Sorption of phenanthrene on agricultural soils

Polyaromatic hydrocarbon (PAH) sorption to soil is a key process deciding the transport and fate of PAH, and potential toxic impacts in the soil and groundwater ecosystems, for example in connection with atmospheric PAH deposition on soils. There are numerous studies on PAH sorption in relatively low organic porous media such as urban soils and groundwater sediments, but less attention has been given to cultivated soils. In this study, the phenanthrene partition coefficient, KD (liter per kilogram), was measured on 143 cultivated Danish soils (115 topsoils, 0–0.25-m soil depth and 28 subsoils, 0.25–1-m depth) by the single-point adsorption method. The organic carbon partition coefficient, KOC (liter per kilogram) for topsoils was found generally to fall between the KOC values estimated by the two most frequently used models for PAH partitioning, the Abdul et al. (Hazardous Waste & Hazardous Materials 4(3):211– 222, 1987) model and Karickhoff et al. (Water Research 13:241–248, 1979) model. A less-recognized model by Karickhoff (Chemosphere 10:833–846, 1981), yielding a KOC of 14,918 Lkg−1, closely corresponded to the average measured KOC value for the topsoils, and this model is therefore recommended for prediction of phenanthrene mobility in cultivated topsoils. For lower subsoils (0.25–1-m depth), the KOC values were closer to and mostly below the estimate by the Abdul et al. (Hazardous Waste & Hazardous Materials 4(3):211–222, 1987) model. This implies a different organic matter composition and higher PAH sorption strength in cultivated topsoils, likely due to management effects including more rapid carbon turnover. Finally, we applied the recent Dexter et al. (Geoderma 144:620–627, 2008) theorem, and calculated the complexed organic carbon and non-complexed organic carbon fractions (COC and NCOC, grams per gram). Multiple regression analyses showed that the NCOC-based phenanthrene partition coefficient (KNCOC) could be markedly higher than the COCbased partition coefficient (KCOC) for soils with a clay/OC ratio <10. This possibly higher PAH sorption affinity to the NCOC fraction needs further investigations to develop more realistic and accurate models for PAH mobility and effects in the environment, also with regard to colloid-facilitated PAH transport.

A fractional approach to the Fermi-Pasta-Ulam problem

This paper studies the Fermi-Pasta-Ulam problem having in mind the generalization provided by Fractional Calculus (FC). The study starts by addressing the classical formulation, based on the standard integer order differential calculus and evaluates the time and frequency responses. A first generalization to be investigated consists in the direct replacement of the springs by fractional elements of the dissipative type. It is observed that the responses settle rapidly and no relevant phenomena occur. A second approach consists of replacing the springs by a blend of energy extracting and energy inserting elements of symmetrical fractional order with amplitude modulated by quadratic terms. The numerical results reveal a response close to chaotic behaviour.

Fractional calculus: a survey of useful formulas

This paper presents a survey of useful, established formulas in Fractional Calculus, systematically collected for reference purposes.