Hydrodynamic correlation functions of a driven granular fluid in steady state

We study a homogeneously driven granular fluid of hard spheres at intermediate volume fractions and focus on time-delayed correlation functions in the stationary state. Inelastic collisions are modeled by incomplete normal restitution, allowing for efficient simulations with an event-driven algorithm. The incoherent scattering function Fincoh(q,t ) is seen to follow time-density superposition with a relaxation time that increases significantly as the volume fraction increases. The statistics of particle displacements is approximately Gaussian. For the coherent scattering function S(q,ω), we compare our results to the predictions of generalized fluctuating hydrodynamics, which takes into account that temperature fluctuations decay either diffusively or with a finite relaxation rate, depending on wave number and inelasticity. For sufficiently small wave number q we observe sound waves in the coherent scattering function S(q,ω) and the longitudinal current correlation function Cl(q,ω). We determine the speed of sound and the transport coefficients and compare them to the results of kinetic theory.

Gold Phosphonates as Transfer Agents in Palladium Catalyzed Hirao Reactions

Through a cross-coupling reaction, aryl phosphonates are produced in high yields when the corresponding aryl bromides are reacted with a gold phosphorylating agent in the presence of a palladium catalyst and an appropriate ligand. To the best of our knowledge, this transformation is the first example involving the transfer of a phosphonate functional group from a gold complex to palladium that has been reported. Throughout the investigation, three gold phosphorylating agents were screened for activity towards the phosphorylation of aryl bromides. Aryl bromides with electrondonating and electron-withdrawing groups were successfully employed in the crosscoupling reactions. All cross-coupling reactions were carried out in THF at room temperature (25ºC) or in a microwave reactor (CEM Discover) at 60ºC for 30 or 60 minutes. The effects of changing reaction parameters such as time, temperature, catalyst and free ligand loading have been investigated. All aryl bromide substrates tested in the cross-coupling reactions produced phosphorylated products.