Fractional Hamiltonian analysis of higher order derivatives systems

The fractional Hamiltonian analysis of 1+1 dimensional field theory is investigated and the fractional Ostrogradski's formulation is obtained. The fractional path integral of both simple harmonic oscillator with an acceleration-squares part and a damped oscillator are analyzed. The classical results are obtained when fractional derivatives are replaced with the integer order derivatives.Comment: 13 page

Hamiltonian formulation of systems with linear velocities within Riemann-Liouville fractional derivatives

The link between the treatments of constrained systems with fractional derivatives by using both Hamiltonian and Lagrangian formulations is studied. It is shown that both treatments for systems with linear velocities are equivalent.Comment: 10 page

Lagrangian formulation of classical fields within Riemann-Liouville fractional derivatives

The classical fields with fractional derivatives are investigated by using the fractional Lagrangian formulation.The fractional Euler-Lagrange equations were obtained and two examples were studied.Comment: 9 page

Response of a catalytic reaction to periodic variation of the CO pressure: Increased CO_2 production and dynamic phase transition

We present a kinetic Monte Carlo study of the dynamical response of a Ziff-Gulari-Barshad model for CO oxidation with CO desorption to periodic variation of the CO presure. We use a square-wave periodic pressure variation with parameters that can be tuned to enhance the catalytic activity. We produce evidence that, below a critical value of the desorption rate, the driven system undergoes a dynamic phase transition between a CO_2 productive phase and a nonproductive one at a critical value of the period of the pressure oscillation. At the dynamic phase transition the period-averged CO_2 production rate is significantly increased and can be used as a dynamic order parameter. We perform a finite-size scaling analysis that indicates the existence of power-law singularities for the order parameter and its fluctuations, yielding estimated critical exponent ratios $\beta/\nu \approx 0.12$ and $\gamma/\nu \approx 1.77$. These exponent ratios, together with theoretical symmetry arguments and numerical data for the fourth-order cumulant associated with the transition, give reasonable support for the hypothesis that the observed nonequilibrium dynamic phase transition is in the same universality class as the two-dimensional equilibrium Ising model.Comment: 18 pages, 10 figures, accepted in Physical Review

Decay of metastable phases in a model for the catalytic oxidation of CO

We study by kinetic Monte Carlo simulations the dynamic behavior of a Ziff-Gulari-Barshad model with CO desorption for the reaction CO + O $\to$ CO$_2$ on a catalytic surface. Finite-size scaling analysis of the fluctuations and the fourth-order order-parameter cumulant show that below a critical CO desorption rate, the model exhibits a nonequilibrium first-order phase transition between low and high CO coverage phases. We calculate several points on the coexistence curve. We also measure the metastable lifetimes associated with the transition from the low CO coverage phase to the high CO coverage phase, and {\it vice versa}. Our results indicate that the transition process follows a mechanism very similar to the decay of metastable phases associated with {\it equilibrium} first-order phase transitions and can be described by the classic Kolmogorov-Johnson-Mehl-Avrami theory of phase transformation by nucleation and growth. In the present case, the desorption parameter plays the role of temperature, and the distance to the coexistence curve plays the role of an external field or supersaturation. We identify two distinct regimes, depending on whether the system is far from or close to the coexistence curve, in which the statistical properties and the system-size dependence of the lifetimes are different, corresponding to multidroplet or single-droplet decay, respectively. The crossover between the two regimes approaches the coexistence curve logarithmically with system size, analogous to the behavior of the crossover between multidroplet and single-droplet metastable decay near an equilibrium first-order phase transition.Comment: 27 pages, 22 figures, accepted by Physical Review

A study of the photometric variability of the peculiar magnetic white dwarf WD1953-011

We present and interpret simultaneous new photometric and spectroscopic observations of the peculiar magnetic white dwarf WD1953-011. The flux in the V-band filter and intensity of the Balmer spectral lines demonstrate variability with the rotation period of about 1.45 days. According to previous studies, this variability can be explained by the presence of a dark spot having a magnetic nature, analogous to a sunspot. Motivated by this idea, we examine possible physical relationships between the suggested dark spot and the strong-field magnetic structure (magnetic "spot", or "tube") recently identified on the surface of this star. Comparing the rotationally-modulated flux with the variable spectral observables related to the magnetic "spot" we establish their correlation, and therefore their physical relationship. Modeling the variable photometric flux assuming that it is associated with temperature variations in the stellar photosphere, we argue that the strong-field area and dark, low-temperature spot are comparable in size and located at the same latitudes, essentially overlapping each other with a possible slight longitudinal shift. In this paper we also present a new, improved value of the star's rotational period and constrain the characteristics of the thermal inhomogeneity over the degenerate's surface.Comment: accepted to the Ap

