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Etablissement d'une approche perturbative pour le calcul d'observables de systemes a n electrons inhomogenes qui incorpore un algorithme pour le choix d'une approximation optimisee d'ordre zero dans le sens que des perturbations d'ordre superieur convergent rapidement et d'une maniere controlee

This is a collection of state-of-the-art reviews and original research work dealing with statistical and mathematical methodology relevant to the AIDS epidemic. It will be of interest and practical application to researchers and students in statistics, epidemology and public health.

C16H18N2·2 C12H4N4, C40H26N10, Mr = 646.7, crystallizes in space group P1̄ with a = 6.843(2), 6 = 7.845(3), c = 16.208(7) Å, α = 84.59(3), β = 81.63(3), γ = 75.75(3)°, V = 832.9 Å3 , Z = 1, dc = 1.29 Mgm-3 . Final weighted R = 0.107 based on 2894 reflections. The structure consists of stacks of TCNQ π-dimers with interplanar distances of 3.25(1) Å within a dimer and 3.54(1) A between dimers. The phenazine species do not form stacks and show no electronic interaction with adjacent E2P or TCNQ molecules.

A ϕ4 theory interacting with a (non-local) external potential strong enough to induce zero-mass modes is considered. Such a theory has served as a model for π condensation and, in solid state physics, to explain giant magnetic moments in metals. We show that such a zero-mass mode, in general, does not induce a phase transition to a condensed state because of temporal fluctuations produced by instantons which tend to restore initially broken symmetries. Numerical order of magnitude estimates for the relaxation time are given.

High-temperature or, equivalently, strong coupling expansions are established by applying heat-kernel techniques to the Green's functional of the Schrodinger picture of quantum field theory. The trace of the Green's functional is considered and a high-temperature expansion for the partition function is derived. It is shown that a simple, physically motivated rescaling of parameters leads to well-defined expressions. A generalized Thomas-Fermi expansion for the density of states is finally obtained.

A pharmacokinetic model is presented to describe the biotransformation of 2-butanol (2-OL) and its metabolites (2-butanone, 3-hydroxy-2-butanone, and 2, 3-butanediol) using in vivo experimental blood concentration. A flow limited model is developed to simulate 2-OL, 2-butanone (2-ONE), 3-hydroxy-2-butanone (3H-2B), and 2,3-butanediol (2,3-RD) blood concentrations in rats after oral administration of 2-OL. Assuming the only important site of 2-OL biotransformation is the liver, the tissues included are the liver and a volume of distribution, essentially body water in the case of 2-OL and its metabolites. A distribution coefficient is found to be necessary to describe the low concentration of 3H-2B in blood after administration of 2-OL. The need for this coefficient may be due to partitioning, binding, or altered transport rates from the liver. Inhibition of 2-ONE metabolism to 3H-2B by 2-OL has been included to explain a time delay in the appearance of 3H-2B after administration of 2-OL. Subsequent experimental verification confirms the mixed function oxidase inhibitory properties of 2-OL. The model is able to simulate blood concentrations and elimination of all four compounds after the oral administration of 2-OL. Additionally, the model also simulates the results obtained after i.v. administration of 3H-3B and 2,3-BD.

The Schrodinger picture of Quantum Field Theory is taken as the general framework for the formulation of a relativistic many-body theory. The main emphasis is put on many-electron systems within the scope of Quantum Electrodynamics. Relativistic mean-field theories are discussed and a perturbative scheme is introduced. Hamilton's principle is proposed as a criterion for the construction of mean-fields which allow for optimisation. Criteria for the choice of the latter are discussed.

A method to determine light-cone singularities of Green’s functions in quantum field theory is illustrated. From partial differential equations for then-loop contributions to a (e.g. time-ordered) field product we derive its light-cone singularities using a procedure contrived by Hadamard. We then calculate the leading nontrivial light-cone singularities of an arbitrary matrix element of the time-ordered product of two renormalized field operators in a ϕ3-theory. Our method can be applied to almost any «sensible» field theory.

