Uniform Initial Conditions Research Articles

Stability of the steady states and transient behavior for a non-isothermal bimolecular langmuir-hinshelwood reaction

The steady state stability and transient behavior of a catalytic reaction following the bimolecular Langmuir-Hinshelwood expression, phenomenologically adequate for carbon monoxide and hydrocarbon oxidation on noble metal catalysts, is describe. The corresponding steady state problem was discussed earlier. Some unique features of the isothermal and non-isothemal transient behavior with uniform initial conditions are identified.

Three-dimensional dynamics of protostellar evolution

view Abstract Citations (41) References (12) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Three-dimensional dynamics of protostellar evolution. Cook, T. L. ; Harlow, F. H. Abstract A three-dimensional finite-difference numerical technique is outlined for self-gravitating rotating gaseous systems. The full nonlinear time-dependent equations describing a rotating self-gravitating fluid are solved in rotating cylindrical coordinates, and the time-dependent adiabatic collapse of gravitationally bound rotating protostellar clouds is analyzed for specified uniform and nonuniform initial conditions. It is found that uniform clouds can form axisymmetric rotating toroidal configurations, that nonuniform clouds can collapse to axisymmetric ellipsoids if the thermal pressure is high, and that the collapsing cloud is unstable to perturbations for low thermal pressures. The ensuing fragmentation of unstable protostellar clouds is examined by studying the response of self-gravitating equilibrium toroids to nonaxisymmetric perturbations. The results show that the detailed evolution of a fragmenting toroid depends on a nondimensional function of the initial entropy, as well as the total mass in the toroid, the rotational angular velocity, and the number of perturbation wavelengths around the circumference of the toroid. Publication: The Astrophysical Journal Pub Date: November 1978 DOI: 10.1086/156568 Bibcode: 1978ApJ...225.1005C Keywords: Finite Difference Theory; Protostars; Stellar Evolution; Stellar Models; Chandrasekhar Equation; Dynamic Models; Gravitational Collapse; Rotating Matter; Toroids; Astrophysics; Collapse:Protostellar Clouds; Hydrodynamics:Star Formation full text sources ADS |

Impurity Quenching of Molecular Excitons. I. Kinetic Comparison of Förster—Dexter and Slowly Quenched Frenkel Excitons in Linear Chains

The quenching kinetics of tightly bound excitons for two different one-dimensional models are compared. The quenching of fully incoherent, or Förster—Dexter, excitons is described by a standard master equation, and that of fully coherent, or Frenkel, excitons by an ad hoc linear differential equation whose eigenvalues are complex. Moments of the chain excitation function (probability that excitation remains at time t) are calculated on each model for finite chains with either localized or uniform initial conditions, free-end or periodic boundary conditions, one disruptive or one nondisruptive quencher, and various quencher locations, but with only nearest-neighbor interactions included. The ad hoc equation is treated only in the limit that the quenching is slow enough not to affect the exciton wave functions in first order. In that limit of Frenkel exciton quenching, an analytic expression is given for the mean de-excitation time in the presence of uniform decay processes such as fluorescence. The master equation is treated for arbitrary relative quencher strength with simple analytic expressions for the zeroth moment obtained by an inverse matrix method. Infinite chains with randomly placed disruptive quenchers are also treated. It is shown that for the Förster—Dexter model the nth moment Mn is proportional to N2n+2 for large N (finite chains) or to c−(2n+2) for small c (infinite chains); for the Frenkel model with an incoherent initial condition, Mn ∝ N(3n+2) or c−(3n+2). This implies that kinetic differences between quenching of Frenkel and Förster—Dexter excitons appear only in higher (than zero) moments and not, e.g., in fluorescence yields. It is also concluded that, because of their ``boundary-avoiding tendency,'' Frenkel excitons can be quenched much more slowly in some situations than Förster—Dexter excitons. Finally, the intuitive notion that excited-state energy transfer is a two-step process—consisting of migration to the quencher neighborhood and subsequent quenching—is substantiated for Förster—Dexter excitons but not for Frenkel excitons.