– We present generalized Green-Kubo expressions for thermal transport coefficients μ in fluid-type systems, of the generic form, μ = μ∞ + ∫ ∞ 0 dt V −1〈Jǫ exp(tL)J〉0, i.e. a sum of an instantaneous transport coefficient μ∞, and a time integral over a time correlation function in a state of thermal equilibrium between a current J and a transformed current Jǫ. The streaming operator exp(tL) gener...

Four explicit finite difference schemes, including Lax-Friedrichs, Nessyahu-Tadmor, Lax-Wendroff and Lax-Wendroff with a nonlinear filter are applied to solve water hammer equations. The schemes solve the equations in a reservoir-pipe-valve with an instantaneous and gradual closure of the valve boundary. The computational results are compared with those of the method of characteristics (MOC), a...

In the present work we investigate the numerical simulation of liquid-vapor phase change in compressible flows. Each phase is modeled as a compressible fluid equipped with its own Equation of State (EOS). We suppose that inter-phase equilibrium processes in the medium operate at a short time-scale compared to the other physical phenomena such as convection or thermal diffusion. This assumption ...

Two impatient players bargain about the division of a pie under a standard bargaining protocol in discrete time with time-invariant recognition probabilities. Instantaneous utility is linear, but players discount the future by a constant factor. Before bargaining starts, a player can commit to a utility level. This commitment is perfectly binding initially. However, once so much time has passed...

Viscosity is an important property of out-of-equilibrium systems such as active biological materials and driven non-Newtonian fluids, for fields ranging from biomaterials to geology, energy technologies medicine. Non-invasive viscosity measurements typically require integration times seconds. Here, we demonstrate measurement speeds reaching 20 ?s, with uncertainty dominated by thermal molecular...