos e com os coordenadores dos cursos de Administração Diurno e Ciências Contábeis Noturno e dos novos cursos Administração Noturno e Ciências Contábeis Vespertino. Foram alcançados 95 alunos evadidos e os quatro coordenadores, sendo aplicado questionário semiaberto aos alunos evadidos e feitas entrevistas semiestruturadas com os coordenadores. Dados do sistema acadêmico (SIE/UFES) foram utilizados para o levantamento das variáveis. Os números fornecem evidências de que o resultado da aprendizagem traduzido pelo desempenho acadêmico torna-se um forte causador da evasão por abandono. O baixo coeficiente de rendimento relacionou-se ao desligamento por abandono na maioria dos casos. Em relação às formas de evasão, a desistência e o desligamento por abandono totalizaram 87,4% dos casos, com maior incidência de evasão no segundo e terceiro ano do curso. O ponto crítico da evasão parece confirmar-se do 2º ao 5º semestre e 62% dos casos de evasão que se situaram nesse lapso temporal apresentaram coeficiente de rendimento de 0,00 a 3,00. Os resultados evidenciaram os motivos que mais influenciaram os alunos a deixar o curso: i) a necessidade de trabalhar enquanto frequentava o curso, ii) a descoberta de novos interesses; iii) a incompatibilidade entre os horários do trabalho e do curso; iv) a escolha da carreira profissional ainda muito jovem e v) a falta de orientação aos alunos sobre normas, penalidades, planejamento do curso, periodização, etc. e deficiências na comunicação institucional.

Equilibrium self-assembly of colloids with distinct interaction sites: Thermodynamics, percolation, and cluster distribution functions

We calculate the equilibrium thermodynamic properties, percolation threshold, and cluster distribution functions for a model of associating colloids, which consists of hard spherical particles having on their surfaces three short-ranged attractive sites (sticky spots) of two different types, A and B. The thermodynamic properties are calculated using Wertheim's perturbation theory of associating fluids. This also allows us to find the onset of self-assembly, which can be quantified by the maxima of the specific heat at constant volume. The percolation threshold is derived, under the no-loop assumption, for the correlated bond model: In all cases it is two percolated phases that become identical at a critical point, when one exists. Finally, the cluster size distributions are calculated by mapping the model onto an effective model, characterized by a-state-dependent-functionality (f) over bar and unique bonding probability (p) over bar. The mapping is based on the asymptotic limit of the cluster distributions functions of the generic model and the effective parameters are defined through the requirement that the equilibrium cluster distributions of the true and effective models have the same number-averaged and weight-averaged sizes at all densities and temperatures. We also study the model numerically in the case where BB interactions are missing. In this limit, AB bonds either provide branching between A-chains (Y-junctions) if epsilon(AB)/epsilon(AA) is small, or drive the formation of a hyperbranched polymer if epsilon(AB)/epsilon(AA) is large. We find that the theoretical predictions describe quite accurately the numerical data, especially in the region where Y-junctions are present. There is fairly good agreement between theoretical and numerical results both for the thermodynamic (number of bonds and phase coexistence) and the connectivity properties of the model (cluster size distributions and percolation locus).

The condensation and ordering of models of empty liquids

We consider a simple model consisting of particles with four bonding sites ("patches"), two of type A and two of type B, on the square lattice, and investigate its global phase behavior by simulations and theory. We set the interaction between B patches to zero and calculate the phase diagram as the ratio between the AB and the AA interactions, epsilon(AB)*, varies. In line with previous work, on three-dimensional off-lattice models, we show that the liquid-vapor phase diagram exhibits a re-entrant or "pinched" shape for the same range of epsilon(AB)*, suggesting that the ratio of the energy scales - and the corresponding empty fluid regime - is independent of the dimensionality of the system and of the lattice structure. In addition, the model exhibits an order-disorder transition that is ferromagnetic in the re-entrant regime. The use of low-dimensional lattice models allows the simulation of sufficiently large systems to establish the nature of the liquid-vapor critical points and to describe the structure of the liquid phase in the empty fluid regime, where the size of the "voids" increases as the temperature decreases. We have found that the liquid-vapor critical point is in the 2D Ising universality class, with a scaling region that decreases rapidly as the temperature decreases. The results of simulations and theoretical analysis suggest that the line of order-disorder transitions intersects the condensation line at a multi-critical point at zero temperature and density, for patchy particle models with a re-entrant, empty fluid, regime. (C) 2011 American Institute of Physics. [doi: 10.1063/1.3657406]

