Quantitative corrections to mass sum rules involving baryons containing heavy quarks

Quantitative corrections are estimated to three of Franklin's sum rules involving the masses of baryons containing at least one charmed quark and to three analogous sum rules for baryons containing at least one bottom quark. The corrections arise from three-body contributions to baryon interaction energies and are calculated from a semiempirical formula for the colormagnetic contributions to baryon masses.Comment: 4 pages, plainte

Impacts of Agricultural Nutrient Regulation in a Heterogeneous Region

Nonpoint sources of water pollutants, in particular, nutrients like nitrogen and phosphorus, are increasingly a focus of US water pollution policy. In most cases, agriculture is the largest contributor of these pollutants, in part because, until recently, it has largely remained unregulated. Recently, however, a number of initiatives have targeted nutrient runoff and leaching from animal agriculture. Many states have promulgated new nutrient management regulations stipulating that manure be disposed of in ways that limit runoff and leaching to acceptably low levels. Stricter state regulations have been especially common in the Mid-Atlantic and Southeast, where excess nutrients have proven particularly problematic (Gollehon et al.). In 2003, the US Environmental Protection Agency updated its regulatory oversight of confined animal feeding operations. The new regulations apply to a larger subset of such operations than in the past, most notably large poultry producers. In addition, they require all such operations to create and implement nutrient management plans that restrict land application of manure such that the quantity of nutrients a crop needs are correlated with the amount of nutrients applied to the crop. Several studies have examined the economics of nutrient management regulations. Fleming et al. assess the profitability of land application of swine manure for a single operation using data from Iowa. Innes presents a theoretical analysis for manure application in a region in cases where manure may be subject to both leaching and catastrophic spills into nearby water bodies in extreme weather events. Goetz and Zilberman present a theoretical analysis of optimal manure application and pollution taxes in a spatially differentiated region where phosphorus runoff is a stock pollutant. Feinerman et al. analyze least-cost combinations of manure and chemical fertilizer use at a regional level under nitrogen- and phosphorus-based nutrient management plans in the case of a linear-with-plateau von Liebig production technology both theoretically and empirically using data from Virginia. All of the aforementioned studies, except Goetz and Zilberman, assume that land is homogeneous in terms of its potential for nutrient runoff and leaching. In most cases, however, there is substantial heterogeneity in pollution potential due to differences in such factors as proximity to water bodies, soils, topography, phosphorus status, and BMP implementation. In many parts of the US, for instance, nutrient management regulations are based explicitly on the phosphorus site index (PSI), which incorporates information about soil phosphorus levels, leaching potential, and indicators of potential environmental damage. This paper examines the impacts of nutrient management regulations in a heterogeneous region. We extend existing frameworks in several ways that are critical from the perspective of practical regulation. First, both nitrogen and phosphorus are potential sources of water quality degradation; thus, nutrient management regulation needs to take both nutrients into account. Second, manure contributes to stocks of nutrients held in soils and nutrients are released only gradually, i.e., carryover is significant. As noted above for the case of phosphorus, nutrient management regulations are often conditioned on these soil stocks. Third, land heterogeneity determines nutrient application rates as well as runoff and leaching rates. Fourth, the use of manure can involve extra application costs and, in some instances, significant costs of transportation to suitable sites. Fifth, manure may have other uses than application to cropland, e.g., composting, pelletization for export, energy production, and forest fertilization. We develop a theoretical model of optimal manure application and chemical fertilizer use that incorporates all of these elements. Returns to crop production are modeled as a general function of nitrogen and phosphorus uptake. Available nitrogen is modeled as the sum of chemical fertilizer input plus releases from a stock of soil organic matter less land-type-specific losses to leaching and runoff. Changes in soil stocks of organic matter are assumed to equal additions from manure less releases to available nitrogen. Changes in soil phosphorus stocks are equal to additions from manure less crop uptake and losses to the environment at rates that depend on land type and existing stock levels. All soil phosphorus is assumed to be bioavailable. Environmental damage is assumed to depend on aggregate losses of nitrogen and phosphorus to the environment. We use the model to derive field- (land-type-) specific nutrient management recommendations for both manure application and chemical fertilizer use. We distinguish conditions under which nutrient management leads to (a) reliance on chemical fertilizer only, (b) reliance on manure application only, and (c) simultaneous use of chemical fertilizer and manure. We discuss the evolution of those recommendations over time as manure nutrient levels change due to alterations in feed, and as soil phosphorus and organic matter stocks change. We also discuss steady state recommendations. We apply the model empirically to the case of the Delmarva Peninsula, where regulators in Maryland and Delaware have introduced strict nutrient management regulations to address problems of phosphorus and nitrogen runoff into the Chesapeake Bay, with an emphasis on the management of poultry litter. This region has been identified as having large excesses of nitrogen and phosphorus relative to assimilative capacity, suggesting a need for long-distance export of much of the region's poultry litter (Gollehon et al.). We combine PSI estimates derived from soil test data with agronomic information on crop uptake rates to derive land-type-specific nutrient application rates under nitrogen- and phosphorus-based nutrient management regulations. We use a spatial model to estimate poultry litter transportation costs. We use engineering and agronomic studies to estimate demand for poultry litter in uses other than land application; they indicate that land application is likely the highest value use. In contrast to Gollehon et al., our results suggest a minimal need for long-distance transport under nutrient management regulations intended to limit leaching and runoff. The distribution of pollution potential is highly skewed: There is a small amount of land with extremely high PSI while most land has very low PSI. As a result, estimates based on county-level averages are highly misleading. In the short run, export from the Peninsula is not needed; in a steady state, some export may be needed. Overall, the impact of strict nutrient management regulations in this region will depend on the acceptability of land application of poultry litter to lands that are currently only using commercial fertilizer. Keeping those impacts low depends on the success of educational programs that promote poultry litter use (predominantly nutrient management programs) and on the creation of marketing institutions that minimize transaction costs of manure marketing.Environmental Economics and Policy,

On the local nature and scaling of chaos in weakly nonlinear disordered chains

The dynamics of a disordered nonlinear chain can be either regular or chaotic with a certain probability. The chaotic behavior is often associated with the destruction of Anderson localization by the nonlinearity. In the presentwork it is argued that at weak nonlinearity chaos is nucleated locally on rare resonant segments of the chain. Based on this picture, the probability of chaos is evaluated analytically. The same probability is also evaluated by direct numerical sampling of disorder realizations and quantitative agreement between the two results is found