Phase diagram of a model for a binary mixture of nematic molecules on a Bethe lattice

We investigate the phase diagram of a discrete version of the Maier-Saupe model with the inclusion of additional degrees of freedom to mimic a distribution of rodlike and disklike molecules. Solutions of this problem on a Bethe lattice come from the analysis of the fixed points of a set of nonlinear recursion relations. Besides the fixed points associated with isotropic and uniaxial nematic structures, there is also a fixed point associated with a biaxial nematic structure. Due to the existence of large overlaps of the stability regions, we resorted to a scheme to calculate the free energy of these structures deep in the interior of a large Cayley tree. Both thermodynamic and dynamic-stability analyses rule out the presence of a biaxial phase, in qualitative agreement with previous mean-field results

‘Unequal mobilities’ in the Lisbon Metropolitan Area: daily travel choices and private car use

Mobilities have been looked at in increasingly greater depth over the last few decades, posing a growing set of theoretical and methodological problems for urban studies. One of the approaches that are being taken in this field is to consider the relationship between social inequalities and the various different mobility conditions. The present article seeks to show the extent to which mobility behaviours of Lisbon Metropolitan Area residents vary in accordance with a range of inequality variables, such as gender, education, social class, and age, thus generating clearly marked social profiles. Special attention is paid to car use. Statistical analysis of a questionnaire applied to 1,500 residents shows that regular car use is still relatively circumscribed to one social group, to which it offers the advantage of less time spent on daily travel, notwithstanding the increased costs. On the other hand, populations who regularly use public transport are at a disadvantage, spending more of their day travelling from one place to another.info:eu-repo/semantics/publishedVersio

Condiciones ambientales y diferenciación social en los patrones de movilidad: el caso de las desigualdades de género en el Área Metropolitana de Lisboa

Place determinants and social dimensions interact to produce mobility patterns. The article seeks to measure to what extent the physical and social conditions of the residency place modulate the intensity of mobility particularly in what concerns gender inequalities. To do so, we first present the theoretical framework, which guides our perspective on mobility inequalities and the geographical focus: Lisbon Metropolitan Area (LMA). Secondly, using logistic regression on representative data from a survey to LMA inhabitants we elaborate on the concept of environmental motility and its relationship to various types of inequality. Lastly, we systematize a view on accumulated inequalities examining how local environments may increase the mobilities gender gap.info:eu-repo/semantics/publishedVersio

Statistical models of mixtures with a biaxial nematic phase

We consider a simple Maier-Saupe statistical model with the inclusion of disorder degrees of freedom to mimic the phase diagram of a mixture of rod-like and disc-like molecules. A quenched distribution of shapes leads to the existence of a stable biaxial nematic phase, in qualitative agreement with experimental findings for some ternary lyotropic liquid mixtures. An annealed distribution, however, which is more adequate to liquid mixtures, precludes the stability of this biaxial phase. We then use a two-temperature formalism, and assume a separation of relaxation times, to show that a partial degree of annealing is already sufficient to stabilize a biaxial nematic structure.Comment: 11 pages, 2 figure

The geometry of thermodynamic control

A deeper understanding of nonequilibrium phenomena is needed to reveal the principles governing natural and synthetic molecular machines. Recent work has shown that when a thermodynamic system is driven from equilibrium then, in the linear response regime, the space of controllable parameters has a Riemannian geometry induced by a generalized friction tensor. We exploit this geometric insight to construct closed-form expressions for minimal-dissipation protocols for a particle diffusing in a one dimensional harmonic potential, where the spring constant, inverse temperature, and trap location are adjusted simultaneously. These optimal protocols are geodesics on the Riemannian manifold, and reveal that this simple model has a surprisingly rich geometry. We test these optimal protocols via a numerical implementation of the Fokker-Planck equation and demonstrate that the friction tensor arises naturally from a first order expansion in temporal derivatives of the control parameters, without appealing directly to linear response theory

Soliton surfaces associated with symmetries of ODEs written in Lax representation

The main aim of this paper is to discuss recent results on the adaptation of the Fokas-Gel'fand procedure for constructing soliton surfaces in Lie algebras, which was originally derived for PDEs [Grundland, Post 2011], to the case of integrable ODEs admitting Lax representations. We give explicit forms of the \g-valued immersion functions based on conformal symmetries involving the spectral parameter, a gauge transformation of the wave function and generalized symmetries of the linear spectral problem. The procedure is applied to a symmetry reduction of the static $\phi^4$-field equations leading to the Jacobian elliptic equation. As examples, we obtain diverse types of surfaces for different choices of Jacobian elliptic functions for a range of values of parameters.Comment: 14 Pages, 2 figures Conference Proceedings for QST7 Pragu

Generalization of Linearized Gouy-Chapman-Stern Model of Electric Double Layer for Nanostructured and Porous Electrodes: Deterministic and Stochastic Morphology

