Martin curve

Most modem N-cycle models simulate N export using one or the other of these approaches, but details vary and some models combine aspects of expHcit sinking and reminerahzation with Martin curve parameterizations. For example, Chai et al (1996) modeled a 5-component N-based ecosystem including a detrital N compartment with explicit sinking, but did not permit detrital remineralization within the euphotic zone. In contrast, Christian et al (2002a) used a Martin curve to redistribute detrital N vertically, but rather than remineralizing at the specified depth, it is returned to the... 

Said [1] developed the Martin concept [2] to derive the elution curve equation in the following way. 

The Brown and Martin [9] curve of Figure 8-49 is also used in about the same manner, and produces essentially the same results, but is based on internal vapor and liquid flows. 

The averaged function e(y/dc) can be well represented by a relationship established by Martin [7] consisting of a parabolic and an attenuated cosine part. The parameters for Eqs. (3.2.14) and (3.2.15) given by Martin were newly determined based on MRI results of the type shown in Figure 3.2.9. The differing curves shown in Figure 3.2.9 can be taken as proof of the difficulty of measuring e with conventional means. Data... 

Adolf and Martin [15] postulated, since the near critical gels are self-similar, that a change in the extent of cure results in a mere change in scale, but the functional form of the relaxation modulus remains the same. They accounted for this change in scale by redefinition of time and by a suitable redefinition of the equilibrium modulus. The data were rescaled as G /Ge(p) and G"/Ge(p) over (oimax(p). The result is a set of master curves, one for the sol (Fig. 23a) and one for the gel (Fig. 23 b). 

The examination of the electrolytic conductivity of soap solutions has, however, indicated that they are relatively good conductors and the conductivity concentration curve exhibits the interesting property of a definite minimum. The values for the specific conductivity of potassium palmitate are (McBain and Martin, J.G.S. ov. 967, 1914) plotted in the following curve. 

Solute equilibrium between the mobile and stationary phases is never achieved in the chromatographic column except possibly (as Giddings points out) at the maximum of a peak (1). As stated before, to circumvent this non equilibrium condition and allow a simple mathematical treatment of the chromatographic process, Martin and Synge (2) borrowed the plate concept from distillation theory and considered the column consisted of a series of theoretical plates in which equilibrium could be assumed to occur. In fact each plate represented a dwell time for the solute to achieve equilibrium at that point in the column and the process of distribution could be considered as incremental. It has been shown that employing this concept an equation for the elution curve can be easily obtained and, from that basic equation, others can be developed that describe the various properties of a chromatogram. Such equations will permit the calculation of efficiency, the calculation of the number of theoretical plates required to achieve a specific separation and among many applications, elucidate the function of the heat of absorption detector. 

K. Troshin, "The Generalized Hugoniot Adiabatic Curve Ibid, p 789 (Overcompressed detonation waves) 56) F.J. Martin D.R. White Formation and Structure of Gaseous Detonatio n Waves, Ibid, 856—65 56a) F.H. 

Figure 8-6. The ratio of demixing parameters t ( AB 4= 0)/t °(LAB = 0), calculated with the Manning model, as a function of Curve parameter is the jump frequency ratio r= vA/vB. v, is obtained from D =g-A 2-vi-fi [M. Martin (1991)1.

Fig. V-5. Absorption coefficients of HI and contribution of the transitions to the absorption continuum in the ultraviolet region. Solid curve, absorption coefficients of HI in units of 1 mol" 1 cm 1 base 10 at room temperature. Reprinted with permission from B. J. Huebcrt and R. M. Martin, J. Phys. Chem. 72, 3046 (1968). Copyright by the American Chemical Society. Dashed curves, absorption coefficients of the transitions fl.-T, Hq- Lf, and n- E. The n, and ll states dissociate into H + l(2P)/z). while the ll, state dissociates into H + The arrows indicate four incident...

The retention factors of the polymers in 60 % THF were calculated from gradient elution and discussed together with those directly measured for oligomers with 2-12 repeat units or 2000, 4000, and 9000 g/mol molar mass. On a lOOnm-pore packing, the Martin equation was fulfilled for n = 19 repeat units. At higher values, the curve... 

Figure 31. Laboratory angular distributions for He (2 S) + Ar at five collision energies from Pittsburgh laboratory. Solid curves are calculated from optical potential due to Martin et al.109 (see Figs. 32 and 35).

FIGURE 2.3 Caffeine solubility in dioxane-water binary solvents. The curve is an interpolation between calculated values. (Reproduced from Adjei, A., J. Newburger, andA. Martin. D9P i.arm. Sci69 659-661. Copyright 1980, American Pharmacists Association. Reprinted with permission from Wiley-Liss, Inc., a subsidiary of John Wiley Sons, Inc.)... 

Recently, Bonin and Simpson (2007) showed in their study that polycyclic aromatic hydrocarbons sorptive behavior could not be solely attributed to a specific SOM chemical characteristic (i.e., aliphaticity or aromaticity) and concluded that both structure and OM physical conformation are important in sorption processes. Martin-Neto et al. (1994b) used analysis of microwave power saturation curves (Weil et al., 1994) to obtain information about HA conformation. They observed that at pH > 3.5 a typical curve of homogeneous saturation was obtained for the oxisol HA, whereas at pH 2.3 inhomogeneous saturation occurred. The peat HA showed only homogeneous saturation. However, a similar inhomogeneous trend ... 

The SG/TC mode of SECM was also applied by Martin et al. [86] to study the oxidation of DMPPD. The generator was a 2-mm2 substrate electrode, and the collector was a 25-pm diameter Pt disk electrode. The substrate potential was stepped from 0 V versus Ag quasi reference electrode, where no Faradic process took place, to +500 mV, where the oxidation of DMPPD was diffusion controlled. The tip potential was held at 0 V, at which the oxidized form of DMPPD could be reduced at a diffusion controlled rate. After the tip-substrate separation was found from the positive feedback current-distance curve, the rate constant was obtained from the current transient at the tip. The feedback and SG/TC modes were also used to study the reduction of... 

It was used Sparteine, from Sigma, as an internal standard, and the final concentration of Sparteine in the samples was 0.102 g/1. The lupanine used to make the calibration curves of the chromatograph was extracted from the lupine flour using methanol and separated by using the thin-layer chromatography, according the method described by Cho and Martin (1971). 

Graphical representation of the probability that there be more than one compound per peak. The peak capacity is along the n axis. The m axis is the number of acceptable constituents that have the probability indicated next to each curve of having only one compound per peak. The statistical analysis used to produce this graph is slightly different from that leading to the equation in the text. Redrawn from Martin M., Herman D.P. and Guiochon G., Anal. Chem., 58, 2200, 1986, with permission. 

Figure 4.24 Tensile and compressive stress-strain curves of PBZO fibers under different conditions as spun, as coagulated, and heat-treated (Martin and Thomas, 1989 Kumai 1990a). Note the very low strength in compression.

For the purpose of outlining the results which we have obtained In studying supersonic sodium expansions, the data presented in Figure 2 will be useful. Here we consider calculated RKR potential curves for the X Zg" , A Zy" ", and 8 11 states of Na2 and a rough schematic of two cuts through the Naa potential surface based, in part, on the recent quantum chemical calculations of Martin and Davidson (40). For Na2, the location of the... 

Martin et al. (1961) have shown that the titration curve of suspensions of freshly precipitated collagen fibrils depends markedly on the pH at which aggregation to fibrils takes place. As this pH increases the count of imidazole groups decreases, and there is a corresponding increase in the number of groups titrated in the carboxyl region (in which the fibrils go into solution). 

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