Positive Solutions of the Dirichlet Problem for the One-dimensional Minkowski-Curvature Equation

We discuss existence and multiplicity of positive solutions of the Dirichlet problem for the quasilinear ordinary differential equation-(u' / root 1 - u'(2))' = f(t, u). Depending on the behaviour of f = f(t, s) near s = 0, we prove the existence of either one, or two, or three, or infinitely many positive solutions. In general, the positivity of f is not required. All results are obtained by reduction to an equivalent non-singular problem to which variational or topological methods apply in a classical fashion.

Patching up dipoles: can dipolar particles be viewed as patchy colloids?

We investigate whether the liquid-vapour phase transition of strongly dipolar fluids can be understood using a model of patchy colloids. These consist of hard spherical particles with three short-ranged attractive sites (patches) on their surfaces. Two of the patches are of type A and one is of type B. Patches A on a particle may bond either to a patch A or to a patch B on another particle. Formation of an AA (AB) bond lowers the energy by epsilon AA (epsilon AB). In the limit [image omitted], this patchy model exhibits condensation driven by AB-bonds (Y-junctions). Y-junctions are also present in low-density, strongly dipolar fluids, and have been conjectured to play a key role in determining their critical behaviour. We map the dipolar Yukawa hard-sphere (DYHS) fluid onto this 2A + 1B patchy model by requiring that the latter reproduce the correct DYHS critical point as a function of the isotropic interaction strength epsilon Y. This is achieved for sensible values of epsilon AB and the bond volumes. Results for the internal energy and the particle coordination number are in qualitative agreement with simulations of DYHSs. Finally, by taking the limit [image omitted], we arrive at a new estimate for the critical point of the dipolar hard-sphere fluid, which agrees with extrapolations from simulation.

Le moment venu ou l’eveil dês editoriaux. Mutations de la littérature des années quatre-vingt vues par les revues littéraires

Les années quatre-vingt signalent un point de bascule dans et une mutation majeure dans les caractéristiques narratives de la littérature française. D’une certaine façon, elles entament la contemporanéité littéraire telle que nous la connaissons du point de vue critique. Nous insisterons sur le rôle des revues et des éditoriaux dans ce processus. Ils manifestent quelques hésitations de la critique par rapport à la littérature naissante.

Three-dimensional patchy lattice model for empty fluids

The phase diagram of a simple model with two patches of type A and ten patches of type B (2A10B) on the face centred cubic lattice has been calculated by simulations and theory. Assuming that there is no interaction between the B patches the behavior of the system can be described in terms of the ratio of the AB and AA interactions, r. Our results show that, similarly to what happens for related off-lattice and two-dimensional lattice models, the liquid-vapor phase equilibria exhibit reentrant behavior for some values of the interaction parameters. However, for the model studied here the liquid-vapor phase equilibria occur for values of r lower than 1/3, a threshold value which was previously thought to be universal for 2AnB models. In addition, the theory predicts that below r = 1/3 (and above a new condensation threshold which is < 1/3) the reentrant liquid-vapor equilibria are so extreme that it exhibits a closed loop with a lower critical point, a very unusual behavior in single-component systems. An order-disorder transition is also observed at higher densities than the liquid-vapor equilibria, which shows that the liquid-vapor reentrancy occurs in an equilibrium region of the phase diagram. These findings may have implications in the understanding of the condensation of dipolar hard spheres given the analogy between that system and the 2AnB models considered here. (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.4771591]

Harvesting dynamic aspects from a real rational map : the bulb of period 5

This journal provides immediate open access to its content on the principle that making research freely available to the public supports a greater global exchange of knowledge.

