Critical properties of an aperiodic model for interacting polymers

We investigate the effects of aperiodic interactions on the critical behavior of an interacting two-polymer model on hierarchical lattices (equivalent to the Migadal-Kadanoff approximation for the model on Bravais lattices), via renormalization-group and tranfer-matrix calculations. The exact renormalization-group recursion relations always present a symmetric fixed point, associated with the critical behavior of the underlying uniform model. If the aperiodic interactions, defined by s ubstitution rules, lead to relevant geometric fluctuations, this fixed point becomes fully unstable, giving rise to novel attractors of different nature. We present an explicit example in which this new attractor is a two-cycle, with critical indices different from the uniform model. In case of the four-letter Rudin-Shapiro substitution rule, we find a surprising closed curve whose points are attractors of period two, associated with a marginal operator. Nevertheless, a scaling analysis indicates that this attractor may lead to a new critical universality class. In order to provide an independent confirmation of the scaling results, we turn to a direct thermodynamic calculation of the specific-heat exponent. The thermodynamic free energy is obtained from a transfer matrix formalism, which had been previously introduced for spin systems, and is now extended to the two-polymer model with aperiodic interactions.Comment: 19 pages, 6 eps figures, to appear in J. Phys A: Math. Ge

Critical Behavior of a Three-State Potts Model on a Voronoi Lattice

We use the single-histogram technique to study the critical behavior of the three-state Potts model on a (random) Voronoi-Delaunay lattice with size ranging from 250 to 8000 sites. We consider the effect of an exponential decay of the interactions with the distance,$J(r)=J_0\exp(-ar)$, with $a>0$, and observe that this system seems to have critical exponents $\gamma$ and $\nu$ which are different from the respective exponents of the three-state Potts model on a regular square lattice. However, the ratio $\gamma/\nu$ remains essentially the same. We find numerical evidences (although not conclusive, due to the small range of system size) that the specific heat on this random system behaves as a power-law for $a=0$ and as a logarithmic divergence for $a=0.5$ and $a=1.0$Comment: 3 pages, 5 figure

Deblocking of interacting particle assemblies: from pinning to jamming

A wide variety of interacting particle assemblies driven by an external force are characterized by a transition between a blocked and a moving phase. The origin of this deblocking transition can be traced back to the presence of either external quenched disorder, or of internal constraints. The first case belongs to the realm of the depinning transition, which, for example, is relevant for flux-lines in type II superconductors and other elastic systems moving in a random medium. The second case is usually included within the so-called jamming scenario observed, for instance, in many glassy materials as well as in plastically deforming crystals. Here we review some aspects of the rich phenomenology observed in interacting particle models. In particular, we discuss front depinning, observed when particles are injected inside a random medium from the boundary, elastic and plastic depinning in particle assemblies driven by external forces, and the rheology of systems close to the jamming transition. We emphasize similarities and differences in these phenomena.Comment: 20 pages, 8 figures, submitted for a special issue of the Brazilian Journal of Physics entitled: Statistical Mechanics of Irreversible Stochastic Models - I

Analytical results for long time behavior in anomalous diffusion

We investigate through a Generalized Langevin formalism the phenomenon of anomalous diffusion for asymptotic times, and we generalized the concept of the diffusion exponent. A method is proposed to obtain the diffusion coefficient analytically through the introduction of a time scaling factor $\lambda$. We obtain as well an exact expression for $\lambda$ for all kinds of diffusion. Moreover, we show that $\lambda$ is a universal parameter determined by the diffusion exponent. The results are then compared with numerical calculations and very good agreement is observed. The method is general and may be applied to many types of stochastic problem

