Confined systems and the modified virial theorem from semiclassical considerations

We show that two simple semiclassical strategies, one based on the Wilson–Sommerfeld rule and the other on the uncertainty principle, yield the exact modified form of the virial theorem for confined systems. An alternative, easier quantum mechanical route to arrive at this result is also sketched. Pilot calculations on confined oscillators reveal decisive trends. © 2004 Wiley Periodicals, Inc. Int J Quantum Chem, 2005     

Origin of the Landau-Lifshitz hydrodynamic fluctuations in nonequilibrium systems and a new method for reducing the Boltzmann equation

The Landau-Lifshitz fluctuating fluxes in fluctuating hydrodynamics are derived from the deterministic Boltzmann equation with the aid of a reduction method developed by Fujisaka and Mori. Thus it is shown that the hydrodynamic fluctuations innonequilibrium systems are generated by the reduction of variables from the-space distribution function to its five momentum moments, i.e., the hydrodynamic variables. This differs from the Bixon-Zwanzig and Fox-Uhlenbeck theories, in which the Landau-Lifshitz fluctuating fluxes are derived from the molecular fluctuating force in thestochastic Boltzmann-Langevin equation, which is, however, negligible in nonequilibrium systems. Thus the present method improves the Chapman-Enskog reduction method so as to include the hydrodynamic fluctuations generated by the reduction of variables.Supported in part by the Scientific Research Fund of the Ministry of Education.     

Methodology for the calculation of the potential of mean force for a cation-pi complex in water.

We report potential of mean force (PMF) calculations on the interaction between the p-sulfonatocalix[4]arene and a monovalent cation (Cs(+)). It has been recently shown from microcalorimetry and (133)Cs NMR experiments that the association with Cs(+) is governed by favourable cation-pi interactions and is characterized by the insertion of the cation into the cavity of the macrocycle. We show that the PMF calculation based upon a classical model is not able to reproduce both the thermodynamic properties of association and the insertion of the cation. In order to take into account the different contributions of the cation-pi interactions, we develop a new methodology consisting of changing the standard PMF by an additional contribution resulting from quantum calculations. The calculated thermodynamic properties of association are thus in line with the microcalorimetry and (133)Cs NMR experiments and the structure of the complex at the Gibbs free-energy minimum shows the insertion of the cation into the cavity of the calixarene.     

An implicit function theorem: Comment

In Ref. 1, Jittorntrum proposed an implicit function theorem for a continuous mappingF:R ⁿ ×R ^m R ⁿ, withF(x ⁰,y ⁰)=0, that requires neither differentiability ofF nor nonsingularity of _x F(x ⁰,y ⁰). In the proof, the local one-to-one condition forF(·,y):A R ⁿ R ⁿ for ally B is consciously or unconsciously treated as implying thatF(·,y) mapsA one-to-one ontoF(A, y) for ally B, and the proof is not perfect. A proof can be given directly, and the theorem is shown to be the strongest, in the sense that the condition is truly if and only if.     

A central limit theorem for age- and density-dependent population processes

Consider a population consisting of one type of individual living in a fixed region with area A. In [8], we constructed a stochastic population model in which the death rate is affected by the age of the individual and the birth rate is affected by the population density P_A(t), i.e., the population size divided by the area A of the given region. In [8], we proposed a continuous deterministic model which in general is a nonlinear Volterra type integral equation and proved that under appropriate conditions the sequence P_A(t) would converge to the solution P(t) of our integral equation in the sense that

$\text{lim}\text{→∞}\text{P}\text{sup}\text{0?s?t}\text{|P}{}_{\mathrm{A}}\text{(s) ? P(s)|>ε}\text{=0}\text{for every}\text{ε > 0}$

.In this paper, we obtain a “central limit theorem” for the random element √A(P_A(t)?P(t)). We prove that under appropriate conditions √A(P_A(t)?P(t)) will converge to a Gaussian process. (See Theorem 3.4 for the explicit formula of this Gaussian process.)     

Structure and dynamics of hydrated NH(4) (+): an ab initio QM/MM molecular dynamics simulation

A combined ab initio quantum mechanical/molecular mechanical (QM/MM) molecular dynamics simulation has been performed to investigate solvation structure and dynamics of NH(4) (+) in water. The most interesting region, the sphere includes an ammonium ion and its first hydration shell, was treated at the Hartree-Fock level using DZV basis set, while the rest of the system was described by classical pair potentials. On the basis of detailed QM/MM simulation results, the solvation structure of NH(4) (+) is rather flexible, in which many water molecules are cooperatively involved in the solvation shell of the ion. Of particular interest, the QM/MM results show fast translation and rotation of NH(4) (+) in water. This phenomenon has resulted from multiple coordination, which drives the NH(4) (+) to translate and rotate quite freely within its surrounding water molecules. In addition, a "structure-breaking" behavior of the NH(4) (+) is well reflected by the detailed analysis on the water exchange process and the mean residence times of water molecules surrounding the ion.     

