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Full-Text Articles in Physical Sciences and Mathematics
Lattice Boltzmann Simulations Of Thermal Convective Flows In Two Dimensions, Jia Wang, Donghai Wang, Pierre Lallemand, Li-Shi Luo
Lattice Boltzmann Simulations Of Thermal Convective Flows In Two Dimensions, Jia Wang, Donghai Wang, Pierre Lallemand, Li-Shi Luo
Mathematics & Statistics Faculty Publications
In this paper we study the lattice Boltzmann equation (LBE) with multiple-relaxation-time (MRT) collision model for incompressible thermo-hydrodynamics with the Boussinesq approximation. We use the MRT thermal LBE (TLBE) to simulate the following two flows in two dimensions: the square cavity with differentially heated vertical walls and the Rayleigh-Benard convection in a rectangle heated from below. For the square cavity, the flow parameters in this study are the Rayleigh number Ra = 103-106, and the Prandtl number Pr = 0.71; and for the Rayleigh-Benard convection in a rectangle, Ra = 2 . 103, 10 …
Mesoscopic Methods In Engineering And Science, Jos Derksen, Dmitry Eskin, Li-Shi Luo, Manfred Krafczyk
Mesoscopic Methods In Engineering And Science, Jos Derksen, Dmitry Eskin, Li-Shi Luo, Manfred Krafczyk
Mathematics & Statistics Faculty Publications
(First paragraph) Matter, conceptually classified into fluids and solids, can be completely described by the microscopic physics of its constituent atoms or molecules. However, for most engineering applications a macroscopic or continuum description has usually been sufficient, because of the large disparity between the spatial and temporal scales relevant to these applications and the scales of the underlying molecular dynamics. In this case, the microscopic physics merely determines material properties such as the viscosity of a fluid or the elastic constants of a solid. These material properties cannot be derived within the macroscopic framework, but the qualitative nature of the …
Duality Of The Weak Parallelogram Laws On Banach Spaces, Raymond Cheng, Charles B. Harris
Duality Of The Weak Parallelogram Laws On Banach Spaces, Raymond Cheng, Charles B. Harris
Mathematics & Statistics Faculty Publications
This paper explores a family of weak parallelogram laws for Banach spaces. Some basic properties of such spaces are obtained. The main result is that a Banach space satisfies a lower weak parallelogram law if and only if its dual satisfies an upper weak parallelogram law, and vice versa. Connections are established between the weak parallelogram laws and the following: subspaces, quotient spaces, Cartesian products, and the Rademacher type and co-type properties.