Decay Rates in Probability Metrics Towards Homogeneous Cooling States for the Inelastic Maxwell Model

We quantify the long-time behavior of solutions to the nonlinear Boltzmann equation for spatially uniform freely cooling inelastic Maxwell molecules by means of the contraction property of a suitable metric in the set of probability measures. Existence, uniqueness, and precise estimates of overpopulated high energy tails of the self-similar profile proved in ref. 9 are revisited and derived from this new Liapunov functional. For general initial conditions the solutions of the Boltzmann equation are then proved to converge with computable rate as t → ∞ to the self-similar solution in this distance, which metrizes the weak convergence of measures. Moreover, we can relate this Fourier distance to the Euclidean Wasserstein distance or Tanaka functional proving also its exponential convergence towards the homogeneous cooling states. The findings are relevant in the understanding of the conjecture formulated by Ernst and Brito in refs. 15, 16, and complement and improve recent studies on the same problem of Bobylev and Cercignani⁽⁹⁾ and Bobylev, Cercignani and one of the authors.⁽¹¹⁾     

Marine Sediments and Snow from Ross Sea Region (Antarctica) Dating by 210Pb Method

Abstract

²¹⁰Pb is widely used to determine accumulation rates in order to obtain a time scale in environmental samples. The most accurate method uses the determination of ²¹⁰Pb via its grand-daughter ²¹⁰Po by alpha spectrometry. Unfortunately this method requires a complex wet-chemistry procedure to achieve the separation of ²¹⁰Po from its matrix. In this work a simplified procedure for the chemical separation of ²¹⁰Po is proposed and applied to three marine sediment cores and a 10 m snow core collected in Antarctica. The calculated sedimentation rates for marine sediments range from 0.053 to 0.071 cm y^?1. The mean annual accumulation rate for the snow is 16.6 cm y^?1 w.e. A comparison with literature data in the same region is given.     

Boosting Conjugate Addition to Nitroolefins Using Lithium Tetraorganozincates: Synthetic Strategies and Structural Insights

We report the first transition metal catalyst- and ligand-free conjugate addition of lithium tetraorganozincates (R₄ZnLi₂) to nitroolefins. Displaying enhanced nucleophilicity combined with unique chemoselectivity and functional group tolerance, homoleptic aliphatic and aromatic R₄ZnLi₂ provide access to valuable nitroalkanes in up to 98 % yield under mild conditions (0 °C) and short reaction time (30 min). This is particularly remarkable when employing β-nitroacrylates and β-nitroenones, where despite the presence of other electrophilic groups, selective 1,4 addition to the C=C is preferred. Structural and spectroscopic studies confirmed the formation of tetraorganozincate species in solution, the nature of which has been a long debated issue, and allowed to unveil the key role played by donor additives on the aggregation and structure of these reagents. Thus, while chelating N,N,N’,N’-tetramethylethylenediamine (TMEDA) and (R,R)-N,N,N’,N’-tetramethyl-1,2-diaminocyclohexane (TMCDA) favour the formation of contacted-ion pair zincates, macrocyclic Lewis donor 12-crown-4 triggers an immediate disproportionation process of Et₄ZnLi₂ into equimolar amounts of solvent-separated Et₃ZnLi and EtLi.     

Superior Antibacterial Activity of Integral Lemon Pectin Extracted via Hydrodynamic Cavitation

Pectin extracted via hydrodynamic cavitation in water only from waste lemon peel and further isolated via freeze drying displays significant antibacterial activity against Staphylococcus aureus, a Gram positive pathogen which easily contaminates food. The antibacterial effect of the new IntegroPectin is largely superior to that of commercial citrus pectin, opening the way to advanced applications of a new bioproduct now obtainable in large amounts and at low cost from citrus juice industry's waste.     

The evaporation–condensation problem for a binary mixture of rarefied gases

Continuum Mechanics and Thermodynamics - Half space problems of evaporation and condensation for a binary mixture of inert gases are investigated when the dynamics is governed by a system of...