Generic tropical varieties

We show that in the constant coefficient case the generic tropical variety of a graded ideal exists. This can be seen as an analogue to the existence of the generic initial ideal in Gröbner basis theory. We determine the generic tropical variety as a set in general and as a fan for principal ideals and linear ideals.     

Manifold sensitivity improvement of swelling-based sensors

The sensitivity of swelling-based gold core-organic shell nanoparticle vapor sensors is improved manifold by cooling sensors below ambient temperature. This is due to the reduced volatility of the analyte. Sensitivity to a particular analyte scales with temperature like that of analyte's saturated vapor pressure, thus allowing quantitative prediction of sensitivity enhancement. We believe our conclusions apply to all swelling-based sensors.     

Accounting for risk aversion in derivatives purchase timing

We study the problem of optimal timing to buy/sell derivatives by a risk-averse agent in incomplete markets. Adopting the exponential utility indifference valuation, we investigate this timing flexibility and the associated delayed purchase premium. This leads to a stochastic control and optimal stopping problem that combines the observed market price dynamics and the agent??s risk preferences. Our results extend recent work on indifference valuation of American options, as well as the authors?? first paper (Leung and Ludkovski, SIAM J Finan Math 2(1) 768?C793, 2011). In the case of Markovian models of contracts on non-traded assets, we provide analytical characterizations and numerical studies of the optimal purchase strategies, with applications to both equity and credit derivatives.     

Investigations into the kinetics and thermodynamics of Sb(III) adsorption on goethite (alpha-FeOOH)

This study reports thermodynamic and kinetic data of Sb(III) adsorption from single metal solutions onto synthetic aqueous goethite (alpha-FeOOH). Batch equilibrium sorption experiments were carried out at 25 degrees C over a Sb:Fe molar range of 0.005-0.05 and using a goethite concentration of 0.44 g Fe/L. Experimental data were successfully modelled using Langmuir (R2 > or = 0.891) and Freundlich (R2 > or = 0.990) isotherms and the following parameters were derived from triplicate experiments: Kf = 1.903 +/- 0.030 mg/g and 1/n = 0.728 +/- 0.019 for the Freundlich model and b = 0.021 +/- 0.003 L/mg and Qmax = 61 +/- 8 mg/g for the Langmuir model. The thermodynamic parameters determined were the equilibrium constant, Keq =1.323 +/- 0.045, and the Gibb's free energy, DeltaG0 = -0.692 +/- 0.083 kJ/mol. The sorption process is very fast. At a Sb:Fe molar ratio of 0.05, 40-50% of the added Sb is adsorbed within 15 min and a steady state is achieved. The experimental data also suggest that desorption can occur within 24 h of reaction due to the oxidation of Sb(III) on the goethite surface. Finally, calculated pH of the aqueous solution using MINTEQ2 agrees well with the measured pH (3.9 +/- 0.7; n = 30). At pH 4, the dominant Sb species in solution are Sb(OH)3 and HSbO2 which both likely adsorb as inner sphere complexes to the positively charged goethite surface.     

Gas electron diffraction study of the vapour over dimethylamine-gallane leading to an improved structure for dimeric dimethylamidogallane, [Me2NGaH2]2: a cautionary tale

Dimethylamine-gallane is relatively slow to decompose in a closed system and vaporises at low temperature primarily as Me2(H)N.GaH3 molecules which can be trapped in a solid Ar matrix and characterised by their IR spectrum. Under the conditions needed to secure a useful gas electron diffraction (GED) pattern, however, the vapour was found to consist of dimeric dimethylamidogallane molecules, [Me2NGaH2]2, formed from the secondary amine adduct by elimination of H2, and the most reliable structure for which has been determined. Salient structural parameters (r(hl) structure) were found to be: r(Ga-N) 202.6(2), r(Ga-H) 155.6(8), r(N-C) 148.0(3), r(C-H) 111.2(6) pm; Ga-N-Ga 90.7(1), C-N-C 109.3(5), N-C-H 109.9(10) and H-Ga-H 119.4(42) degrees.     

Thermodynamics of water octamer in a uniform electric field

We study the water octamer in a uniform electric field using the all-exchanges parallel tempering Monte Carlo method in the canonical ensemble. The heat capacity, quenched energy configurations, and the order parameter Q(4) are employed to understand the phase changes observed as a function of temperature and the strength of the applied electric field. At a low field strength of 0.1 V A(-1) a solidlike to liquidlike "melting" transition is detected. The corresponding heat capacity peak appears around 206 K, where Q(4) shows a significant change of slope. For E> or =0.5 V A(-1) such features are absent. However, at E=0.5 V A(-1) we find a solidlike to solidlike transition between cubic and extended structures around T approximately 25 K.