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A novel algorithm is proposed for the acceleration of the exact stochastic simulation algorithm by a predefined number of reaction firings (R-leaping) that may occur across several reaction channels. In the present approach, the numbers of reaction firings are correlated binomial distributions and the sampling procedure is independent of any permutation of the reaction channels. This enables the algorithm to efficiently handle large systems with disparate rates, providing substantial computational savings in certain cases. Several mechanisms for controlling the accuracy and the appearance of negative species are described. The advantages and drawbacks of R-leaping are assessed by simulations on a number of benchmark problems and the results are discussed in comparison with established methods.

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We investigate numerically the Navier-Stokes dynamics of reconnecting vortex rings at small Reynolds number for a variety of configurations. We find that reconnections are dissipative due to the smoothing of vorticity gradients at reconnection kinks and to the formation of secondary structures of stretched antiparallel vorticity which transfer kinetic energy to small scales where it is subsequently dissipated efficiently. In addition, the relaxation of the reconnection kinks excites Kelvin waves which due to strong damping are of low wave number and affect directly only large scale properties of the flow. DOI: 10.1103/PhysRevLett.90.054501 PACS numbers: 47.32.Cc, 47.27.Eq In flow phenomena as diverse as quantum [1], magnetic [2], and incompressible [3] fluids, it is useful to study the physics of turbulence by modeling the system as a collection of tubular flux loops which in the case of vortical fields are called vortex filaments. An intrinsic property of such highly structured systems is their ability to dynamically change their topology via reconnection mechanisms. Does this change in topology affect in turn properties of fluid turbulence such as intermittency and scalar mixing (which depend directly on the structure of the flow) or the dynamics of energy in wave number space? Or is it the case that reconnection events are not generic and thus have no direct impact on the mean properties of turbulent flows? The aim of this Letter is to address these issues by fully resolving the NavierStokes dynamics of interacting vortex rings for three simple geometries having great potential for illuminating the physics of reconnection. Although the flows considered are not strictly turbulent, the hope is that in a future structural approach to the problem of turbulence a significant part of the flow complexity could be traced back to the physics of similar vortex interactions.Incompressible vortex reconnections have an extensive bibliography (for a review of the work up to 1994, see [4,5]). In [6,7] reconnections of vortex tubes were considered with an emphasis on the possibility of singularity formation as Re ! 1. In [8] the strong interactions between vortex rings were computed with the interest in developing numerical methods and turbulence models rather than in focusing on the physics of reconnection. In [9] it is discussed how a linked vortex configuration could be achieved starting from an unlinked initial state, and in [10] it is considered how the mixing of a nondiffusing passive scalar is affected during vortex ring collision. The reconnection of two approaching (but not colliding) vortex rings was studied experimentally in [11] and theoretically in [12]. This Letter extends these studies by considering generic vortex configurations and by capturing more features of vortex reconnections in a turbulent flow.We solve the Navier-Stokes equations for an unbounded three-dimensional incompressible viscous flow. We employ the vorticity formulation:where u is the velocity and ! is the vorticity. We use a vortex parti...

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