Theory of weakly nonlinear self sustained detonations

We propose a theory of weakly nonlinear multi-dimensional self sustained detonations based on asymptotic analysis of the reactive compressible Navier-Stokes equations. We show that these equations can be reduced to a model consisting of a forced, unsteady, small disturbance, transonic equation and a rate equation for the heat release. In one spatial dimension, the model simplifies to a forced Burgers equation. Through analysis, numerical calculations and comparison with the reactive Euler equations, the model is demonstrated to capture such essential dynamical characteristics of detonations as the steady-state structure, the linear stability spectrum, the period-doubling sequence of bifurcations and chaos in one-dimensional detonations and cellular structures in multi- dimensional detonations

Does High Inflation Affect Growth in the Long and Short Run?

This paper investigates the relationship between inflation and output in the context of an economy facing persistent high inflation. By analyzing the case of Brazil, we find that inflation does not impact real output in the long run, but that in the short run there exists a negative effect from inflation on output. These results support Sidrauski’s (1967) superneutrality of money in the long run, but cast doubt on the short run implications of the model for separable utility functions in consumption and real money balances, as exposed by Fischer (1979). The results are more likely to support a class of utility functions in which real money balances and consumption are perfect complements.inflation; growth; output

Laser-induced nonsequential double ionization: kinematic constraints for the recollision-excitation-tunneling mechanism

We investigate the physical processes in which an electron, upon return to its parent ion, promotes a second electron to an excited state, from which it subsequently tunnels. Employing the strong-field approximation and saddle-point methods, we perform a detailed analysis of the dynamics of the two electrons, in terms of quantum orbits, and delimit constraints for their momentum components parallel to the laser-field polarization. The kinetic energy of the first electron, upon return, exhibits a cutoff slightly lower than $10U_p$, where $U_p$ is the ponderomotive energy, as in rescattered above-threshold ionization (ATI). The second electron leaves the excited state in a direct ATI-like process, with the maximal energy of $2U_p$. We also compute electron-momentum distributions, whose maxima agree with our estimates and with other methods.Comment: 13 pages, 4 figure

Stabilization not for certain and the usefulness of bounds

Stabilization is still a somewhat controversial issue concerning its very existence and also the precise conditions for its occurrence. The key quantity to settle these questions is the ionization probability, for which hitherto no computational method exists which is entirely agreed upon. It is therefore very useful to provide various consistency criteria which have to be satisfied by this quantity, whose discussion is the main objective of this contribution. We show how the scaling behaviour of the space leads to a symmetry in the ionization probability, which can be exploited in the mentioned sense. Furthermore, we discuss how upper and lower bounds may be used for the same purpose. Rather than concentrating on particular analytical expressions we obtained elsewhere for these bounds, we focus in our discussion on the general principles of this method. We illustrate the precise working of this procedure, its advantages, shortcomings and range of applicability. We show that besides constraining possible values for the ionization probability these bounds, like the scaling behaviour, also lead to definite statements concerning the physical outcome. The pulse shape properties which have to be satitisfied for the existence of asymptotical stabilization is the vanishing of the total classical momentum transfer and the total classical displacement and not smoothly switched on and off pulses. Alternatively we support our results by general considerations in the Gordon-Volkov perturbation theory and explicit studies of various pulse shapes and potentials including in particular the Coulomb- and the delta potential.Comment: 12 pages Late

Analytical treatment of stabilization

We present a summarizing account of a series of investigations whose central topic is to address the question whether atomic stabilization exists in an analytical way. We provide new aspects on several issues of the matter in the theoretical context when the dynamics is described by the Stark Hamiltonian. The main outcome of these studies is that the governing parameters for this phenomenon are the total classical momentum transfer and the total classical displacement. Whenever these two quantities vanish, asymptotically weak stabilization does exist. For all other situations we did not find any evidence for stabilization. We found no evidence that strong stabilization might occur. Our results agree qualitatively with the existing experimental findings