Fractional Dirac Bracket and Quantization for Constrained Systems

So far, it is not well known how to deal with dissipative systems. There are many paths of investigation in the literature and none of them present a systematic and general procedure to tackle the problem. On the other hand, it is well known that the fractional formalism is a powerful alternative when treating dissipative problems. In this paper we propose a detailed way of attacking the issue using fractional calculus to construct an extension of the Dirac brackets in order to carry out the quantization of nonconservative theories through the standard canonical way. We believe that using the extended Dirac bracket definition it will be possible to analyze more deeply gauge theories starting with second-class systems.Comment: Revtex 4.1. 9 pages, two-column. Final version to appear in Physical Review

Trends in method-specific suicide in Brazil from 2000 to 2017

Purpose: Understanding long-term patterns of suicide methods can inform public health policy and prevention strategies. In Brazil, firearm-related policies may be one salient target for suicide prevention. This study describes trends in method-specific suicide at the national and state-levels in Brazil, with a particular focus on firearm-related suicides. / Methods: Brazilian mortality data for suicide and undetermined intent among people aged 10 years and older between 2000 and 2017 were obtained from the National Mortality Information System. We examined national and state-level trends in age-standardised suicide rates for hanging, self-poisoning, firearms, jumping from a high place, other, and unspecified methods. We also compared total rates of mortality from suicide and undetermined intent over the period. Applying Joinpoint regression, we tested changes in trends of firearm-specific suicide rates. / Results: The total suicide rate increased between 2000 and 2017. Rates of hanging, self-poisoning by drugs or alcohol and jumping from a high place showed the largest increases, while firearm-specific suicide rates decreased over the study period. Trends in methods of suicide varied by sex and state. / Conclusion: It is of public health concern that suicide rates in Brazil have risen this millennium. Restricting access to firearms might be an effective approach for reducing firearm-specific suicides, especially in states where firearm availability remains particularly high. Treatment and management of substance misuse may also be an important target for suicide prevention policies. More work is needed to understand the causes of rising suicide rates in Brazil and to improve the mental health of the population

Association between homicide rates and suicide rates: a countrywide longitudinal analysis of 5507 Brazilian municipalities

Objective: To estimate the association between homicide and suicide rates in Brazilian municipalities over a period of 7 years. / Design: We conducted a longitudinal ecological study using annual mortality data from 5507 Brazilian municipalities between 2008 and 2014. Multivariable negative binomial regression models were used to examine the relationship between homicide and suicide rates. Robustness of results was explored using sensitivity analyses to examine the influence of data quality, population size, age and sex on the relationship between homicide and suicide rates. / Setting: A nationwide study of municipality-level data. / Participants: Mortality data and corresponding population estimates for municipal populations aged 10 years and older. / Primary and secondary outcome measures: Age-standardised suicide rates per 100 000. / Results: Municipal suicide rates were positively associated with municipal homicide rates; after adjusting for socioeconomic and demographic factors, a doubling of the homicide rate was associated with 22% increase in suicide rate (rate ratio=1.22, 95% CI: 1.13 to 1.33). A dose–response effect was observed with 4% increase in suicide rates at the third quintile, 9% at the fourth quintile and 12% at the highest quintile of homicide rates compared with the lowest quintile. The observed effect estimates were robust to sensitivity analyses. / Conclusions: Municipalities with higher homicide rates have higher suicide rates and the relationship between homicide and suicide rates in Brazil exists independently of many sociodemographic and socioeconomic factors. Our results are in line with the hypothesis that changes in homicide rates lead to changes in suicide rates, although a causal association cannot be established from this study. Suicide and homicide rates have increased in Brazil despite increased community mental health support and incarceration, respectively; therefore, new avenues for intervention are needed. The identification of a positive relationship between homicide and suicide rates suggests that population-based interventions to reduce homicide rates may also reduce suicide rates in Brazil