We generalize linearized Gouy-Chapman-Stern theory of electric double layer for nanostructured and morphologically disordered electrodes. Equation for capacitance is obtained using linear Gouy-Chapman (GC) or Debye-$\rm{\ddot{u}}$ckel equation for potential near complex electrode/electrolyte interface. The effect of surface morphology of an electrode on electric double layer (EDL) is obtained using "multiple scattering formalism" in surface curvature. The result for capacitance is expressed in terms of the ratio of Gouy screening length and the local principal radii of curvature of surface. We also include a contribution of compact layer, which is significant in overall prediction of capacitance. Our general results are analyzed in details for two special morphologies of electrodes, i.e. "nanoporous membrane" and "forest of nanopillars". Variations of local shapes and global size variations due to residual randomness in morphology are accounted as curvature fluctuations over a reference shape element. Particularly, the theory shows that the presence of geometrical fluctuations in porous systems causes enhanced dependence of capacitance on mean pore sizes and suppresses the magnitude of capacitance. Theory emphasizes a strong influence of overall morphology and its disorder on capacitance. Finally, our predictions are in reasonable agreement with recent experimental measurements on supercapacitive mesoporous systems

Frenet-Serret dynamics

We consider the motion of a particle described by an action that is a functional of the Frenet-Serret [FS] curvatures associated with the embedding of its worldline in Minkowski space. We develop a theory of deformations tailored to the FS frame. Both the Euler-Lagrange equations and the physical invariants of the motion associated with the Poincar\'e symmetry of Minkowski space, the mass and the spin of the particle, are expressed in a simple way in terms of these curvatures. The simplest non-trivial model of this form, with the lagrangian depending on the first FS (or geodesic) curvature, is integrable. We show how this integrability can be deduced from the Poincar\'e invariants of the motion. We go on to explore the structure of these invariants in higher-order models. In particular, the integrability of the model described by a lagrangian that is a function of the second FS curvature (or torsion) is established in a three dimensional ambient spacetime.Comment: 20 pages, no figures - replaced with version to appear in Class. Quant. Grav. - minor changes, added Conclusions sectio

Persistence of Left Superior Vena Cava Associated to Esophageal Atresia: Presentation of 5 Cases

Objectivos: A atresia do esófago está associada a uma variedade de malformações congénitas de outros órgãos. A persistência da veia cava superior esquerda e uma das malformações venosas torácicas mais comuns, ocorrendo em 0,3% da população. O objectivo deste estudo é caracterizar a persistência da veia cava superior esquerda nos doentes com atresia do esófago tratados no Hospital Dona Estefânia. Métodos: Estudo retrospectivo dos doentes admitidos por atresia do esófago desde Janeiro 2002 a Dezembro 2013. As seguintes variáveis foram estudadas, considerando, idade gestacional, o peso à nascença, o sexo, tipo de atresia do esófago, ecocardiograma no pré-operatório, malformações associadas, abordagem cirúrgica, eventual ecocardiograma no pós-operatório e angioressonância. Resultados: De um total de 107 doentes, em cinco casos foi diagnosticada persistência da veia cava superior esquerda. Destes, apenas um tinha diagnostico pré-natal. A restante investigação revelou um doente com atresia duodenal e outro com malformação do aparelho urinário, coloboma e malformação bilateral dos pavilhões auriculares. Todos os cinco doentes foram submetidos a toracotomia, esofagoesofagostomia primária após laqueação da fístula traqueo-esofágica e angio-ressonância para caracterizar a malformação vascular. Não houve registo de complicações, quer intra-operatórias quer pós-operatórias. Conclusão: Apesar do estudo pré-operatório, apenas se diagnosticou persistência da veia cava superior esquerda num dos doentes. O diagnóstico é geralmente feito de forma incidental durante a colocação rotineira de catéteres venosos centrais à esquerda. É importante identificar estes doentes e caracterizar o seu padrão de retorno venoso cardíaco, pelo risco de complicações embó1icas paradoxais para o sistema arterial

Twelve Years of Kawasaki Disease in Portugal: Epidemiology in Hospitalized Children

Kawasaki disease (KD) is the leading cause of acquired heart disease in developed countries. Reported incidences vary worldwide but incidence of KD has not been established in Portugal. The aims of the study were to describe the epidemiologic characteristics and estimate incidence rates of KD among hospitalized children in Portugal. METHODS: This study was a descriptive, population-based study, which used hospital discharge records of patients <20 years of age diagnosed with KD from the Hospital Register database for 2000-2011. Incidence rates were calculated using the number of KD patients and corresponding National census data. RESULTS: There were 533 hospitalizations of 470 patients with KD as the primary diagnosis in Portugal, 63 hospitalizations were transfers of patients between hospitals and there were no relapses. The mean age at admission was 2.8 years, with male predominance (male-to-female ratio: 1.6:1). Children <5 years and infants <1 year represented 83% and 23% of all the patients admitted, respectively. Mean annual incidence was 6.5 per 100,000 children <5 years, 4.5 per 100,000 infants <1 year and 7.8 per 100,000 infants 1-4 years. We found considerable differences between national territorial regions, with majority of cases in most dense regions. The mean length of hospital stay was 9 days, and the incidence peaked in spring (35%) and spring/winter (63%). Coronary aneurysms were reported in 8.5% of patients with a higher male-to-female ratio (3.4:1) and a lower mean age (1.93 years). Reported mortality was 0.4%. CONCLUSIONS: This is the first large-scale epidemiologic study of KD in Portugal. The highest incidences occurred among male children 1-4 years of age and in spring/winter.info:eu-repo/semantics/publishedVersio