QCD at Zero Baryon Density and the Polyakov Loop Paradox

We compare the grand canonical partition function at fixed chemical potential mu with the canonical partition function at fixed baryon number B, formally and by numerical simulations at mu=0 and B=0 with four flavours of staggered quarks. We verify that the free energy densities are equal in the thermodynamic limit, and show that they can be well described by the hadron resonance gas at T T_c. Small differences between the two ensembles, for thermodynamic observables characterising the deconfinement phase transition, vanish with increasing lattice size. These differences are solely caused by contributions of non-zero baryon density sectors, which are exponentially suppressed with increasing volume. The Polyakov loop shows a different behaviour: for all temperatures and volumes, its expectation value is exactly zero in the canonical formulation, whereas it is always non-zero in the commonly used grand-canonical formulation. We clarify this paradoxical difference, and show that the non-vanishing Polyakov loop expectation value is due to contributions of non-zero triality states, which are not physical, because they give zero contribution to the partition function.Comment: 21 pages, 7 figure

A probabilistic model for information and sensor validation

This paper develops a new theory and model for information and sensor validation. The model represents relationships between variables using Bayesian networks and utilizes probabilistic propagation to estimate the expected values of variables. If the estimated value of a variable differs from the actual value, an apparent fault is detected. The fault is only apparent since it may be that the estimated value is itself based on faulty data. The theory extends our understanding of when it is possible to isolate real faults from potential faults and supports the development of an algorithm that is capable of isolating real faults without deferring the problem to the use of expert provided domain-specific rules. To enable practical adoption for real-time processes, an any time version of the algorithm is developed, that, unlike most other algorithms, is capable of returning improving assessments of the validity of the sensors as it accumulates more evidence with time. The developed model is tested by applying it to the validation of temperature sensors during the start-up phase of a gas turbine when conditions are not stable; a problem that is known to be challenging. The paper concludes with a discussion of the practical applicability and scalability of the model

Symmetry-preserving Observers

This paper presents three non-linear observers on three examples of engineering interest: a chemical reactor, a non-holonomic car, and an inertial navigation system. For each example, the design is based on physical symmetries. This motivates the theoretical development of invariant observers, i.e, symmetry-preserving observers. We consider an observer to consist in a copy of the system equation and a correction term, and we give a constructive method (based on the Cartan moving-frame method) to find all the symmetry-preserving correction terms. They rely on an invariant frame (a classical notion) and on an invariant output-error, a less standard notion precisely defined here. For each example, the convergence analysis relies also on symmetries consideration with a key use of invariant state-errors. For the non-holonomic car and the inertial navigation system, the invariant state-errors are shown to obey an autonomous differential equation independent of the system trajectory. This allows us to prove convergence, with almost global stability for the non-holonomic car and with semi-global stability for the inertial navigation system. Simulations including noise and bias show the practical interest of such invariant asymptotic observers for the inertial navigation system.Comment: To be published in IEEE Automatic Contro

Equilibrium route to colloidal gellation: mixtures of hard sphere-like colloids

The binodals and the non-ergodicity lines of a binary mixture of hard sphere-like particles with large size ratio are computed for studying the interplay between dynamic arrest and phase separation in depletion-driven colloidal mixtures. Contrarily to the case of hard core plus short range effective attraction, physical gellation without competition with the fluid-phase separation can occur in such mixtures. This behavior due to the oscillations in the depletion potential should concern all simple mixtures with non-ideal depletant, justifying further studies of their dynamic properties

Quantal Extension of Mean-Field Dynamics

A method is presented for numerical implementation of the extended TDHF theory in which two-body correlations beyond the mean-field approximation are incorporated in the form of a quantal collision term. The method is tested in a model problem in which the exact solution can be obtained numerically. Whereas the usual TDHF fails to reproduce the long time evolution, a very good agreement is found between the extended TDHF and the exact solution.Comment: 22 Latex pages including 7 figure

Cataclysmic Variables with Evolved Secondaries and the Progenitors of AM CVn Stars

We present the results of a systematic study of cataclysmic variables (CVs) and related systems, combining detailed binary-population synthesis (BPS) models with a grid of 120 binary evolution sequences calculated with a Henyey-type stellar evolution code. In these sequences, we used 3 masses for the white dwarf (0.6, 0.8, 1.0 Msun) and seven masses for the donor star in the range of 0.6-1.4 Msun. The shortest orbital periods were chosen to have initially unevolved secondaries, and the longest orbital period for each secondary mass was taken to be just longer than the bifurcation period (16 - 22 hr), beyond which systems evolve towards long orbital periods. These calculations show that systems which start with evolved secondaries near the end or just after their main-sequence phase become ultra-compact systems with periods as short as 7 min. These systems are excellent candidates for AM CVn stars. Using a standard BPS code, we show how the properties of CVs at the beginning of mass transfer depend on the efficiency for common-envelope (CE) ejection and the efficiency of magnetic braking. In our standard model, where CE ejection is efficient, some 10 per cent of all CVs have initially evolved secondaries (with a central hydrogen abundance X_c < 0.4) and ultimately become ultra-compact systems (implying a Galactic birthrate for AM CVn-like stars of 10^{-3} yr^{-1}). Almost all CVs with orbital periods longer than 5 hr are found to have initially evolved or relatively massive secondaries. We show that their distribution of effective temperatures is in good agreement with the distribution of spectral types obtained by Beuermann et al. (1998).Comment: 16 pages, 6 figures (Fig. 4 in reduced format). Submitted to MNRA

On the role of recombination in common-envelope ejections

The energy budget in common-envelope events (CEEs) is not well understood, with substantial uncertainty even over to what extent the recombination energy stored in ionised hydrogen and helium might be used to help envelope ejection. We investigate the reaction of a red-giant envelope to heating which mimics limiting cases of energy input provided by the orbital decay of a binary during a CEE, specifically during the post-plunge-in phase during which the spiral-in has been argued to occur on a time-scale longer than dynamical. We show that the outcome of such a CEE depends less on the total amount of energy by which the envelope is heated than on how rapidly the energy was transferred to the envelope and on where the envelope was heated. The envelope always becomes dynamically unstable before receiving net heat energy equal to the envelope's initial binding energy. We find two types of outcome, both of which likely lead to at least partial envelope ejection: "runaway" solutions in which the expansion of the radius becomes undeniably dynamical, and superficially "self-regulated" solutions, in which the expansion of the stellar radius stops but a significant fraction of the envelope becomes formally dynamically unstable. Almost the entire reservoir of initial helium recombination energy is used for envelope expansion. Hydrogen recombination is less energetically useful, but is nonetheless important for the development of the dynamical instabilities. However, this result requires the companion to have already plunged deep into the envelope; therefore this release of recombination energy does not help to explain wide post-common-envelope orbits.Comment: 17 pages, 10 figures, submitted to MNRAS. Comments are welcom