Finding critical exponents for two-dimensional Hamiltonian maps

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

The aggregation process in tetraethoxysilane-derived sonogels as an analogy to the critical phenomenon

The structural evolution in silica sols prepared from tetraethoxysilane (TEOS) sonohydrolysis was studied 'in situ' using small-angle x-ray scattering (SAXS). The structure of the gelling system can be reasonably well described by a correlation function given by gamma(r) similar to (1/R(2))(1/r) exp(- r/xi), where xi is the structure correlation length and R is a chain persistence length, as an analogy to the Ornstein-Zernike theory in describing critical phenomenon. This approach is also expected for the scattering from some linear and branched molecules as polydisperse coils of linear chains and random f-functional branched polycondensates. The characteristic length. grows following an approximate power law with time t as xi similar to t(1) (with the exponent quite close to 1) while R remains undetermined but with a constant value, except at the beginning of the process in which the growth of. is slower and R increases by only about 15% with respect to the value of the initial sol. The structural evolution with time is compatible with an aggregation process by a phase separation by coarsening. The mechanism of growth seems to be faster than those typically observed for pure diffusion controlled cluster-cluster aggregation. This suggests that physical forces (hydrothermal forces) could be actuating together with diffusion in the gelling process of this system. The data apparently do not support a spinodal decomposition mechanism, at least when starting from the initial stable acid sol studied here.

Quasilinear dirichlet problems in RN with critical growth

In this study, a given quasilinear problem is solved using variational methods. In particular, the existence of nontrivial solutions for GP is examined using minimax methods. The main theorem on the existence of a nontrivial solution for GP is detailed.

Critical behavior in a cross-situational lexicon learning scenario

The associationist account for early word learning is based on the co-occurrence between referents and words. Here we introduce a noisy cross-situational learning scenario in which the referent of the uttered word is eliminated from the context with probability gamma, thus modeling the noise produced by out-of-context words. We examine the performance of a simple associative learning algorithm and find a critical value of the noise parameter gamma(c) above which learning is impossible. We use finite-size scaling to show that the sharpness of the transition persists across a region of order tau(-1/2) about gamma(c), where tau is the number of learning trials, as well as to obtain the learning error (scaling function) in the critical region. In addition, we show that the distribution of durations of periods when the learning error is zero is a power law with exponent -3/2 at the critical point. Copyright (C) EPLA, 2012

Finite-size corrections of the entanglement entropy of critical quantum chains

Using the density matrix renormalization group, we calculated the finite-size corrections of the entanglement alpha-Renyi entropy of a single interval for several critical quantum chains. We considered models with U(1) symmetry such as the spin-1/2 XXZ and spin-1 Fateev-Zamolodchikov models, as well as models with discrete symmetries such as the Ising, the Blume-Capel, and the three-state Potts models. These corrections contain physically relevant information. Their amplitudes, which depend on the value of a, are related to the dimensions of operators in the conformal field theory governing the long-distance correlations of the critical quantum chains. The obtained results together with earlier exact and numerical ones allow us to formulate some general conjectures about the operator responsible for the leading finite-size correction of the alpha-Renyi entropies. We conjecture that the exponent of the leading finite-size correction of the alpha-Renyi entropies is p(alpha) = 2X(epsilon)/alpha for alpha > 1 and p(1) = nu, where X-epsilon denotes the dimensions of the energy operator of the model and nu = 2 for all the models.

Mean-Field critical behavior and ergodicity break in a nonequilibrium one-dimensional RSOS growth model

We investigate the nonequilibrium roughening transition of a one-dimensional restricted solid-on-solid model by directly sampling the stationary probability density of a suitable order parameter as the surface adsorption rate varies. The shapes of the probability density histograms suggest a typical Ginzburg-Landau scenario for the phase transition of the model, and estimates of the "magnetic" exponent seem to confirm its mean-field critical behavior. We also found that the flipping times between the metastable phases of the model scale exponentially with the system size, signaling the breaking of ergodicity in the thermodynamic limit. Incidentally, we discovered that a closely related model not considered before also displays a phase transition with the same critical behavior as the original model. Our results support the usefulness of off-critical histogram techniques in the investigation of nonequilibrium phase transitions. We also briefly discuss in the appendix a good and simple pseudo-random number generator used in our simulations.

