Dynamical changes from harmonic vibrations of a limited power supply driving a Duffing oscillator

The harmonic oscillations of a Duffing oscillator driven by a limited power supply are investigated as a function of the alternative strength of the rotor. The semi-trivial and non-trivial solutions are derived. We examine the stability of these solutions and then explore the complex behaviors associated with the bifurcations sequences. Interestingly, a 3D diagram provides a global view of the effects of alternate strength on the appearance of chaos and hyperchaos on the system.

Generalized Metropolis dynamics with a generalized master equation: An approach for time-independent and time-dependent Monte Carlo simulations of generalized spin systems

The extension of Boltzmann-Gibbs thermostatistics, proposed by Tsallis, introduces an additional parameter q to the inverse temperature beta. Here, we show that a previously introduced generalized Metropolis dynamics to evolve spin models is not local and does not obey the detailed energy balance. In this dynamics, locality is only retrieved for q = 1, which corresponds to the standard Metropolis algorithm. Nonlocality implies very time-consuming computer calculations, since the energy of the whole system must be reevaluated when a single spin is flipped. To circumvent this costly calculation, we propose a generalized master equation, which gives rise to a local generalized Metropolis dynamics that obeys the detailed energy balance. To compare the different critical values obtained with other generalized dynamics, we perform Monte Carlo simulations in equilibrium for the Ising model. By using short-time nonequilibrium numerical simulations, we also calculate for this model the critical temperature and the static and dynamical critical exponents as functions of q. Even for q not equal 1, we show that suitable time-evolving power laws can be found for each initial condition. Our numerical experiments corroborate the literature results when we use nonlocal dynamics, showing that short-time parameter determination works also in this case. However, the dynamics governed by the new master equation leads to different results for critical temperatures and also the critical exponents affecting universality classes. We further propose a simple algorithm to optimize modeling the time evolution with a power law, considering in a log-log plot two successive refinements.

Stopping power and depth dose profile of H+ and He+ ion beams in hydroxyapatite thin films.

Hadron therapy is a promising technique to treat deep-seated tumors. For an accurate treatment planning, the energy deposition in the soft and hard human tissue must be well known. Water has been usually employed as a phantom of soft tissues, but other biomaterials, such as hydroxyapatite (HAp), used as bone substitute, are also relevant as a phantom for hard tissues. The stopping power of HAp for H+ and He+ beams has been studied experimentally and theoretically. The measurements have been done using the Rutherford backscattering technique in an energy range of 450-2000 keV for H+ and of 400-5000 keV for He+ projectiles. The theoretical calculations are based in the dielectric formulation together with the MELF-GOS (Mermin Energy-Loss Function – Generalized Oscillator Strengths) method [1] to describe the target excitation spectrum. A quite good agreement between the experimental data and the theoretical results has been found. The depth dose profile of H+ and He+ ion beams in HAp has been simulated by the SEICS (Simulation of Energetic Ions and Clusters through Solids) code [2], which incorporates the electronic stopping force due to the energy loss by collisions with the target electrons, including fluctuations due to the energy-loss straggling, the multiple elastic scattering with the target nuclei, with their corresponding nuclear energy loss, and the dynamical charge-exchange processes in the projectile charge state. The energy deposition by H+ and He+ as a function of the depth are compared, at several projectile energies, for HAp and liquid water, showing important differences.