An application of pp-adic integration to the dynamics of a birational transformation preserving a fibration

Let $f\colon X \dashrightarrow X$ be a birational transformation of a projective manifold $X$ whose Kodaira dimension $\kappa(X)$ is non-negative. We show that, if there exist a meromorphic fibration $\pi \colon X\dashrightarrow B$ and a pseudo-automorphism $f_B\colon B\dashrightarrow B$ which preserves a big line bundle $L\in Pic(B)$ and such that $f_B\circ \pi=\pi\circ f$, then $f_B$ has finite order. As a corollary we show that, for projective irreducible symplectic manifolds of type $K3^{[n]}$ or generalized Kummer, the first dynamical degree characterizes the birational transformations admitting a Zariski-dense orbit

On the primitivity of birational transformations of irreducible symplectic manifolds

Let $f\colon X\dashrightarrow X$ be a bimeromorphic transformation of a complex irreducible symplectic manifold $X$. Some important dynamical properties of $f$ are encoded by the induced linear automorphism $f^*$ of $H^2(X,\mathbb Z)$. Our main result is that a bimeromorphic transformation such that $f^*$ has at least one eigenvalue with modulus $>1$ doesn't admit any invariant fibration (in particular its generic orbit is Zariski-dense)

Low-dimensional modelling of flame dynamics in heated microchannels

This paper presents simulations of stoichiometric methane/air premixed flames into a microchannel at atmospheric pressure. These simulations result from numerical resolutions of reduced-order models. Indeed, combustion control into microchannels would be allowed by fast simulations that in turn enable real-time adjustments of the device's parameters. Former experimental studies reported the occurrence of a Flame Repetitive Extinction/Ignition (FREI) phenomenon provided that a temperature gradient is sustained at the channel's walls. Conducting unsteady one-dimensional simulations including complex chemistry, a late numerical study tried to explain the occurrence of this phenomenon. The present study therefore explores low-dimensional models that potentially reproduce the FREI phenomenon. Provided a calibration of some empirical constants, an unsteady two-dimensional model including one-step chemical reaction is shown to decently reproduce the FREI regime all along the range of mixture flow rates investigated by the experimental studies. Complementing the aforementioned numerical study, furthermore, when the channel's diameter is varied, the two-dimensional model unveils an unstable regime that a one-dimensional model cannot capture. As two-dimensional hydrodynamics appears to play a key role into the flame's dynamics, therefore the heat rate released by the microcombustor, one-dimensional models are not believed to deliver an adequate strategy of combustion control into such microchannels.Comment: 37 pages, 12 figure

Reaction spreading on percolating clusters

Reaction-diffusion processes in two-dimensional percolating structures are investigated. Two different problems are addressed: reaction spreading on a percolating cluster and front propagation through a percolating channel. For reaction spreading, numerical data and analytical estimates show a power-law behavior of the reaction product as M(t) \sim t^dl, where dl is the connectivity dimension. In a percolating channel, a statistically stationary traveling wave develops. The speed and the width of the traveling wave are numerically computed. While the front speed is a low-fluctuating quantity and its behavior can be understood using a simple theoretical argument, the front width is a high-fluctuating quantity showing a power-law behavior as a function of the size of the channelComment: 7 pages, 8 figure

Metabolic Algorithm with Time-varying Reaction Maps

A symbolic-based approach to modelling biochemical processes and cellular dynamics is likely to turn useful in computational biology, where attempts to represent the cell as a huge, complex dynamic system must trade with the linguistic nature of the DNA and the individual behavior of the organelles living within. The early version of the metabolic algorithm gave a first answer to the problem of representing oscillatory biological phenomena, so far being treated with traditional (differential) mathematical tools, in terms of rewriting systems. We are now working on a further version of this algorithm, in which the rule application is tuned by reaction maps depending on the specific phenomenon under consideration. Successful simulations of the Brusselator, the Lotka-Volterra population dynamics and the PKC activation foster potential applications of the algorithm in systems biology

Modelling of combustion and knock onset risk in a high-performance turbulent jet ignition engine

The reduction of CO2 emissions, and hence of fuel consumption, is currently a key driver for the development of innovative SI engines for passenger car applications. In recent years, motorsport technical regulations in the highest categories have seen the introduction of limits concerning the fuel flow rate and the total amount of fuel per race, thus driving engine development toward further reduction of specific fuel consumption. Among the different techniques that can be shared between conventional and high-performance SI engines, turbocharging, compression ratio increase and Turbulent Jet Ignition (TJI) have shown a significant potential for fuel consumption reduction. The combination of turbocharging and compression ratio increase, however, can promote the onset of knocking combustion, with detrimental effects on engine’s efficiency and durability. Additionally, engines equipped with TJI systems show unusual combustion development and knock onset. In this study a methodology for the 3D-CFD modelling of combustion and knock onset risk was developed for a high-performance turbocharged engine featuring a passive TJI system. First, a comprehensive numerical study was carried out in a commercially available software, CONVERGE 2.4, in order to develop a 3D-CFD model able to reproduce the available experimental data. The resulting 3D-CFD model was then validated on different working conditions featuring different spark advances. Lastly, a methodology for the assessment of knock onset risk was developed, which led to the definition of two novel knock-risk indexes based on the progress of chemical reactions within the combustion chamber. The proposed knock-risk indexes showed good agreement with the experimental data

GRB 980425, SN1998bw and the EMBH model

The EMBH model, previously developed using GRB 991216 as a prototype, is here applied to GRB 980425. We fit the luminosity observed in the 40-700 keV, 2-26 keV and 2-10 keV bands by the BeppoSAX satellite. In addition we present a novel scenario in which the supernova SN1998bw is the outcome of an ``induced gravitational collapse'' triggered by GRB 980425, in agreement with the GRB-Supernova Time Sequence (GSTS) paradigm (Ruffini et al. 2001c). A further outcome of this astrophysically exceptional sequence of events is the formation of a young neutron star generated by the SN1998bw event. A coordinated observational activity is recommended to further enlighten the underlying scenario of this most unique astrophysical system.Comment: 10 pages, 3 figures, in the Proceedings of the 34th COSPAR scientific assembly, Elsevier. Fixed some typos in this new versio