Many-Polaron States in the Holstein–Hubbard Model

A variational approach is proposed to study some properties of the adiabatic Holstein–Hubbard model which describes an assembly of fermionic charges interacting with a static atomic lattice. The sum of the electronic energy and the lattice elastic energy is proved to have minima with a many-polaron structure in a certain domain of model parameters. Our analytical work consists in expanding these energy minima from the zero electronic transfer limit which remarkably holds for a finite amplitude of the onsite Hubbard repulsion and for an unbounded lattice size.     

Pseudo-symplectic Runge-Kutta methods

Apart from specific methods amenable to specific problems, symplectic Runge-Kutta methods are necessarily implicit. The aim of this paper is to construct explicit Runge-Kutta methods which mimic symplectic ones as far as the linear growth of the global error is concerned. Such method of orderp have to bepseudo-symplectic of pseudosymplecticness order2p, i.e. to preserve the symplectic form to within ⊗(h ^2p )-terms. Pseudo-symplecticness conditions are then derived and the effective construction of methods discussed. Finally, the performances of the new methods are illustrated on several test problems.     

Formulation–composition map of a lecithin-based emulsion

Formulation–composition map is an interesting tool to predict the nature of an emulsion, stability, viscosity and nevertheless to decide the mixing protocol of its ingredients. Information based on optimum formulation (environmental conditions at which the affinity of an emulsifier for oil and for aqueous phase is same), which is depicted through hydrophilic–lipophilic deviation (HLD) concept, is necessary to make a formulation–composition map of an emulsion. In order to apply this concept in food emulsions, it is necessary to determine characteristic constants of each component of the system, i.e. the aqueous phase, the oil phase and the emulsifier at equilibrium. In this work formulation–composition map of a sunflower oil–water–lecithin system, based on the knowledge of phase behavior of lecithin at equilibrium and emulsification, was made. The shape of inversion line on formulation–composition map was not the classical stair type rather an almost vertical inversion line at water-fraction (f_w) near 0.20 was observed. It was supposed to be linked to the viscosity of oil phase which was 50 times the viscosity of aqueous phase. Additionally, emulsions were of oil-in-water (O/W) type for f_w higher than 0.20, but their viscosity and the drop size behavior with respect to salt concentration as formulation variable did not show the existence of transitional inversion line on formulation–composition map. Such map in advance can certainly facilitate the guidelines for dynamic emulsification.     

A pipecolic acid (Pip)‐containing dipeptide,Boc‐d‐Ala‐l‐Pip‐NHiPr

The title dipeptide, 1‐(tert‐butoxy­carbonyl‐d ‐alanyl)‐N‐iso­propyl‐l ‐pipecol­amide or Boc‐d ‐Ala‐l ‐Pip‐NHⁱPr (H‐Pip‐OH is pipecolic acid or piperidine‐2‐carboxylic acid), C₁₇H₃₁N₃­O₄, with a d –l heterochiral sequence, adopts a type II′β‐­turn conformation, with all‐trans amide functions, where the C‐terminal amide NH group interacts with the Boc carbonyl O atom to form a classical i+3 i intramolecular hydrogen bond. The C^α substituent takes an axial position [H^α (Pip) equatorial] and the trans pipecolamide function is nearly planar.     

Diffraction dissociation of nuclei in 450 GeV/c proton-nucleus collisions

Diffractive dissociation of nuclei (Be, Al, W) in collisions with 450 GeV/c protons,pApX, has been measured with the HELIOS spectrometer at the CERN Super Proton synchrotron. The dependence of the single-diffraction cross-section on the nuclear massA can be parametrized as _SD mb×A ^0.35±0.02, showing the peripheral nature of the process. The differential cross-section d_SD=(3.8±0.3)mb ×A ^0.35±0.02, is exponential with the slope parameter, increasing from 6.2±0.4 (GeV/c)^–2 for beryllium to 7.9±0.5 (GeV/c)^–2 for tungsten. The slope parameter also increases with increasing massM _X of the diffractively produced state. The rapidity, multiplicity, and transverse-momentum distributions of the particles of the diffractively produced stateX show a longitudinal phase-space population and are remarkably insensitive to the nuclear mass. This, together with theA ^1/3 dependence of _SD, suggests that the dominant process of nuclear diffractive excitation is the dissociation of single nucleons.Deceased     

Optimal focusing by spatio-temporal inverse filter. I. Basic principles

A focusing technique based on the inversion of the propagation operator relating an array of transducers to a set of control points inside a medium was proposed in previous work [Tanter et al., J. Acoust. Soc. Am. 108, 223-234 (2000)] and is extended here to the time domain. As the inversion of the propagation operator is achieved both in space and time, this technique allows calculation of the set of temporal signals to be emitted by each element of the array in order to optimally focus on a chosen control point. This broadband inversion process takes advantage of the singular-value decomposition of the propagation operator in the Fourier domain. The physical meaning of this decomposition is explained in a homogeneous medium. In particular, a definition of the number of degrees of freedom necessary to define the acoustic field generated by an array of limited aperture in a focal plane of limited extent is given. This number corresponds to the number of independent signals that can be created in the focal area both in space and time. In this paper, this broadband inverse-focusing technique is compared in homogeneous media with the classical focusing achieved by simple geometrical considerations but also with time-reversal focusing. It is shown that, even in a simple medium, slight differences appear between these three focusing strategies. In the companion paper [Aubry et al., J. Acoust. Soc. Am. 110, 48-58 (2001)] the three focusing techniques are compared in heterogeneous, absorbing, or complex media where classical focusing is strongly degraded. The strong improvement achieved by the spatio-temporal inverse-filter technique emphasizes the great potential of multiple-channel systems having the ability to apply completely different signal waveforms on each transducer of the array. The application of this focusing technique could be of great interest in various ultrasonic fields such as medical imaging, nondestructive testing, and underwater acoustics.     

