Cooling Process for Inelastic Boltzmann Equations for Hard Spheres, Part I: The Cauchy Problem

We develop the Cauchy theory of the spatially homogeneous inelastic Boltzmann equation for hard spheres, for a general form of collision rate which includes in particular variable restitution coefficients depending on the kinetic energy and the relative velocity as well as the sticky particles model. We prove (local in time) non-concentration estimates in Orlicz spaces, from which we deduce weak stability and existence theorem. Strong stability together with uniqueness and instantaneous appearance of exponential moments are proved under additional smoothness assumption on the initial datum, for a restricted class of collision rates. Concerning the long-time behaviour, we give conditions for the cooling process to occur or not in finite time. Mathematics Subject Classification (2000): 76P05 Rarefied gas flows, Boltzmann equation [See also 82B40, 82C40, 82D05].     

Comparison of the Active Species in the RF and Microwave Flowing Discharges of N<Subscript>2</Subscript> and Ar–20 %N<Subscript>2</Subscript>

We report a detailed comparison between RF and microwave (HF) plasmas of N₂ and Ar–20 %N₂ as well as in the corresponding afterglows by comparing densities of active species at nearly the same discharge conditions of tube diameter (5–6 mm), gas pressure (6–8 Torr), flow rate (0.6–1.0 slm) and applied power (50–150 W). The analysis reveals an interesting difference between the two cases; the length of the RF plasma (~25 cm) is measured to be much longer than that of HF (6 cm). This ensures a much longer residence time (10^?2 s) of the active species in the N₂ RF plasma [compared to that (10^?3 s) of HF], providing a condition for an efficient vibrational excitation of N₂(X, v) by (V–V) climbing-up processes, making the RF plasma more vibrationally excited than the HF one. As a result of high V–V plasma excitation in RF, the densities of the vibrationally excited N₂(X, v > 13) molecules are higher in the RF afterglow than in the HF afterglow. Destruction of N₂(X, v) due to the tube wall is estimated to be very similar between the two system as can be inferred from the γ_v destruction probability of N₂(X, v > 3–13) on the tube wall (2–3 × 10^?3 for both cases) obtained from a comparison between the density of N₂(X, v > 3–9) in the plasmas to that of the N₂(X, v > 13) in the long afterglows. Interestingly enough, densities of N-atoms and N₂(A) metastable molecules in the afterglow regions, however, are measured to be very similar with each other. The measured lower density of N₂ ⁺ ions than expected in the HF afterglow is rationalized from a high oxygen impurity in our HF setup since N₂ ⁺ ions are very sensitive to oxygen impurity .     

A Markov dilation for self-adjoint Schur multipliers

We give a formula for Markov dilation in the sense of Anantha- raman-Delaroche for real positive Schur multipliers on .

     

Estimating the temperature dependence of peptide folding entropies and free enthalpies from total energies in molecular dynamics simulations

The temperature dependence of thermodynamic quantities, such as heat capacity, entropy and free enthalpy, may be obtained by using well-known equations that relate these quantities to the enthalpy of the molecular system of interest at a range of temperatures. In turn, the enthalpy of a molecular system can be estimated from molecular dynamics simulations of an appropriate model. To demonstrate this, we have investigated the temperature dependence of the enthalpy, heat capacity, entropy and free enthalpy of a system that consists of a beta-heptapeptide in methanol and have used the statistical mechanics relationships to describe the thermodynamics of the folding/unfolding equilibrium of the peptide. The results illustrate the power of current molecular simulation force fields and techniques in establishing the link between thermodynamic quantities and conformational distributions.     

Operation of the proton wire in green fluorescent protein. A quantum dynamics simulation

A nuclear quantum dynamical simulation of the proton shuttle operating in the green fluorescent protein has been carried out on a high-quality, high-dimensionality potential energy surface describing the photoactive pipi* excited state, and including motion of both the three protons and of the donor and acceptor atoms of the hydrogen bonds in a closed proton wire. The results of the simulations show that proton transfer along the wire is essentially concerted, synchronous, and very fast, with a substantial amount of the green fluorescent species forming within several tens of femtoseconds. In this regard, analysis of the population of the fluorescent species indicates that at least two dynamical regimes are present for its formation. Within the first hundreds of femtoseconds, dynamics is very fast and impulsive. Later on, a slower pace of formation appears. It is discussed that the two largest decay times for the protonated chromophore reported experimentally (Chattoraj, M.; King, B. A.; Bublitz, G. U.; Boxer, S. G. Proc. Natl. Acad. Sci. U.S.A. 1996, 93, 8362-8367) might correspond to some irreversible process occurring after formation of the fluorescent species, rather than to cleavage of the chromophore's phenolic O-H bond.     

1-Phosphanorbornadienes in Enantioselective Catalysis

Recent developments in the chemisty of 1-phosphanorbornadienes are reviewed. Due to their bicyclic structure with a non-racemisable phosphorus atom at the bridgehead, they are ideally suited to enantioselective catalysis as transition metal complexes. Amongst this family, two enantiopure species play a special role, i.e., the so-called BIPNOR, a 2,2'-bis-1,1'-phosphanorbornadienyl ( 1 ), and a 2-formyl-1-phosphanorbornadiene ( 2 ). BIPNOR displays high enantioselectivities for a range of rhodium-catalyzed reactions. The carboxyaldehyde ( 2 ) is an ideal starting point for the synthesis of a series of enantiopure chelating 1-phosphanorbornadienes whose structures can be optimized for various catalytic enantioselective reactions. Examples of both approaches are given.     

The evolutionary ecology of technological innovations

Technological evolution has been compared to biological evolution by many authors over the last two centuries. As a parallel experiment of innovation involving economic, historical, and social components, artifacts define a universe of evolving properties that displays episodes of diversification and extinction. Here, we critically review previous work comparing the two types of evolution. Like biological evolution, technological evolution is driven by descent with variation and selection, and includes tinkering, convergence, and contingency. At the same time, there are essential differences that make the two types of evolution quite distinct. Major distinctions are illustrated by current specific examples, including the evolution of cornets and the historical dynamics of information technologies. Due to their fast and rich development, the later provide a unique opportunity to study technological evolution at all scales with unprecedented resolution. Despite the presence of patterns suggesting convergent trends between man‐made systems end biological ones, they provide examples of planned design that have no equivalent with natural evolution.     

Establishment of multivariate specifications for food commodities with discriminant partial least squares

A novel method for establishing multivariate specifications of food commodities is proposed. The specifications are established for discriminant partial least squares (DPLS) by setting limits on the predictions of the DPLS model together with Hotelling T² and square error of prediction (SPE). These limits can be tuned depending on whether type I error (i.e. a correct sample is declared out-of-specification) or type II error (i.e. an out-of-specification sample is declared within specifications) need to be minimized. The methodology is illustrated with a set of NIR spectra of Italian olive oils, corresponding to five regions and the class Liguria is the class of interest. The results demonstrate the possibility of establishing multivariate specification for olive oils from the Liguria region on the basis of spectral data obtaining type I and type II errors lower than 5%.