The Navier-Stokes Equations with Time Delay

In the present paper we use a time delay epsilon > 0 for an energy conserving approximation of the nonlinear term of the non-stationary Navier-Stokes equations. We prove that the corresponding initial value problem (N_epsilon)in smoothly bounded domains G \subseteq R^3 is well-posed. Passing to the limit epsilon \rightarrow 0 we show that the sequence of stabilized solutions has an accumulation point such that it solves the Navier-Stokes problem (N_0) in a weak sense (Hopf).

Femtosecond real-time probing of reactions. 13. Multiphoton dynamics of IHgI

Real-time studies of the dynamics were performed on the reaction of HgI_2 in a molecular beam. Excitation was by either one or multi pump photons (311 nm), leading to two separate sets of dynamics, each of which could be investigated by a time-delayed probe laser (622 nm) that ionized the parent molecule and the fragments by REMPI processes. These dynamics were distinguished by combining the information from transients taken at each mass (HgI_2, HgI, I_2, Hg, and I) with the results of pump (and probe) power dependence studies on each mass. A method of plotting the slope of the intensity dependence against the pump-probe time delay proved essential. In the preceding publication, we detailed the dynamics of the reaction initiated by a one photon excitation to the A-continuum. Here, we present studies of higher-energy states. Multiphoton excitation accesses predissociative states of HgI_2, for which there are crossings into the symmetric and asymmetric stretch coordinates. The dynamics of these channels, which lead to atomic (I or Hg) and diatomic (HgI) fragments, are discussed and related to the nature of the intermediates along the reaction pathway.

Femtosecond time-resolved molecular multiphoton ionization and fragmentation of Na_2

We present a comparison between experimental and theoretical results for pump/probe multiphoton ionizing transitions of the sodium dimer, initiated by femtosecond laser pulses. It is shown that the motion of vibrational wavepackets in two electronic states is probed simultaneously and their dynamics is reflected in the total Na^+_2 ion signal which is recorded as a function of the time delay between pump and probe pulse. The time dependent quantum calculations demonstrate that two ionization pathways leading to the same final states of the molecularion exist: one gives an oscillating contribution to the ion signal, the other yields a constant background. From additional measurements of the Na^+ -transient photofragmentation spectrum it is deduced that another ionization process leading to different final ionic states exists. The process includes the excitation of a doubly excitedbound Rydberg state. This conclusion is supported by the theoretical simulation.

An analysis of household farm investment decisions under varying land tenure arrangements in Ghana

Land tenure insecurity is widely perceived as a disincentive for long-term land improvement investment hence the objective of this paper is to evaluate how tenure (in)security associated with different land use arrangements in Ghana influenced households’ plot level investment decisions and choices. The paper uses data from the Farmer-Based Organisations (FBO) survey. The FBO survey collected information from 2,928 households across three ecological zones of Ghana using multistaged cluster sampling. Probit and Tobit models tested the effects of land tenancy and ownership arrangements on households’ investment behaviour while controlling other factors. It was found that marginal farm size was inversely related to tenure insecurity while tenure insecurity correlate positively with value of farm land and not farm size. Individual ownership and documentation of land significantly reduced the probability of households losing uncultivated lands. Individual land ownership increased both the probability of investing and level of investments made in land improvement and irrigation probably due to increasing importance households place on land ownership. Two possible explanations for this finding are: First, that land markets and land relations have changed significantly over the last two decades with increasing money transaction and fixed agreements propelled by population growth and increasing value of land. Secondly, inclusion of irrigation investment as a long term investment in land raises the value of household investment and the time period required to reap the returns on the investments. Households take land ownership and duration of tenancy into consideration if the resource implications of land investments are relatively huge and the time dimension for harvesting returns to investments is relatively long.