Traveling waves in high energy QCD

Saturation is expected to occur when a high density of partons (mainly gluons)- or equivalently strong fields in Quantum Chromodynamics (QCD) - is realized in the weak coupling regime. A way to reach saturation is through the high-energy evolution of an extended target probed at a fixed hard scale. In this case, the transition to saturation is expected to occur from nonlinear perturbative QCD dynamics. We discuss this approach to saturation, which is mathematically characterized by the appearance of traveling wave patterns in a suitable kinematical representation. A short review on traveling waves in high energy QCD and a first evidence of this phenomenon in deep-inelastic proton scattering are presented.Comment: 10 pages, 5 figures, talk given at the XXXVth International Symposium on Multiparticle Dynamics (ISMD05), Kromeriz, Czech Republic, August 9-15 200

The language of certain conflicts of a nondeterministic process

The language of certain conflicts is the most general set of behaviours of a nondeterministic process, which certainly lead to a livelock or deadlock when accepted by another process running in parallel. It is of great use in model checking to detect livelocks or deadlocks in very large systems, and in process-algebra to obtain abstractions preserving livelock and deadlock. Unfortunately, the language of certain conflicts is difficult to compute and has only been approximated in previous work. This paper presents an effective algorithm to calculate the language of certain conflicts for any given nondeterministic finite-state process and discusses its properties. The algorithm is shown to be correct and of exponential complexity

Dynamical entropy of dense QCD states

We discuss dense states of QCD matter formed in high-energy hadronic and heavy-ion collisions from the point of view of statistical physics of non-equilibrium processes. For this sake, we first propose a formulation of the dynamical entropy of dense QCD states in the "saturation regime" leading to a color glass condensate (CGC). The statistical physics description amounts to describe the modification of the color correlation length with energy as a compression process for which non equilibrium thermodynamic properties are applicable. We derive an expression of the dynamical entropy in terms of the rapidity evolution of the unintegrated gluon distributions in the colliding nuclei, verifying suitable positivity and irreversibility properties. We extend this approach to the initial pre-equilibrium (glasma) state of an heavy-ion collision. It allows for a definition of the initial entropy before the evolution towards the hydrodynamic regime as a function of the glasma correlation length and an overlap parameter characterizing the low-momentum spectrum of the glasma state. This initial entropy, by extension to the N=4 SYM theory, is then matched as the key input parameter to the strong coupling evaluation of thermalization towards the hydrodynamic regime based on the AdS/CFT correspondence. It thus allows to cast a bridge between the weak and strong coupling phases of an heavy-ion reaction.Comment: Version mildly updated to match publication. Adding a discussion of the k_T factorization formula. Results and conclusions unchange

Star formation efficiency in turbulent clouds

Here we present a simple, but nevertheless, instructive model for the star formation efficiency in turbulent molecular clouds. The model is based on the assumption of log-normal density distribution which reflects the turbulent nature of the interstellar medium (ISM). Together with the number count of cloud cores, which follows a Salpeter-like core mass function (CMF), and the minimum mass for the collapse of individual cloud cores, given by the local Jeans mass, we are able to derive the SFE for clouds as a function of their Jeans masses. We find a very generic power-law, SFE \propto (M_cloud/M_J)^{-0.26} and a maximum SFE_max \sim 1/3 for the Salpeter case. This result is independent of the turbulent Mach number but fairly sensitive to variations of the CMF.Comment: submitted to A&A, comments are welcom

On the set of certain conflicts of a given language

Two concurrent processes are said to be in conflict if they can get trapped in a situation where they both are waiting or running endlessly, forever unable to complete their common task. In the design of reactive systems, this is a common fault which can be very subtle and hard to detect. This paper studies conflicts in more detail and characterises the most general set of behaviours of a process which certainly leads to a conflict when accepted by another process running in parallel. It shows how this set of certain conflicts can be used to simplify the automatic detection of conflicts and thus the verification of reactive systems

Generalised Nonblocking

This paper studies the nonblocking check used in supervisory control of discrete event systems and its limitations. Different examples with different liveness requirements are discussed. It is shown that the standard nonblocking check can be used to specify most requirements of interest, but that it lacks expressive power in a few cases. A generalised nonblocking check is proposed to overcome the weakness, and its relationship to standard nonblocking is explored. Results suggest that generalised nonblocking, while having the same useful properties with respect to synthesis and compositional verification, can provide for more concise problem representations in some cases

Compositional nonblocking verificationusing generalised nonblocking abstractions

This paper proposes a method for compositional verification of the standard and generalized nonblocking properties of large discrete event systems. The method is efficient as it avoids the explicit construction of the complete state space by considering and simplifying individual subsystems before they are composed further. Simplification is done using a set of abstraction rules preserving generalized nonblocking equivalence, which are shown to be correct and computationally feasible. Experimental results demonstrate the suitability of the method to verify several large-scale discrete event systems models both for standard and generalized nonblocking

Modular control-loop detection

This paper presents an efficient algorithm to detect control-loops in large finite-state systems. The proposed algorithm exploits the modular structure present in many models of practical relevance, and often successfully avoids the explicit synchronous composition of subsystems and thereby the state explosion problem. Experimental results show that the method can be used to verify industrial applications of considerable complexity