In this paper we present solutions of evolution equations for inclusive distribution of gluons as produced by jet traversing quark-gluon plasma. We reformulate the original equations in such a form that virtual and unresolved-real emissions as well as unresolved collisions with medium are resummed in a Sudakov-type form factor. The resulting integral equations are then solved most efficiently with use of newly developed Markov Chain Monte Carlo algorithms implemented in a dedicated program called MINCAS. Their results for a gluon energy density are compared with an analytical solution and a differential numerical method. Some results for gluon transverse-momentum distributions are also presented. They exhibit interesting patterns not discussed so far in the literature, in particular a departure from the Gaussian behaviour -which does not happen in approximate analytical solutions.

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Purpose-The holistic numerical model based on cellular automata (CA) and Lattice Boltzmann methods (LBM) is being developed as part of an integrated modelling approach applied to study the interaction of different physical mechanisms in laser assisted additive layer manufacturing (ALM) of orthopaedic implants. Several physical events occuring in sequence or simultaneously are considered in the holistic model. They include a powder bed deposition, laser energy absorption and heating of the powder bed by the moving laser beam leading to powder melting or sintering, fluid flow in the melted pool, flow through partly or not melted material and solidification. Design/methodology/approach-The mentioned physical events are accompanied by heat transfer in solid and liquid phases including interface heat transfer at the boundaries. The sintering/melting model is being developed using LBM as an independent numerical method for hydrodynamic simulations originated from lattice-gas cellular automata (LGCA). It is going to be coupled with the CA based model of powder bed generation. Findings-The entire laser assisted ALM process has been analised and divided on several stages considering the relevant physical phenomema. The entire holistic model consisting of four interrelated submodels has currently been developed to a different extent. The submodels include the CA based

We study evolution equations describing jet propagation through quark-gluon plasma (QGP). In particular we investigate the contribution of momentum transfer during branching and find that such a contribution is sizeable. Furthermore, we study various approximations, such as the Gaussian approximation and the diffusive approximation to the jet-broadening term. We notice that in order to reproduce the BDIM equation (without the momentum transfer in the branching) the diffusive approximation requires a very large value of the jet-quenching parameter $$ \hat{q} $$ q ̂ .

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