TRAUMATIC SPINAL CORD INJURY: Neurologic and Functional Recovery

Objectivo: Avaliar a recuperação neurológica e funcional dos doentes com Traumatismo Vertebro-Medular (TVM). Métodos: Foi realizado um estudo retrospectivo, que incluiu os 93 doentes com o diagnóstico de TVM admitidos no Serviço de Fisiatria do Hospital Geral de Santo António, entre Janeiro de 1993 e Dezembro de 2002. Os dados demográficos e médicos foram recolhidos dos processos clínicos. O registo da avaliação de cada doente foi efectuado na admissão, à data da alta hospitalar e 1 e 3 anos após a lesão. O estado neurológico foi classificado de acordo com os critérios da American Spinal Injury Association (ASIA), e o estado funcional através da Medida de Independência Funcional (MIF). Resultados: 87% doentes eram do sexo masculino, sendo a média de idades de 40 anos. Os acidentes de viação e as quedas foram a causa mais frequente da lesão. A maioria dos traumatismos foi dorsal e cervical (45% e 42% respectivamente). O tratamento inicial incluiu: administração intravenosa de metilprednisolona, que ocorreu nas primeiras oito horas após lesão em 54% dos casos; intervenção cirúrgica precoce, realizada em 77%. Registou-se maior recuperação nos doentes com lesão medular incompleta, particularmente naqueles classificados como C na escala da ASIA. Foi encontrada uma associação estatisticamente significativa entre os resultados obtidos no internamento e os registados no período de três anos de follow-up. A recuperação neurológica não se correlacionou com a idade dos doentes, o nível de lesão, administração de corticoides em altas doses ou cirurgia realizada nas primeiras 24 horas após a lesão (p >0,05). Os resultados funcionais registados através da MIF revelaram-se bastante favoráveis, particularmente os que foram alcançados em regime de internamento. Conclusões: Os resultados revelados neste estudo demonstram o considerável potencial para uma recuperação neurológica após um TVM, enfatizando a importância do investimento na continuidade dos programas de reabilitação nos anos que se seguem à lesão, particularmente nas lesões incompletas. Study Design: A retrospective study was conducted Objective: Evaluate the neurologic and functional recovery in patients with Traumatic Spinal Cord Injury (TSCI). Methods: A retrospective study was conducted, including the 93 patients with a diagnosis of TSCI admitted for rehabilitation in the Physical and Rehabilitation Medicine Department, Santo António General Hospital, between January 1993 and December 2002. Demographic and clinical data were collected from the hospital charts. The patients were evaluated at admission for rehabilitation, before discharging, 1 year and 3 years after injury. Neurologic status was registered according to the standards of the American Spinal Injury Association (ASIA) and functional status by the Functional Independence Measure (FIM). Results: The sample population was 87% men, with a mean age of 40 years. Motor vehicle accidents and falls were the commonest mechanism of injury. The majority sustained dorsal and cervical lesions (45% and 42% respectively). The initial management included: intravenous high dose methylprednisolone, administered within eight hours after injury in 54% of the sample; early surgical stabilization, performed on 77%. Incomplete cord injury carried a better prognosis of motor improvement, especially the patients classified as C on the ASIA Impairment Scale (AIS). A significant statistical association was found between the outcomes obtained during the initial rehabilitation, and the ones achieved on the 3 year followup period. The neurologic recovery was not related with the patient’s age, injury level, high dose steroid administration or surgery performed in the first 24 hours after injury (p >0,05). The FIM scores demonstrated the favourable functional outcomes achieved, especially during the inpatient rehabilitation. Conclusions: The results of this study further demonstrate the considerable potential for neurologic recovery after TSCI, emphasizing the importance of the rehabilitation investment continuity, especially for the ones with incomplete cord injury

Non-Local Product Rules for Percolation

Despite original claims of a first-order transition in the product rule model proposed by Achlioptas et al. [Science 323, 1453 (2009)], recent studies indicate that this percolation model, in fact, displays a continuous transition. The distinctive scaling properties of the model at criticality, however, strongly suggest that it should belong to a different universality class than ordinary percolation. Here we introduce a generalization of the product rule that reveals the effect of non-locality on the critical behavior of the percolation process. Precisely, pairs of unoccupied bonds are chosen according to a probability that decays as a power-law of their Manhattan distance, and only that bond connecting clusters whose product of their sizes is the smallest, becomes occupied. Interestingly, our results for two-dimensional lattices at criticality shows that the power-law exponent of the product rule has a significant influence on the finite-size scaling exponents for the spanning cluster, the conducting backbone, and the cutting bonds of the system. In all three cases, we observe a continuous variation from ordinary to (non-local) explosive percolation exponents.Comment: 5 pages, 4 figure