Collisionless magnetic reconnection in a two dimensional plasma is analyzed, using a two-fluid model where electron mass and pressure effects are important. Numerical simulations show the formation of current and vorticity layers along two branches crossing at the stagnation point of the plasma flow. These structures are interpreted on the basis of the Hamiltonian Casimirs (conserved fields) of the fluid plasma model. [S0031-9007(98)06155-9] PACS numbers: 52.35.Py, 47.65. + a, 52.65.Kj, 94.30.GmThe problem of magnetic reconnection in collisionless regimes was originally motivated by applications to space plasma processes, such as reconnection events occurring in the Earth magnetotail [1]. Renewed interest in this problem was prompted by the observation of fast relaxations in high temperature laboratory plasmas of thermonuclear interest. One well known example is the so called "sawtooth crash" of the central temperature of a tokamak plasma, which may occur on a time scale short compared to the average electron-ion collision time [2]. Recently it was shown [3,4] that electron inertia may account for the fast time scales observed in the experiments.The first aim of this Letter is to extend this analysis to finite temperature regimes, where electron pressure effects are important. We find that in the early nonlinear phase the growth of the magnetic island is even faster than in the cold electron limit of Ref. [4]. The fast collisionless evolution in this early nonlinear regime is a non-steady-state process, characterized by the formation of increasingly narrower microscales below the electron skin depth. The long term behavior is likely to require kinetic considerations outside the scope of the fluid model adopted in this paper.The second aim is the investigation of the role played by the Casimir invariants. Indeed, it can be shown that the adopted collisionless model admits a Hamiltonian structure [5,6]. While magnetic flux is reconnected in the course of plasma evolution, the conserved fields associated with the Casimirs preserve their initial topology. The nature of collisionless reconnection under these circumstances is entirely different from that of resistive reconnection.The model we consider is an extension of reduced magnetohydrodynamic [7] to a two-fluid description, where electron inertia, associated with the inertial skin depth, d e c͞v pe , and the electron pressure terms are retained in the generalized Ohm's law [8] (a more general model is the four field model of Ref.[9]). More specifically, we adopt an isothermal equation of state for the electrons and disregard diamagnetic effects associated with equilibrium pressure gradients, a valid approximation as long as the electron diamagnetic frequency is small compared with the characteristic growth rate of the reconnection process. On the other hand, we retain the divergence of the electron stress tensor (electron gyroviscosity) in the generalized Ohm's law. The parallel electron compressibility introduces the characteristic scale length, s p T e ͞m i ͞v c...

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A generalized Semenov model is proposed to describe the dynamics of compartment fires. It is shown that the transitions to flashover or to extinction can be described in the context of the catastrophe theory (or the theory of dynamical systems) by introducing a suitable potential function of the smoke layer temperature. The effect on the fire dynamics of random perturbations is then studied by introducing a random noise term accounting for internal and external perturbations with an arbitrary degree of correlation. While purely Gaussian perturbations (white noise) do not change the behaviour of the fire with respect to the deterministic model, perturbations depending on the model variable ('coloured' noise) may drive the system to different states. This suggests that the compartment fires can be controlled or driven to extinction by introducing appropriate external perturbations.

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