Mapping stability : real rational maps of degree zero

In memory of our beloved Professor José Rodrigues Santos de Sousa Ramos (1948-2007), who João Cabral, one of the authors of this paper, had the honor of being his student between 2000 and 2006, we wrote this paper following the research by experimentation, using the new technologies to capture a new insight about a problem, as him so much love to do it. His passion was to create new relations between different fields of mathematics. He was a builder of bridges of knowledge, encouraging the birth of new ways to understand this science. One of the areas that Sousa Ramos researched was the iteration of maps and the description of its behavior, using the symbolic dynamics. So, in this issue of this journal, honoring his memory, we use experimental results to find some stable regions of a specific family of real rational maps, the ones that he worked with João Cabral. In this paper we describe a parameter space (a,b) to the real rational maps fa,b(x) = (x2 −a)/(x2 −b), using some tools of dynamical systems, as the study of the critical point orbit and Lyapunov exponents. We give some results regarding the stability of these family of maps when we iterate it, specially the ones connected to the order 3 of iteration. We hope that our results would help to understand better the behavior of these maps, preparing the ground to a more efficient use of the Kneading Theory on these family of maps, using symbolic dynamics.

How patchy can one get and still condense? The role of dissimilar patches in the interactions of colloidal particles

We investigate the influence of strong directional, or bonding, interactions on the phase diagram of complex fluids, and in particular on the liquid-vapour critical point. To this end we revisit a simple model and theory for associating fluids which consist of spherical particles having a hard-core repulsion, complemented by three short-ranged attractive sites on the surface (sticky spots). Two of the spots are of type A and one is of type B; the interactions between each pair of spots have strengths [image omitted], [image omitted] and [image omitted]. The theory is applied over the whole range of bonding strengths and results are interpreted in terms of the equilibrium cluster structures of the coexisting phases. In systems where unlike sites do not interact (i.e. where [image omitted]), the critical point exists all the way to [image omitted]. By contrast, when [image omitted], there is no critical point below a certain finite value of [image omitted]. These somewhat surprising results are rationalised in terms of the different network structures of the two systems: two long AA chains are linked by one BB bond (X-junction) in the former case, and by one AB bond (Y-junction) in the latter. The vapour-liquid transition may then be viewed as the condensation of these junctions and we find that X-junctions condense for any attractive [image omitted] (i.e. for any fraction of BB bonds), whereas condensation of the Y-junctions requires that [image omitted] be above a finite threshold (i.e. there must be a finite fraction of AB bonds).

Criticality of colloids with distinct interaction patches: The limits of linear chains, hyperbranched polymers, and dimers

We use a simple model of associating fluids which consists of spherical particles having a hard-core repulsion, complemented by three short-ranged attractive sites on the surface (sticky spots). Two of the spots are of type A and one is of type B; the bonding interactions between each pair of spots have strengths epsilon(AA), epsilon(BB), and epsilon(AB). The theory is applied over the whole range of bonding strengths and the results are interpreted in terms of the equilibrium cluster structures of the phases. In addition to our numerical results, we derive asymptotic expansions for the free energy in the limits for which there is no liquid-vapor critical point: linear chains (epsilon(AA)not equal 0, epsilon(AB)=epsilon(BB)=0), hyperbranched polymers (epsilon(AB)not equal 0, epsilon(AA)=epsilon(BB)=0), and dimers (epsilon(BB)not equal 0, epsilon(AA)=epsilon(AB)=0). These expansions also allow us to calculate the structure of the critical fluid by perturbing around the above limits, yielding three different types of condensation: of linear chains (AA clusters connected by a few AB or BB bonds); of hyperbranched polymers (AB clusters connected by AA bonds); or of dimers (BB clusters connected by AA bonds). Interestingly, there is no critical point when epsilon(AA) vanishes despite the fact that AA bonds alone cannot drive condensation.

The Portuguese law on social economy

This study is a reflection on the Portuguese Framework Law on Social Economy, highlighting, from a critical point-of-view, its contribution to the explicit institutional and legal recognition of the social economy sector. It does so by defining the concept of social economy and listing the entities engaged in this sector, by defining its guiding principles and the mechanisms for its promotion and encouragement, and also by describing the creation of a tax and competition regime which will take into account its specificities. The setting up of this foundations of the social economy was based on the constitutional principle of protection of the social and cooperative sector, which substantiates the adoption of differentiating solutions in view of the positive discrimination of this sector.