Effect of excluded volume on 2D discrete stochastic chemical kinetics

The stochastic simulation algorithm (SSA) is widely used in the discrete stochastic simulation of chemical kinetics. The propensity functions which play a central role in this algorithm have been derived under the point-molecule assumption, i.e., that the total volume of the molecules is negligible compared to the volume of the container. It has been shown analytically that for a one-dimensional system and the A + A reaction, when the point-molecule assumption is relaxed, the propensity function need only be adjusted by replacing the total volume of the system with the free volume of the system. In this paper we investigate via numerical simulations the impact of relaxing the point-molecule assumption in two dimensions. We find that the distribution of times to the first collision is close to exponential in most cases, so that the formalism of the propensity function is still applicable. In addition, we find that the area excluded by the molecules in two dimensions is usually higher than their close-packed area, requiring a larger correction to the propensity function than just the replacement of the total volume by the free volume.     

Quantitative fluorimetrische Mikrobestimmung von Aminen in Flotationsabw?ssern

Ohne Zusammenfassung

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Quantitative fluorimetric microdetermination of amines in flotation effluents

     

Zum Anfangswertproblem zerfallender Zustände

The probability of decay of a quantum mechanical system is completely determined by the energy spectrum of the initial state. An exponential law of decay is obtained only if the spectrum has a long tail. Since the initial state is spatially localized, the decay energy and decay constant are fixed by the poles of theS-function.     

Numerical solution of differential-algebraic equations in mechanical systems simulation

The numerical solution of the differential-algebraic equations of motion of mechanical systems offers many computational challenges. In this paper we describe progress which has been made in understanding the formulation of the equations of motion from the viewpoint of numerical stability, and outline some of the difficulties which must be resolved for efficient and reliable numerical methods in real-time simulation of mechanical systems.     

Über einige Probleme bei instabilen quantenmechanischen Systemen

If an exponential decay law is measured (which clearly need not be found in every case) it cannot be concluded that the line shape must be lorentzian. To show that the possible energy spectra may differ from a Lorentz shape by a well measurable amount an example of such a spectrum is constructed, leading to an exponential decay law in an even better approximation than a lorentzian spectrum. Hereafter various facts about decaying systems are discussed in connection with scattering theory. Finally it is shown that ordinary Mößbauer experiments are not suited for line shape measurements and modified experiments are proposed.     

Buchbesprechungen

Ohne Zusammenfassung     

Nicht-kovariante Dichten. Probleme der Makrokausalität und Teilchendichte in der relativistischen Wellenmechanik. II

In the framework of relativistic wave-mechanics expressions of particle densities ?(x) with causal behaviour are constructed. It turns out that ?(x) can be neither the fourth component of a four vector nor a local observable.