Sutton model

The Sutton equation belongs to a class known as Gaussian dispersion models in which the concentration of odor along any axis perpendicular to the downwind (x) direction is assumed to follow a normal or Gaussian distribution (Fig. 3.1). The dispersion coefficients determine the width of the plume and thus are related to the standard deviation of the concentration along the cross-wind and vertical axes. 

Wright (1958) and Bossert and Wilson (1963) independently introduced the use of Sutton s equation to analyze pheromone dispersion in the wind. Bossert and Wilson solved the equation for the maximum distance of communication  

They estimated a Q/K for the gypsy moth (Lymantria dispar) using this equation with the typical values suggested by Sutton (1953 p. 292) combined with an approximation of based on a report by Collins and Potts (1932) 

The work of Wright (1958) and Bossert and Wilson (1963) implanted the Sutton equation in the pheromone literature, despite the fact that most atmospheric scientists have long since adopted other Gaussian models (Mason, 1973 Fares et al. 1980) and despite the theoretical objections to the use of time average models (Wright, 1958 Aylor, 1976 Aylor et al. 1976). Furthermore, the typical values for n, Cy and Q have been used, regardless of the fact that the conditions under which they apply seldom prevail. 

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The Gaussian plume model estimates the average pheromone flux by multiplying the measured odor concentration by mean wind speed, using the following formula (Elkinton etal, 1984). Everything is the same as in the Sutton model, except that ay and az, respectively, replace the terms Cy and Cz of the Sutton model. Dispersion coefficients are determined for each experiment separately. 

Here ay and az, the horizontal and vertical diffusion coefficients, are the standard deviations of the cloud dimensions in the horizontal and vertical directions, respectively. They are functions of the downwind distance x and, in this, differ from the constants Cv and Cz of the Sutton model ... 

Sutton and Chen extended the potential to longer range to enable the study of certain problems such as the interactions between clusters of afoms [Sutton and Chen 1990]. Their objective was to combine the superior Fiimis-Sinclair description of short-range interactions with a van der Waals tail to model the long-range interactions. The form of the Sutton-Chen potential is ... 

Figure 2 Comparison of measured wet deposition of ammonium at Rothamsted, England with model estimates by Asman et al for regions whieh assume ehanges in emissions are only due to differenees in animal numbers. (Taken from Sutton et al ).

Even if we make the stringent assumption that errors in the measurement of each variable ( >,. , M.2,...,N, j=l,2,...,R) are independently and identically distributed (i.i.d.) normally with zero mean and constant variance, it is rather difficult to establish the exact distribution of the error term e, in Equation 2.35. This is particularly true when the expression is highly nonlinear. For example, this situation arises in the estimation of parameters for nonlinear thermodynamic models and in the treatment of potentiometric titration data (Sutton and MacGregor. 1977 Sachs. 1976 Englezos et al., 1990a, 1990b). 

Sutton SC, Rinaldi MT and Vukovinsky KE (2001) Phenol Red and Comparison of the Gravimetric 14c-Peg-3350 Methods to Determine Water Absorption in the Rat Single-Pass Intestinal Perfusion Model. AAPS Pharm Sci 3 pp 1-5. 

Pheromone propagation by wind depends on the release rate of the pheromone (or any other odor) and air movements (turbulent dispersion). In wind, the turbulent diffusivity overwhelms the diffusion properties of a volatile compound or mixture itself. Diffusion properties are now properties of wind structure and boundary surfaces, and preferably termed dispersion coefficients. Two models have dominated the discussion of insect pheromone propagation. These are the time-average model (Sutton, 1953) and the Gaussian plume model. 

For triggering behavior, the concentration at one point in time is more important than the average concentration. Therefore, in the real world, considerable deviation from time-averaging models is observed. In addition to timeaveraging models, peak concentrations of odors in turbulent systems have to be considered. Aylor (1976) estimated peak concentrations for air currents in forests. Average concentrations, as calculated by the Sutton formula, may be as low as only a few percent of maximmn (peak) concentrations. It is often the latter, however, that would trigger an animal s response. 

The jellium model of the free-electron gas can account for the increased abundance of alkali metal clusters of a certain size which are observed in mass spectroscopy experiments. This occurrence of so-called magic numbers is related directly to the electronic shell structure of the atomic clusters. Rather than solving the Schrodinger equation self-consistently for jellium clusters, we first consider the two simpler problems of a free-electron gas that is confined either within a sphere of radius, R, or within a cubic box of edge length, L (cf. problem 28 of Sutton (1993)). This corresponds to imposing hard-wall boundary conditions on the electrons, namely... 

Sutton, J.L., Maccecchini, M.L., Kajander, K.C. The kainate receptor antagonist 2S,4R-4-methylglutamate attenuates mechanical allodynia and thermal hyperalgesia in a rat model of nerve injury, Neuroscience 1999, 91, 283-292. 

An expression of the same linear form will be obtained for the growth of a needle if the tip is modeled as a hemisphere. Further results bearing on the diffusion- or interface-limited growth (and shrinkage) of particles have been reviewed by Sutton and Balluffi [6]. 

Dore AJ, Kryza M, Hall JR, Hallsworth S, Keller VJD, Vieno M, Sutton MA (2012) The influence of model grid resolution on estimation of national scale nitrogen deposition and exceedance of critical loads. Biogeosciences 9 1597-1609... 

Dragosits U, Sutton MA, Place CJ, Bayley AA (1998) Modelling the spatial distribution of agricultural ammonia emissions in the UK. Environ Pollut 102 195-203... 

Kleber, M., Sollins, P, and Sutton, R. (2007). A conceptual model of organo-mineral interactions in soils Self-assembly of organic molecular fragments into zonal structures on mineral surfaces. Biogeochemistry 85(1), 9-24. 

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