Model checking probabilistic and stochastic extensions of the pi-calculus

We present an implementation of model checking for probabilistic and stochastic extensions of the pi-calculus, a process algebra which supports modelling of concurrency and mobility. Formal verification techniques for such extensions have clear applications in several domains, including mobile ad-hoc network protocols, probabilistic security protocols and biological pathways. Despite this, no implementation of automated verification exists. Building upon the pi-calculus model checker MMC, we first show an automated procedure for constructing the underlying semantic model of a probabilistic or stochastic pi-calculus process. This can then be verified using existing probabilistic model checkers such as PRISM. Secondly, we demonstrate how for processes of a specific structure a more efficient, compositional approach is applicable, which uses our extension of MMC on each parallel component of the system and then translates the results into a high-level modular description for the PRISM tool. The feasibility of our techniques is demonstrated through a number of case studies from the pi-calculus literature

The Cauchy problem for the Pavlov equation

Commutation of multidimensional vector fields leads to integrable nonlinear dispersionless PDEs arising in various problems of mathematical physics and intensively studied in the recent literature. This report is aiming to solve the scattering and inverse scattering problem for integrable dispersionless PDEs, recently introduced just at a formal level, concentrating on the prototypical example of the Pavlov equation, and to justify an existence theorem for global bounded solutions of the associated Cauchy problem with small data.Comment: In the new version the analytical technique was essentially revised. The previous version contained a wrong statement about the solvability of the inverse problem for large data. This problem remains ope

Modelling Time-varying Dark Energy with Constraints from Latest Observations

We introduce a set of two-parameter models for the dark energy equation of state (EOS) $w(z)$ to investigate time-varying dark energy. The models are classified into two types according to their boundary behaviors at the redshift $z=(0,\infty)$ and their local extremum properties. A joint analysis based on four observations (SNe + BAO + CMB + $H_0$) is carried out to constrain all the models. It is shown that all models get almost the same $\chi^2_{min}\simeq 469$ and the cosmological parameters $(\Omega_M, h, \Omega_bh^2)$ with the best-fit results $(0.28, 0.70, 2.24)$, although the constraint results on two parameters $(w_0, w_1)$ and the allowed regions for the EOS $w(z)$ are sensitive to different models and a given extra model parameter. For three of Type I models which have similar functional behaviors with the so-called CPL model, the constrained two parameters $w_0$ and $w_1$ have negative correlation and are compatible with the ones in CPL model, and the allowed regions of $w(z)$ get a narrow node at $z\sim 0.2$. The best-fit results from the most stringent constraints in Model Ia give $(w_0,w_1) = (-0.96^{+0.26}_{-0.21}, -0.12^{+0.61}_{-0.89})$ which may compare with the best-fit results $(w_0,w_1) = (-0.97^{+0.22}_{-0.18}, -0.15^{+0.85}_{-1.33})$ in the CPL model. For four of Type II models which have logarithmic function forms and an extremum point, the allowed regions of $w(z)$ are found to be sensitive to different models and a given extra parameter. It is interesting to obtain two models in which two parameters $w_0$ and $w_1$ are strongly correlative and appropriately reduced to one parameter by a linear relation $w_1 \propto (1+w_0)$.Comment: 30 pages, 7 figure

Robust active magnetic dearing control using stabilizing dynamical compensators

The robust control of active magnetic bearings, based on a linearised interval model, is considered. Through robust stability analysis, all the first-order robust stabilizing dynamical compensators for the interval system are obtained. Disturbance attenuation and minimum control effort are also addressed. The approach is applied to a high-speed flywheel supported by two active and two passive magnetic bearings. Simulation and experimental results both show that it is simple, effective, and robust