Schmidt law

Basic assumptions made in the models by Matteucci and her colleagues (e.g. Matteucci Greggio 1986) involve a star formation law similar to the modified Schmidt law, Eq. (7.15) ... 

The result is that when 8 is large, stars form rapidly, roughly as in a Schmidt Law in volume density with n 2, until star formation is quenched by shocks and there is a saturation conversely, when it is small, there is a much more gradual process. Figure 12.15 shows the resulting metallicity evolution with time for different <5 s, assuming a yield p = 0.02 Z . 

In alternative to the Schmidt law, Kennicutt proposed also the following star formation law, which fits equally well the observational data ... 

Dispersion In tubes, and particiilarly in packed beds, the flow pattern is disturbed by eddies diose effect is taken into account by a dispersion coefficient in Fick s diffusion law. A PFR has a dispersion coefficient of 0 and a CSTR of oo. Some rough correlations of the Peclet number uL/D in terms of Reynolds and Schmidt numbers are Eqs. (23-47) to (23-49). There is also a relation between the Peclet number and the value of n of the RTD equation, Eq. (7-111). The dispersion model is sometimes said to be an adequate representation of a reaclor with a small deviation from phig ffow, without specifying the magnitude ol small. As a point of superiority to the RTD model, the dispersion model does have the empirical correlations that have been cited and can therefore be used for design purposes within the limits of those correlations. 

The simplest possible parameterization of the SFR is to assume that it is just proportional to the surface density of gas (a special case of Schmidt s law, with an exponent of 1). This at least has the merit of simplicity and of taking into account the necessity of having gas as the raw material from which stars are formed, and will be used widely here as it has been elsewhere, while always bearing in mind that the coefficient may vary with ambient conditions (as, e.g., in Kennicutt s alternative law Eq. 7.16) or stochastically. A number of the results of GCE theory are insensitive to the SFR, while others are affected by many other difficulties anyway. 

Fig. 8.34. [S/Fe] and [C/Fe] vs. [Fe/H], adapted from Portinari, Chiosi and Bres-san (1998). Model curves are coded according to the exponent k in the modified Schmidt star formation law, Eq. (8.55). Dotted curve k = 1 solid curve k = 1.5 dashed curve k = 2.

P. W. Schmidt, D. Avnir, D. Levy, A. Hohr, M. Steiner and A. Roll, Small-angle x-ray scattering from the surfaces of reversed-phase silicas Power-law scattering exponents of magnitudes greater than four, J. Chem. Phys., 1991, 94, 1474. 

The diffusion coefficient as defined by Fick s law, Eqn. (3.4-3), is a molecular parameter and is usually reported as an infinite-dilution, binary-diffusion coefficient. In mass-transfer work, it appears in the Schmidt- and in the Sherwood numbers. These two quantities, Sc and Sh, are strongly affected by pressure and whether the conditions are near the critical state of the solvent or not. As we saw before, the Schmidt and Prandtl numbers theoretically take large values as the critical point of the solvent is approached. Mass-transfer in high-pressure operations is done by extraction or leaching with a dense gas, neat or modified with an entrainer. In dense-gas extraction, the fluid of choice is carbon dioxide, hence many diffusional data relate to carbon dioxide at conditions above its critical point (73.8 bar, 31°C) In general, the order of magnitude of the diffusivity depends on the type of solvent in which diffusion occurs. Middleman [18] reports some of the following data for diffusion. 

Cheese is ripened for 6 months to 1 year or longer at 5° to 15°C and 70-75% relative humidity. Cheese ripening is a complex process involving a combination of chemical, biochemical, and physical reactions. Proteolytic enzymes, e.g., rennet and lactic starter culture enzymes, hydrolyze caseins to produce flavor compounds and proper body. Lipase and lactase enzymes also hydrolyze their respective substrates to produce a large number of characteristic flavor compounds (Reiter and Sharpe 1971 Harper 1959 Law 1981 Schmidt etal. 1976), including free fatty acids, methanethiol, methanol, dimethyl sulfide, diacetyl, acetone, and others (Moskowitz 1980). 

EtCentr 9%, so shaped as to burn with const surface, showed that the rate of increase of pressure is proportional to the pressure as given by the equation dp/dt= kp, where k is a constant) NH.Dupuis. MAF 17. 799-830(1938)(Discussion on the laws of burning of colloidal proplnts) 0)H. Muraour G.Aunis. CR 206. 1723 6(193d)(Burning of colloidal proplnts in parallel rows) P)J. Dijpuisgr M.ChalyeCMAF 18, 37-66(1939)(Buming of proplnts in a Krupp-Schmidt bomb) Q)H,... 

CA 45 7792(1951) [Combustion profiles of lamelae of a double-base proplnt consisting of NC 69.1, DEGDN 20.6 St EtCentr 6.9% were detd in air and inert gases, with or w/o wrappings of different thermal conductivity. An interpretation of the various profiles obtd(inverted V, rectilinear, concave or parabolic) was proposed. The factor which mainly detd the geometry of the combustion profile is heat transfer from the flame front to the solid lamelae, thru the ambient media) 8)P. Tavernier St P.Prache, MP 34, 255-75(1952) Sc CA 48, 11060(1954)(Rate of combustion of proplnts in an inert atm under pressure) 9)H. Muraour 8t G. Aunis, MP 35, 287-301(1953) CA 49, 13651(1955) Ger translation by Dr. A. Schmidt in Explosivst 1954, 154-7 1955 6-9(Laws of combustion of colloidal proplnts. A survey of French research between WWI St WWII) 10)C. A. Heller A.S, Gordon, JPhysChem 59, 773-77(1955)... 

Recent work by Schmidt and Schuster (1978a, 1980a) has shown that the addition of any of several easily oxidized, fluorescent aromatic hydrocarbons or amines to solutions of [21] results in greatly enhanced chemiluminescence. Moreover, addition of these molecules accelerates the rate of reaction of [21]. The catalyzed reaction is first order in both [21] and aromatic hydrocarbon or amine (which is termed the activator, act). Acetone is still produced quantitatively, and the activator is not consumed in the reaction, but rather serves as a catalyst for the decomposition of the dioxetanone. The kinetic behavior is thus described by the simple rate law (27), where kt is the rate... 

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