Ion Association in Lanthanide Chloride Solutions

A better understanding of the solution chemistry of the lanthanide (Ln) salts in water would have wide ranging implications in materials processing, waste management, element tracing, medicine and many more fields. This is particularly true for minerals processing, given governmental concerns about lanthanide security of supply and the drive to identify environmentally sustainable processing routes. Despite much effort, even in simple systems, the mechanisms and thermodynamics of Ln^III association with small anions remain unclear. In the present study, molecular dynamics (MD), using a newly developed force field, provide new insights into LnCl₃(aq) solutions. The force field accurately reproduces the structure and dynamics of Nd³⁺, Gd³⁺ and Er³⁺ in water when compared to calculations using density functional theory (DFT). Adaptive-bias MD simulations show that the mechanisms for ion pairing change from dissociative to associative exchange depending upon cation size. Thermodynamics of association reveal that whereas ion pairing is favourable, the equilibrium distribution of species at low concentration is dominated by weakly bound solvent-shared and solvent-separated ion pairs, rather than contact ion pairs, reconciling a number of contrasting observations of Ln^III–Cl association in the literature. In addition, we show that the thermodynamic stabilities of a range of inner sphere and outer sphere coordination complexes are comparable and that the kinetics of anion binding to cations may control solution speciation distributions beyond ion pairs. The techniques adopted in this work provide a framework with which to investigate more complex solution chemistries of cations in water.     

通过脱碳控制全球平均温度

Establishing a reliable method to predict the global mean temperature (T_e) is of great importance because CO₂ reduction activities require political and global cooperation and significant financial resources. The current climate models all seem to predict that the earth's temperature will continue to increase, mainly based on the assumption that CO₂ emissions cannot be lowered significantly in the foreseeable future. Given the earth's multifactor climate system, attributing atmospheric CO₂ as the only cause for the observed temperature anomaly is most likely an oversimplification; the presence of water (H₂O) in the atmosphere should at least be considered. As such, T_e is determined by atmospheric water content controlled by solar activity, along with anthropogenic CO₂ activities. It is possible that the anthropogenic CO₂ activities can be reduced in the future. Based on temperature measurements and thermodynamic data, a new model for predicting T_e has been developed. Using this model, past, current, and future CO₂ and H₂O data can be analyzed and the associated T_e calculated. This new, esoteric approach is more accurate than various other models, but has not been reported in the open literature. According to this model, by 2050, T_e may increase to 15.5 ℃ under "business-as-usual" emissions. By applying a reasonable green technology activity scenario, T_e may be reduced to approximately 14.2 ℃. To achieve CO₂ reductions, the scenario described herein predicts a CO₂ reduction potential of 513 gigatons in 30 years. This proposed scenario includes various CO₂ reduction activities, carbon capturing technology, mineralization, and bio-char production; the most important CO₂ reductions by 2050 are expected to be achieved mainly in the electricity, agriculture, and transportation sectors. Other more aggressive and plausible drawdown scenarios have been analyzed as well, yielding CO₂ reduction potentials of 1051 and 1747 gigatons, respectively, in 30 years, but they may reduce global food production. It is emphasized that the causes and predictions of the global warming trend should be regarded as open scientific questions because several details concerning the physical processes associated with global warming remain uncertain. For example, the role of solar activities coupled with Milankovitch cycles are not yet fully understood. In addition, other factors, such as ocean CO₂ uptake and volcanic activity, may not be negligible.     

Hypersurfaces of prescribed mean curvature enclosing a given body

Given a smooth domain Ω in ℝ ^m+1 with compact closure and a smooth integrable functionh: ℝ ^m+1→ℝ satisfyingh(x)≥H _∂Ω (x) on ∂Ω whereH _∂ω denotes the mean curvature of ∂Ω calculated w.r.t. the interior unit normal we show that there is a setA⊂ℝ ^m+1 with the properties andH _∂A=h on ∂A.     

Lipschitzian inverse functions,directional derivatives,and applications inC 1,1 optimization

The paper shows that Thibault's limit sets allow an iff-characterization of local Lipschitzian invertibility in finite dimension. We consider these sets as directional derivatives and extend the calculus in a way that can be used to clarify whether critical points are strongly stable inC ^1,1 optimization problems.Many fruitful discussions with colleagues D. Klatte and K. Tammer as well as with H. Th. Jongen and F. Nozicka have influenced the present investigations in a very constructive manner. For the original papers concerning the sets f(x; u), the author is indebted to Prof. L. Thibault.