Open Source vs. Proprietary Software: Competition and Compatibility

We use a Hotelling linear city model to study competition between open source and proprietary software, where only the producer of the proprietary software aims at maximizing the profit. The producer of the proprietary software must decide on compatibility. Different compatibility strategies will lead to different network externality, and thus result in different profit for the producer of the proprietary software. We found that the proprietary producer¡¯s choice of compatibility strategy depends on the market coverage conditions. When the market is fully covered, one-way compatibility is the best strategy for the proprietary software. When the market is partly covered, two-way compatibility is the best strategy. Such results are not affected by software quality. Furthermore, when the provider of the open source software pursues the maximum market share rather than reacts passively, two-way compatibility would be the best choice for both the open source and the proprietary software. Moreover, the proprietary software producer does not favor its proprietary rival changing to open source software. Such a change may lower the social welfare.Open Source Software, Proprietary Software, Compatibility, Competition

A modified lattice Bhatnagar-Gross-Krook model for convection heat transfer in porous media

The lattice Bhatnagar-Gross-Krook (LBGK) model has become the most popular one in the lattice Boltzmann method for simulating the convection heat transfer in porous media. However, the LBGK model generally suffers from numerical instability at low fluid viscosities and effective thermal diffusivities. In this paper, a modified LBGK model is developed for incompressible thermal flows in porous media at the representative elementary volume scale, in which the shear rate and temperature gradient are incorporated into the equilibrium distribution functions. With two additional parameters, the relaxation times in the collision process can be fixed at a proper value invariable to the viscosity and the effective thermal diffusivity. In addition, by constructing a modified equilibrium distribution function and a source term in the evolution equation of temperature field, the present model can recover the macroscopic equations correctly through the Chapman-Enskog analysis, which is another key point different from previous LBGK models. Several benchmark problems are simulated to validate the present model with the proposed local computing scheme for the shear rate and temperature gradient, and the numerical results agree well with analytical solutions and/or those well-documented data in previous studies. It is also shown that the present model and the computational schemes for the gradient operators have a second-order accuracy in space, and better numerical stability of the present modified LBGK model than previous LBGK models is demonstrated.Comment: 38pages,50figure