A note on pseudo-symplectic Runge-Kutta methods

Aubry and Chartier introduced (1998) the concept of pseudo-symplecticness in order to construct explicit Runge-Kutta methods, which mimic symplectic ones. Of particular interest are methods of order (p, 2p), i.e., of orderp and pseudo-symplecticness order 2p, for which the growth of the global error remains linear. The aim of this note is to show that the lower bound for the minimal number of stages can be achieved forp=4 andp=5.     

Total synthesis of (-)-heptemerone B and (-)-guanacastepene E

A concise, stereoselective, and convergent total synthesis of the unnatural enantiomer of the neodolastane diterpenoid heptemerone B has been completed. Saponification of (-)-heptemerone afforded (-)-guanacastepene E. The absolute stereochemistry of (-)-heptemerone B was thus established as 5-(S), the same as (-)-guanacastepene E. The longest linear sequence of the synthesis comprises 17 (18) steps from simple known starting materials. Our general synthetic approach integrates a diverse set of reactions, including an intramolecular Heck reaction to create one quaternary stereocenter and a cuprate conjugate addition for the establishment of the other. The central seven-membered ring was closed with an uncommon electrochemical oxidation, whereas the five-membered ring was formed through ring-closing metathesis. The absolute configuration of the two key building blocks was established through an asymmetric reduction and an asymmetric ene reaction.     

Effect of mobile phase pH, aqueous-organic ratio, and buffer concentration on electrospray ionization tandem mass spectrometric fragmentation patterns: implications in liquid chromatography/tandem mass spectrometric bioanalysis

Liquid chromatography/tandem mass spectrometry (LC/MS/MS) based on selected reaction monitoring (SRM) is the standard methodology in quantitative analysis of administered xenobiotics in biological samples. Utilizing two SRM channels during positive electrospray ionization (ESI) LC/MS/MS method development for a drug compound containing two basic functional groups, we found that the response ratio (SRM1/SRM2) obtained using an acidic mobile phase was dramatically different from that obtained using a basic mobile phase. This observation is different from the well-established phenomenon of mobile phase affecting the [M+H](+) response, which is directly related to the amount of the [M+H](+) ions produced during the ionization. Results from follow-up work reported herein revealed that the MS/MS fragmentation patterns of four drug or drug-like compounds are affected not only by the pH, but also by the aqueous-organic ratio of the mobile phase and the buffer concentration at a given apparent pH. The observed phenomenon can be explained by invoking that a mixture of [M+H](+) ions of the same m/z value for the analyte is produced that is composed of two or more species which differ only in the site of the proton attachment, which in turn affects their MS/MS fragmentation pattern. The ratio of the different protonated species changes depending on the pH, aqueous-organic ratio, or ionic strength of the mobile phase used. The awareness of the mobile phase dependency of the MS/MS fragmentation pattern of precursor ions of identical m/z value will influence LC/MS/MS-based bioanalytical method development strategies. Specifically, we are recommending that multiple SRM transitions be monitored during mobile phase screening, with the MS/MS parameters used for each SRM optimized for the composition of the mobile phase (pH, organic percentage, and ionic strength) in which the analyte elutes.     

tert‐Butyl (6S)‐4‐hydroxy‐6‐isobutyl‐2‐oxo‐1,2,5,6‐tetra­hydropyridine‐1‐carboxyl­ate and tert‐butyl (4R,6S)‐4‐hydroxy‐6‐iso­butyl‐2‐oxopiperidine‐1‐carboxyl­ate

X‐ray studies reveal that tert‐butyl (6S)‐6‐iso­butyl‐2,4‐dioxo­piperidine‐1‐carboxyl­ate occurs in the 4‐enol form, viz. tert‐butyl (6S)‐4‐hydroxy‐6‐iso­butyl‐2‐oxo‐1,2,5,6‐tetra­hydropyri­dine‐1‐carboxyl­ate, C₁₄H₂₃NO₄, when crystals are grown from a mixture of di­chloro­methane and pentane, and has an axial orientation of the iso­butyl side chain at the 6‐position of the piperidine ring. Reduction of the keto functionality leads predominantly to the corresponding β‐hydroxy­lated δ‐lactam, tert‐butyl (4R,6S)‐4‐hydroxy‐6‐iso­butyl‐2‐oxo­piperidine‐1‐car­boxyl­ate, C₁₄H₂₅NO₄, with a cis configuration of the 4‐hydroxy and 6‐iso­butyl groups. The two compounds show similar molecular packing driven by strong O—H⋯O=C hydrogen bonds, leading to infinite chains in the crystal structure.