First-order point process time scale

The Chapman-Enskog approximation method leads, at all stages, to hydrod5mamic equations which are first order in the time and can therefore be solved subject to given initial conditions. This procedure by which the boundary-value problem is converted into an initial-value problem is, from the mathematical point of view, somewhat mysterious. It appears likely that the procedure will converge only for processes whose scale of variation is of the order of, or less than, the mean free path (or other characteristic length). The reduction to an initial-value problem would then be impossible for rapidly varying processes. 

By monitoring excitation spectra with a time-resolved detection of the emission, briefly called time-resolved excitation spectroscopy , it is possible, to identify specific relaxation paths. Although, these occur on a ps time scale, only measurements with a ps time resolution are required. It is shown that the relaxation from an excited vibrational state of an individual triplet sublevel takes place by a fast process of intra-system relaxation (on the order of 1 ps) within the same potential surface to its zero-point vibrational level. Only subsequently, a relatively slow crossing to a different sublevel is possible. This latter process is determined by the slow spin-lattice relaxation. A crossing at the energy of an excited vibrational/phonon level from this potential hypersurface to the one of a different substate does not occur (Fig. 24, Ref. [60]). This method of time-resolved excitation spectroscopy, applied for the first time to transition metal complexes, can also be utilized to resolve spectrally overlapping excited state vibrational satellites and to assign these to their triplet substates. 

In paper [1] the curves Q(t) were described in terms of the scaling approaches for low molecular substance reactions [11]. Let us consider the reaction in which particles P of chemical substance are diffused in the environment containing randomly located nonsaturated statistical traps T. At the point of contact of a particle P with trap T the particle disappears. Nonsaturation of a trap means that the reaction P+T T can be repeated an infinite number of times. It is usually considered that if the concentration of particles and traps is large or the reaction proceeds at intense stirring, the process can be considered as classical reaction of the first order. However, if the concentration of the randomly located traps is small, with necessity there exist areas of space, practically free from traps. The particles that are in these areas, can reach traps only for rather long time and, hence, the fall of their number with time grows slower in comparison with the reaction of the first order. The formal analysis of this problem shows that the concentration of particles falls down under the law [11] ... 

A very convenient process for the production of this salt on the small scale is thet recommended by Walch-NEe. A pound of pure crystallized carbonate of soda is dried as perfectly as possible, and then intimately mixed with five ounces of pure sulphur the mixture is gradually heated in a glass or porcelain basin to the melting point of the sulphur, and kept at that tempera-tore for some time, stirring constantly in order to bring every part in contact with the air. The sulphide of sodium formed at first absorbs oxygen from the air, aud is converted with feeble Incandescence into hyposulphite of soda, The mass, when cold, is dissolved in water boiled with sulphur for some time, and the filtrate is evaporated, when very fine and pure crystals separate. If the heat employed be too strong, part of VOL. it. 

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