Critical transport properties of random metals in large magnetic fields

The threshold behavior of the transport properties of a random metal in the critical region near a metal–insulator transition is strongly affected by the measuring electromagnetic fields. In spite of the randomness, the electrical conductivity exhibits striking phase-coherent effects due to broken symmetry, which greatly sharpen the transition compared with the predictions of effective medium theories, as previously explained for electrical conductivities. Here broken symmetry explains the sign reversal of the T → 0 magnetoconductance of the metal–insulator transition in Si(B,P), also previously not understood by effective medium theories. Finally, the symmetry-breaking features of quantum percolation theory explain the unexpectedly very small electrical conductivity temperature exponent α = 0.22(2) recently observed in Ni(S,Se)2 alloys at the antiferromagnetic metal–insulator transition below T = 0.8 K.

Critical behavior of the dilute antiferromagnet in a magnetic field

We study the critical behavior of the diluted antiferromagnet in a field with the tethered Monte Carlo formalism. We compute the critical exponents (including the elusive hyperscaling violations exponent θ). Our results provide a comprehensive description of the phase transition and clarify the inconsistencies between previous experimental and theoretical work. To do so, our method addresses the usual problems of numerical work (large tunneling barriers and self-averaging violations).

Nonequilibrium critical scaling from quantum thermodynamics

The emerging field of quantum thermodynamics is contributing important results and insights into archetypal many-body problems, including quantum phase transitions. Still, the question whether out-of-equilibrium quantities, such as fluctuations of work, exhibit critical scaling after a sudden quench in a closed system has remained elusive. Here, we take a novel approach to the problem by studying a quench across an impurity quantum critical point. By performing density matrix renormalization group computations on the two-impurity Kondo model, we are able to establish that the irreversible work produced in a quench exhibits finite-size scaling at quantum criticality. This scaling faithfully predicts the equilibrium critical exponents for the crossover length and the order parameter of the model, and, moreover, implies a new exponent for the rescaled irreversible work. By connecting the irreversible work to the two-impurity spin correlation function, our findings can be tested experimentally.

Undersampled Critical Branching Processes on Small-World and Random Networks Fail to Reproduce the Statistics of Spike Avalanches

The power-law size distributions obtained experimentally for neuronal avalanches are an important evidence of criticality in the brain. This evidence is supported by the fact that a critical branching process exhibits the same exponent t~3=2. Models at criticality have been employed to mimic avalanche propagation and explain the statistics observed experimentally. However, a crucial aspect of neuronal recordings has been almost completely neglected in the models: undersampling. While in a typical multielectrode array hundreds of neurons are recorded, in the same area of neuronal tissue tens of thousands of neurons can be found. Here we investigate the consequences of undersampling in models with three different topologies (two-dimensional, small-world and random network) and three different dynamical regimes (subcritical, critical and supercritical). We found that undersampling modifies avalanche size distributions, extinguishing the power laws observed in critical systems. Distributions from subcritical systems are also modified, but the shape of the undersampled distributions is more similar to that of a fully sampled system. Undersampled supercritical systems can recover the general characteristics of the fully sampled version, provided that enough neurons are measured. Undersampling in two-dimensional and small-world networks leads to similar effects, while the random network is insensitive to sampling density due to the lack of a well-defined neighborhood. We conjecture that neuronal avalanches recorded from local field potentials avoid undersampling effects due to the nature of this signal, but the same does not hold for spike avalanches. We conclude that undersampled branching-process-like models in these topologies fail to reproduce the statistics of spike avalanches.

Undersampled Critical Branching Processes on Small-World and Random Networks Fail to Reproduce the Statistics of Spike Avalanches

The power-law size distributions obtained experimentally for neuronal avalanches are an important evidence of criticality in the brain. This evidence is supported by the fact that a critical branching process exhibits the same exponent t~3=2. Models at criticality have been employed to mimic avalanche propagation and explain the statistics observed experimentally. However, a crucial aspect of neuronal recordings has been almost completely neglected in the models: undersampling. While in a typical multielectrode array hundreds of neurons are recorded, in the same area of neuronal tissue tens of thousands of neurons can be found. Here we investigate the consequences of undersampling in models with three different topologies (two-dimensional, small-world and random network) and three different dynamical regimes (subcritical, critical and supercritical). We found that undersampling modifies avalanche size distributions, extinguishing the power laws observed in critical systems. Distributions from subcritical systems are also modified, but the shape of the undersampled distributions is more similar to that of a fully sampled system. Undersampled supercritical systems can recover the general characteristics of the fully sampled version, provided that enough neurons are measured. Undersampling in two-dimensional and small-world networks leads to similar effects, while the random network is insensitive to sampling density due to the lack of a well-defined neighborhood. We conjecture that neuronal avalanches recorded from local field potentials avoid undersampling effects due to the nature of this signal, but the same does not hold for spike avalanches. We conclude that undersampled branching-process-like models in these topologies fail to reproduce the statistics of spike avalanches.

