Transition from normal to ballistic diffusion in a one-dimensional impact system

We characterize a transition from normal to ballistic diffusion in a bouncing ball dynamics. The system is composed of a particle, or an ensemble of non-interacting particles, experiencing elastic collisions with a heavy and periodically moving wall under the influence of a constant gravitational field. The dynamics lead to a mixed phase space where chaotic orbits have a free path to move along the velocity axis, presenting a normal diffusion behavior. Depending on the control parameter, one can observe the presence of featured resonances, known as accelerator modes, that lead to a ballistic growth of velocity. Through statistical and numerical analysis of the velocity of the particle, we are able to characterize a transition between the two regimes, where transport properties were used to characterize the scenario of the ballistic regime. Also, in an analysis of the probability of an orbit to reach an accelerator mode as a function of the velocity, we observe a competition between the normal and ballistic transport in the mid range velocity.Comment: To appear in Physical Review E, 201

Stickiness in a bouncer model: A slowing mechanism for Fermi acceleration

Some phase space transport properties for a conservative bouncer model are studied. The dynamics of the model is described by using a two-dimensional measure preserving mapping for the variables velocity and time. The system is characterized by a control parameter $\epsilon$ and experiences a transition from integrable ($\epsilon=0$) to non integrable ($\epsilon\ne 0$). For small values of $\epsilon$, the phase space shows a mixed structure where periodic islands, chaotic seas and invariant tori coexist. As the parameter $\epsilon$ increases and reaches a critical value $\epsilon_c$ all invariant tori are destroyed and the chaotic sea spreads over the phase space leading the particle to diffuse in velocity and experience Fermi acceleration (unlimited energy growth). During the dynamics the particle can be temporarily trapped near periodic and stable regions. We use the finite time Lyapunov exponent to visualize this effect. The survival probability was used to obtain some of the transport properties in the phase space. For large $\epsilon$, the survival probability decays exponentially when it turns into a slower decay as the control parameter $\epsilon$ is reduced. The slower decay is related to trapping dynamics, slowing the Fermi Acceleration, i.e., unbounded growth of the velocityComment: 9 pages, 7 figure

Arabidopsis thaliana SPF1 and SPF2 are nuclear-located ULP2-like SUMO proteases that act downstream of SIZ1 in plant development

Post-translational modifiers such as the small ubiquitin-like modifier (SUMO) peptide act as fast and reversible protein regulators. Functional characterization of the sumoylation machinery has determined the key regulatory role that SUMO plays in plant development. Unlike components of the SUMO conjugation pathway, SUMO proteases (ULPs) are encoded by a relatively large gene family and are potential sources of specificity within the pathway. This study reports a thorough comparative genomics and phylogenetic characterization of plant ULPs, revealing the presence of one ULP1-like and three ULP2-like SUMO protease subgroups within plant genomes. As representatives of an under-studied subgroup, Arabidopsis SPF1 and SPF2 were subjected to functional characterization. Loss-of-function mutants implicated both proteins with vegetative growth, flowering time, and seed size and yield. Mutants constitutively accumulated SUMO conjugates, and yeast complementation assays associated these proteins with the function of ScUlp2 but not ScUlp1. Fluorescence imaging placed both proteins in the plant cell nucleoplasm. Transcriptomics analysis indicated strong regulatory involvement in secondary metabolism, cell wall remodelling, and nitrate assimilation. Furthermore, developmental defects of the spf1-1 spf2-2 (spf1/2) double-mutant opposed those of the major E3 ligase siz1 mutant and, most significantly, developmental and transcriptomic characterization of the siz1 spf1/2 triple-mutant placed SIZ1 as epistatic to SPF1 and SPF2.We thank Mark Hochstrasser (Department of Molecular Biophysics & Biochemistry, Yale University, New Haven, CT, USA) for kindly providing the ulp1-ts yeast mutant strain. This research was funded by FEDER (through COMPETE), and by Fundacao para a Ciencia e Tecnologia (FCT), within the scope of project SUMOdulator (FCOMP-01-0124-FEDER-028459 and PTDC/BIA-PLA/3850/2012). PHC was supported by FCT (SFRH/BD/44484/2008). HA and FF were supported by Norte Portugal Regional Operational Programme (NORTE 2020), under the PORTUGAL 2020 Partnership Agreement, through the European Regional Development Fund (FEDER) (NORTE-01-0145-FEDER-000007 and Norte-01-0145-FEDER-000008, respectively). The work was supported by FEDER through the COMPETE 2020-Operacional Programme for Competitiveness and Internationalisation (POCI), Portugal 2020, and by Portuguese funds through FCT, within the framework of projects 'Rede de Investigacao em Biodiversidade e Biologia Evolutiva' (POCI-01-0145-FEDER-006821) and 'Institute for Research and Innovation in Health Sciences' (POCI-01-0145-FEDER-007274). This research was also supported by a grant from the Spanish Ministerio de Ciencia y Tecnologia (AGL2016-75819-C2-1-R) and FEDER (PCQ, AGC, ERB)

