Hydrodynamic mean field solutions of 1D exclusion processes with spatially varying hopping rates

We analyze the open boundary partially asymmetric exclusion process with smoothly varying internal hopping rates in the infinite-size, mean field limit. The mean field equations for particle densities are written in terms of Ricatti equations with the steady-state current $J$ as a parameter. These equations are solved both analytically and numerically. Upon imposing the boundary conditions set by the injection and extraction rates, the currents $J$ are found self-consistently. We find a number of cases where analytic solutions can be found exactly or approximated. Results for $J$ from asymptotic analyses for slowly varying hopping rates agree extremely well with those from extensive Monte Carlo simulations, suggesting that mean field currents asymptotically approach the exact currents in the hydrodynamic limit, as the hopping rates vary slowly over the lattice. If the forward hopping rate is greater than or less than the backward hopping rate throughout the entire chain, the three standard steady-state phases are preserved. Our analysis reveals the sensitivity of the current to the relative phase between the forward and backward hopping rate functions.Comment: 12 pages, 4 figure

ATM optical contamination study - Reaction control system rocket engine space plume flow fields Interim report

Apollo telescopic experiment contamination by space vehicle exhaust product

Color centers in hexagonal boron nitride monolayers: A group theory and ab-initio analysis

We theoretically study physical properties of the most promising color center candidates for the recently observed single-photon emissions in hexagonal boron nitride (h-BN) monolayers. Through our group theory analysis combined with density functional theory (DFT) calculations we provide several pieces of evidence that the electronic properties of the color centers match the characters of the experimentally observed emitters. We calculate the symmetry-adapted multi-electron wavefunctions of the defects using group theory methods and analyze the spin-orbit and spin-spin interactions in detail. We also identify the radiative and non-radiative transition channels for each color center. An advanced ab-initio DFT method is then used to compute energy levels of the color centers and their zero-phonon-line (ZPL) emissions. The computed ZPLs, the profile of excitation and emission dipole polarizations, and the competing relaxation processes are discussed and matched with the observed emission lines. By providing evidence for the relation between single-photon emitters and local defects in h-BN, this work provides the first steps towards harnessing quantum dynamics of these color centers.Comment: 11 pages, 5 figure