Critical behavior in the site-diluted three-dimensional three-state Potts model

We have studied numerically the effect of quenched site dilution on a weak first-order phase transition in three dimensions. We have simulated the site diluted three-states Potts model studying in detail the secondorder region of its phase diagram. We have found that the n exponent is compatible with the one of the three-dimensional diluted Ising model, whereas the h exponent is definitely different.

Molecular Variations In Aromatic Cosolutes: Critical Role In The Rheology Of Cationic Wormlike Micelles.

Wormlike micelles formed by the addition to cetyltrimethylammonium bromide (CTAB) of a range of aromatic cosolutes with small molecular variations in their structure were systematically studied. Phenol and derivatives of benzoate and cinnamate were used, and the resulting mixtures were studied by oscillatory, steady-shear rheology, and the microstructure was probed by small-angle neutron scattering. The lengthening of the micelles and their entanglement result in remarkable viscoelastic properties, making rheology a useful tool to assess the effect of structural variations of the cosolutes on wormlike micelle formation. For a fixed concentration of CTAB and cosolute (200 mmol L(-1)), the relaxation time decreases in the following order: phenol > cinnamate> o-hydroxycinnamate > salicylate > o-methoxycinnamate > benzoate > o-methoxybenzoate. The variations in viscoelastic response are rationalized by using Mulliken population analysis to map out the electronic density of the cosolutes and quantify the barrier to rotation of specific groups on the aromatics. We find that the ability of the group attached to the aromatic ring to rotate is crucial in determining the packing of the cosolute at the micellar interface and thus critically impacts the micellar growth and, in turn, the rheological response. These results enable us for the first time to propose design rules for the self-assembly of the surfactants and cosolutes resulting in the formation of wormlike micelles with the cationic surfactant CTAB.

[recommendations For Physical Exercise Practice During Pregnancy: A Critical Review].

Physical exercise is recommended for all healthy pregnant women. Regular practice of exercises during pregnancy can provide many physical and psychological benefits, with no evidence of adverse outcomes for the fetus or the newborn when exercise is performed at mild to moderate intensity. However, few pregnant women engage in this practice and many still have fears and doubts about the safety of exercise. The objective of the present study was to inform the professionals who provide care for Brazilian pregnant women about the current recommendations regarding physical exercise during pregnancy based on the best scientific evidence available. In view of the perception that few systematic models are available about this topic and after performing several studies in this specific area, we assembled practical information of interest to both the professionals and the pregnant women. We also provide recommendations about the indications, contraindications, modalities (aerobics, resistance training, stretching and pelvic floor training), frequency, intensity and duration indicated for each gestational trimester. The review addresses physical exercise recommendation both for low risk pregnant women and for special populations, such as athletes and obese, hypertensive and diabetic subjects. The advantages of an active and healthy lifestyle should be always reinforced during and after gestation since pregnancy is an appropriate period to introduce new habits because pregnant women are usually more motivated to adhere to recommendations. Thus, routine exams, frequent returns and supervision are recommended in order to provide new guidelines that will have long-term beneficial effects for both mother and child.

Chronicity Factors Of Temporomandibular Disorders: A Critical Review Of The Literature.

Facial pain often persists long after any identifiable organic pathology has healed. Moreover, in a subgroup of patients with temporomandibular disorder (TMD), no treatment is effective. Knowledge of factors associated with persistent pain in TMD could help identify personalized treatment approaches. Therefore, we conducted a critical review of the literature for the period from January 2000 to December 2013 to identify factors related to TMD development and persistence. The literature findings showed that chronic TMD is marked by psychological distress (somatization and depression, affective distress, fear of pain, fear of movement, and catastrophizing) and characteristics of pain amplification (hyperalgesia and allodynia). Furthermore, these factors seem to interact in TMD development. In addition, our review demonstrates that upregulation of the serotonergic pathway, sleep problems, and gene polymorphisms influence the chronicity of TMD. We conclude that psychological distress and pain amplification contribute to chronic TMD development, and that interactions among these factors complicate pain management. These findings emphasize the importance of multidisciplinary assistance in TMD treatment.