Multiple resonance compensation for betatron coupling and its equivalence with matrix method

Analyses of betatron coupling can be broadly divided into two categories: the matrix approach that decouples the single-turn matrix to reveal the normal modes and the hamiltonian approach that evaluates the coupling in terms of the action of resonances in perturbation theory. The latter is often regarded as being less exact but good for physical insight. The common opinion is that the correction of the two closest sum and difference resonances to the working point is sufficient to reduce the off-axis terms in the 4X4 single-turn matrix, but this is only partially true. The reason for this is explained, and a method is developed that sums to infinity all coupling resonances and, in this way, obtains results equivalent to the matrix approach. The two approaches is discussed with reference to the dynamic aperture. Finally, the extension of the summation method to resonances of all orders is outlined and the relative importance of a single resonance compared to all resonances of a given order is analytically described as a function of the working point.Comment: 22 pages, 10 figure

On the Impact of Fair Best Response Dynamics

In this work we completely characterize how the frequency with which each player participates in the game dynamics affects the possibility of reaching efficient states, i.e., states with an approximation ratio within a constant factor from the price of anarchy, within a polynomially bounded number of best responses. We focus on the well known class of congestion games and we show that, if each player is allowed to play at least once and at most $\beta$ times any $T$ best responses, states with approximation ratio $O(\beta)$ times the price of anarchy are reached after $T \lceil \log \log n \rceil$ best responses, and that such a bound is essentially tight also after exponentially many ones. One important consequence of our result is that the fairness among players is a necessary and sufficient condition for guaranteeing a fast convergence to efficient states. This answers the important question of the maximum order of $\beta$ needed to fast obtain efficient states, left open by [9,10] and [3], in which fast convergence for constant $\beta$ and very slow convergence for $\beta=O(n)$ have been shown, respectively. Finally, we show that the structure of the game implicitly affects its performances. In particular, we show that in the symmetric setting, in which all players share the same set of strategies, the game always converges to an efficient state after a polynomial number of best responses, regardless of the frequency each player moves with

Pion Generalized Parton Distributions within a fully covariant constituent quark model

We extend the investigation of the Generalized Parton Distribution for a charged pion within a fully covariant constituent quark model, in two respects: (i) calculating the tensor distribution and (ii) adding the treatment of the evolution, needed for achieving a meaningful comparison with both the experimental parton distribution and the lattice evaluation of the so-called generalized form factors. Distinct features of our phenomenological covariant quark model are: (i) a 4D Ansatz for the pion Bethe-Salpeter amplitude, to be used in the Mandelstam formula for matrix elements of the relevant current operators, and (ii) only two parameters, namely a quark mass assumed to hold $m_q=~220$ MeV and a free parameter fixed through the value of the pion decay constant. The possibility of increasing the dynamical content of our covariant constituent quark model is briefly discussed in the context of the Nakanishi integral representation of the Bethe-Salpeter amplitude.Comment: Pages 20, figure 11 and table 8. Minor changes. To be published in EPJ

Chaotic dynamics in a storage-ring Free Electron Laser

The temporal dynamics of a storage-ring Free Electron Laser is here investigated with particular attention to the case in which an external modulation is applied to the laser-electron beam detuning. The system is shown to produce bifurcations, multi-furcations as well as chaotic regimes. The peculiarities of this phenomenon with respect to the analogous behavior displayed by conventional laser sources are pointed out. Theoretical results, obtained by means of a phenomenological model reproducing the evolution of the main statistical parameters of the system, are shown to be in a good agreement with experiments carried out on the Super-ACO Free Electron Laser.Comment: submitted to Europ Phys. Journ.

Can a microscopic stochastic model explain the emergence of pain cycles in patients?

A stochastic model is here introduced to investigate the molecular mechanisms which trigger the perception of pain. The action of analgesic drug compounds is discussed in a dynamical context, where the competition with inactive species is explicitly accounted for. Finite size effects inevitably perturb the mean-field dynamics: Oscillations in the amount of bound receptors spontaneously manifest, driven by the noise which is intrinsic to the system under scrutiny. These effects are investigated both numerically, via stochastic simulations and analytically, through a large-size expansion. The claim that our findings could provide a consistent interpretative framework to explain the emergence of cyclic behaviors in response to analgesic treatments, is substantiated.Comment: J. Stat. Mech. (Proceedings UPON2008

Resonance families and their action on betatron motion

The present paper takes one step beyond the single-resonance theory for betatron motion by summing all the members of a given resonance family and expressing the joint influence in a single driving term. As a demonstration and confirmation of this work, the family driving terms are used to derive the classic closed-orbit and betatron-modulation equations of Courant and Snyder. A more serious demonstration is made by applying the family driving terms to the compensation of linear coupling and showing how numerical matrix-based and resonance compensation schemes are related. In a final phase, the Hénon map is used to compare the efficiency of different coupling compensation schemes with respect to dynamic aperture

Stochastic Turing Patterns on a Network

The process of stochastic Turing instability on a network is discussed for a specific case study, the stochastic Brusselator model. The system is shown to spontaneously differentiate into activator-rich and activator-poor nodes, outside the region of parameters classically deputed to the deterministic Turing instability. This phenomenon, as revealed by direct stochastic simulations, is explained analytically, and eventually traced back to the finite size corrections stemming from the inherent graininess of the scrutinized medium.Comment: The movies referred to in the paper are provided upon request. Please send your requests to Duccio Fanelli ([email protected]) or Francesca Di Patti ([email protected]

Non-Gaussian fluctuations in stochastic models with absorbing barriers

The dynamics of a one-dimensional stochastic model is studied in presence of an absorbing boundary. The distribution of fluctuations is analytically characterized within the generalized van Kampen expansion, accounting for higher order corrections beyond the conventional Gaussian approximation. The theory is shown to successfully capture the non Gaussian traits of the sought distribution returning an excellent agreement with the simulations, for {\it all times} and arbitrarily {\it close} to the absorbing barrier. At large times, a compact analytical solution for the distribution of fluctuations is also obtained, bridging the gap with previous investigations, within the van Kampen picture and without resorting to alternative strategies, as elsewhere hypothesized.Comment: 2 figures, submitted to Phys. Rev. Let

parameters identification for scroll expander semi empirical model by using genetic algorithm

Abstract In this paper a small Organic Rankine Cycle (ORC) plant was tested under different operating conditions and by using refrigerants (R245fa) as working fluids. In particular, attention was posed towards the scroll expander of the power plant in order to identify experimental parameters to use in its predictive semi-empirical model. Experimental results obtained by imposing different operating conditions at the expander inlet section (i.e. temperature, pressure, mass flow rate) and different temperature at the condensation section, were used to validate the mathematical model. An in-house code (MatLab®/Scilab® based) using CoolProp® library for the accurate evaluation of fluid properties, was optimized by using a genetic algorithm implemented in modeFrontier® software. Thus, the validated model was used in predictive mode to evaluate the machine performances