Logical Specification and Analysis of Fault Tolerant Systems through Partial Model Checking

This paper presents a framework for a logical characterisation of fault tolerance and its formal analysis based on partial model checking techniques. The framework requires a fault tolerant system to be modelled using a formal calculus, here the CCS process algebra. To this aim we propose a uniform modelling scheme in which to specify a formal model of the system, its failing behaviour and possibly its fault-recovering procedures. Once a formal model is provided into our scheme, fault tolerance - with respect to a given property - can be formalized as an equational µ-calculus formula. This formula expresses in a logic formalism, all the fault scenarios satisfying that fault tolerance property. Such a characterisation understands the analysis of fault tolerance as a form of analysis of open systems and thank to partial model checking strategies, it can be made independent on any particular fault assumption. Moreover this logical characterisation makes possible the fault-tolerance verification problem be expressed as a general µ-calculus validation problem, for solving which many theorem proof techniques and tools are available. We present several analysis methods showing the flexibility of our approach

Lattice computation of structure functions

Recent lattice calculations of hadron structure functions are described.Comment: Plenary talk presented at LATTICE96, LaTeX, 7 pages, 5 figures, espcrc2.sty and epsfig.sty include

A High-Statistics Lattice Calculation of λ1\lambda_1 and λ2\lambda_2 in the BB meson

We present a high-statistics lattice calculation of the kinetic energy $-\lambda_1/2 m_b$ of the heavy quark inside the $B$-meson and of the chromo-magnetic term $\lambda_2$, related to the $B^*$--$B$ mass splitting, performed in the HQET. Our results have been obtained from a numerical simulation based on 600 gauge field configurations generated at $\beta=6.0$, on a lattice volume $24^3 \times 40$ and using, for the meson correlators, the results obtained with the SW-Clover $O(a)$ improved lattice action for the light quarks. For the kinetic energy we found $-\lambda_1=\langle B \vert \bar h (i\vec{D})^{2} h \vert B \rangle /(2 M_B )=-(0.09 \pm 0.14)$~GeV$^2$, which is interesting for phenomenological applications. We also find $\lambda_2= 0.07 \pm 0.01$ GeV$^2$, corresponding to $M^2_{B^*}-M^2_B= 4 \lambda_2= 0.280 \pm 0.060$ GeV$^2$, which is about one half of the experimental value. The origin of the discrepancy with the experimental number needs to be clarified.Comment: 26 pages, latex, 5 figure

DEPENDENCE OF THE CURRENT RENORMALISATION CONSTANTS ON THE QUARK MASS

We study the behaviour of the vector and axial current renormalisation constants $Z_V$ and $Z_A$ as a function of the quark mass, $m_q$. We show that sizeable $O(am_q)$ and $O(g_0^2 a m_q)$ systematic effects are present in the Wilson and Clover cases respectively. We find that the prescription of Kronfeld, Lepage and Mackenzie for correcting these artefacts is not always successful.Comment: Contribution to Lattice'94, 3 pages PostScript, uuencoded compressed

Hermite Calculus

We develop a new method of umbral nature to treat blocks of Her mite and of Hermite like poly- nomials as independent algebraic quantities. The Calculus we propose allows the formulation of a number of ”practical rules” allowing significant simplific ations in computational problem

Dynamics of the modulation instability spectrum in optical fibers with oscillating dispersion

A simple analytical model is developed to analyze and explain the complex dynamics of the multi-peak modulation instability spectrum observed in dispersion oscillating optical fibers [M. Droques et al., 37, 4832-4834 Opt. Lett., (2012)]. We provide a simple expression for the local parametric gain which shows that each of the multiple spectral components grows thanks to a quasi-phase-matching mechanism due to the periodicity of the waveguide parameters, in good agreement with numerical simulations and experiments. This simplified model is also successfully used to tailor the multi-peak modulation instability spectrum shape. These theoretical predictions are confirmed by experiments.Comment: 18 pages, 6 figures. arXiv admin note: substantial text overlap with arXiv:1207.466

Finite-volume effects in the evaluation of the K_L - K_S mass difference

The RBC and UKQCD collaborations have recently proposed a procedure for computing the K_L-K_S mass difference. A necessary ingredient of this procedure is the calculation of the (non-exponential) finite-volume corrections relating the results obtained on a finite lattice to the physical values. This requires a significant extension of the techniques which were used to obtain the Lellouch-Luscher factor, which contains the finite-volume corrections in the evaluation of non-leptonic kaon decay amplitudes. We review the status of our study of this issue and, although a complete proof is still being developed, suggest the form of these corrections for general volumes and a strategy for taking the infinite-volume limit. The general result reduces to the known corrections in the special case when the volume is tuned so that there is a two-pion state degenerate with the kaon.Comment: Presented at the 31st International Symposium on Lattice Field Theory (Lattice 2013), July 29 - August 3 2013, Mainz Germany. To be published in the proceedings PoS(LATTICE 2013) 39

NNLO Unquenched Calculation of the b Quark Mass

By combining the first unquenched lattice computation of the B-meson binding energy and the two-loop contribution to the lattice HQET residual mass, we determine the (\bar{{MS}}) (b)-quark mass, (\bar{m}_{b}(\bar{m}_{b})). The inclusion of the two-loop corrections is essential to extract (\bar{m}_{b}(\bar{m}_{b})) with a precision of ({\cal O}(\Lambda^{2}_{QCD}/m_{b})), which is the uncertainty due to the renormalon singularities in the perturbative series of the residual mass. Our best estimate is (\bar{m}_{b}(\bar{m}_{b}) = (4.26 \pm 0.09) {\rm GeV}), where we have combined the different errors in quadrature. A detailed discussion of the systematic errors contributing to the final number is presented. Our results have been obtained on a sample of (60) lattices of size (24^{3}\times 40) at (\beta =5.6), using the Wilson action for light quarks and the lattice HQET for the (b) quark, at two values of the sea quark masses. The quark propagators have been computed using the unquenched links generated by the T(\chi)L Collaboration.Comment: 19 pages, 1 figur