Escape patterns of chaotic magnetic field lines in a tokamak with reversed magnetic shear and an ergodic limiter

The existence of a reversed magnetic shear in tokamaks improves the plasma confinement through the formation of internal transport barriers that reduce radial particle and heat transport. However, the transport poloidal profile is much influenced by the presence of chaotic magnetic field lines at the plasma edge caused by external perturbations. Contrary to many expectations, it has been observed that such a chaotic region does not uniformize heat and particle deposition on the inner tokamak wall. The deposition is characterized instead by structured patterns called magnetic footprints, here investigated for a nonmonotonic analytical plasma equilibrium perturbed by an ergodic limiter. The magnetic footprints appear due to the underlying mathematical skeleton of chaotic magnetic field lines determined by the manifold tangles. For the investigated edge safety factor ranges, these effects on the wall are associated with the field line stickiness and escape channels due to internal island chains near the flux surfaces. Comparisons between magnetic footprints and escape basins from different equilibrium and ergodic limiter characteristic parameters show that highly concentrated magnetic footprints can be avoided by properly choosing these parameters. (c) 2008 American Institute of Physics.FAPESP (Sao Paulo)Coordenacao de Aperfeicoamento de Pessoal de Nivel Superior (CAPES)CNPqFundacao Araucaria (Parana

Global ballistic acceleration in a bouncing-ball model

The ballistic increase for the velocity of a particle in a bouncing-ball model was investigated. The phenomenon is caused by accelerating structures in phase space known as accelerator modes. They lead to a regular and monotonic increase of the velocity. Here, both regular and ballistic Fermi acceleration coexist in the dynamics, leading the dynamics to two different growth regimes. We characterized deaccelerator modes in the dynamics, corresponding to unstable points in the antisymmetric position of the accelerator modes. In control parameter space, parameter sets for which these accelerations and deaccelerations constitute structures were obtained analytically. Since the mapping is not symplectic, we found fractal basins of influence for acceleration and deacceleration bounded by the stable and unstable manifolds, where the basins affect globally the average velocity of the system.Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq

Transport control in fusion plasmas by changing electric and magnetic field spatial profiles

For magnetically confined plasmas in tokamaks, we have numerically investigated how Lagrangian chaos at the plasma edge affects the plasma confinement. Initially, we have considered the chaotic motion of particles in an equilibrium electric field with a monotonic radial profile perturbed by drift waves. We have showed that an effective transport barrier may be created at the plasma edge by modifying the electric field radial profile. In the second place, we have obtained escape patterns and magnetic footprints of chaotic magnetic field lines in the region near a tokamak wall with resonant modes due to the action of an ergodic magnetic limiter. For monotonic plasma current density profiles we have obtained distributions of field line connections to the wall and line escape channels with the same spatial pattern as the magnetic footprints on the tokamak walls. (c) 2008 Elsevier B.V. All rights reserved