Non-abelian gauge theories are written as the infinite gaugino mass limit of softly broken supersymmetric Yang-Mills theories. Their supersymmetry is exploited by effecting a Nicolai transformation. The average of gauge-invariant objects is then expressed in terms of abelian, transverse, i.e. physical, gauge fields irrespective of the gauge fixing originally chosen; the resulting perturbation theory is ghost-free. Seen from a practical standpoint the computational effort required in either traditional (with linear gauge) or this newly formulated perturbation theory is comparable.

The mobility of Li in β-LiAl formed by cathodic Li incorporation is drastically reduced by small amounts of Si in the parent Al; this is shown by 7Li NMR and electrochemical experiments. During long term cycling, the detrimental effect of lower Li mobility is compensated by the less spongy morphology of Si-doped electrodes. Addition of a few hundred ppm of 1,2-propanediol or methoxyethanol improves the 1st cycle Li-recovery from Si-doped β-LiAl in propylene carbonate electrolytes; paraffin oil is a nonreactive surfactant which slightly decreases the corrosion of β-LiAl.

Coupling constant flow equations are derived for supersymmetric scalar and gauge theories. Thes equations then serve as a starting point for the construction of Nicolai maps. From the fixed-point properties of the latter we establish a large class of stochastic functionals.

Atiyah-Patodi-Singer spectral η-invariants naturally appear as a polarisation charge in the Dirac theory of electrons in an external field. We propose a physical interpretation and discuss the resulting consequences, in particular for strong Coulomb fields. The η-invariant is seen to be discontinuous where zero-modes appear, for Z = Z0 (Z0 = 137 for pointlike Coulomb sources, Z0 > 137 for sources of nuclear extension). A consequence of this picture is that single electron orbitals should never “see” an effective charge exceeding Z0. We discuss this effect in QED.

The ground state of a (2+1) dimensional Georgi-Glashow model is discussed in a dilute monopole gas approximation. In addition to the Coulomb interaction of the latter, we include a Higgs force which is attractive irrespective of the sign of monopole charges. For (Higgs masses) −1 comparable to the mean free distance of monopoles we find a phase transition which is presumably of first order. Strings of monopoles dominate the clustering behaviour near the critical Higgs mass.

The authors calculated oscillator strengths for the principal series of the alkali atoms Li, Na and K from the g-Hartree equation. A mean field optimised by the procedure described in earlier publications is shown to yield a rapidly convergent expansion of the remaining correlation effects: the zero order already yields a substantial improvement over HF and DHF calculations and gives good agreement with experiment. It is noteworthy that the optimised g-Hartree single-particle potential for the excited states interpolates between purely V(N) and V(N-1) potentials.

A method for representing loop graphs as nonlocal $n$-particle couplings is described. An expansion in terms of soft momenta is then derived and used for the eikonalization of one-loop graphs. Loop contributions are shown to give considerable deviations from the Poisson distribution obtained in simple bremsstrahlung models. Average multiplicities and correlations are calculated.

A simple method is developed for fully describing gently curved surfaces with the aid of a computer, using a finite number of point measurements as input data. By means of this method, cut sections through a surface in various directions may be computed and graphically displayed. Similar surfaces, corresponding to a workpiece and its desired shape, may then be compared along a cut section on a command from an operator, resulting in the visual display of the section curves. This technique should prove useful in iterative forming of shallow panels (e.g., aircraft wing sections) and other applications involving gently curved surfaces.

We investigate analytic renormalization procedures for functional integrals, corresponding to field theories defined on compact manifolds, which arise, e.g., from string functionals of the Nambu-Schild-Eguchi type. Although these models belong to the nonrenormalizable class of quantum field theories, we prove finiteness for a rectangular string shape up to three-loop level, for circular boundary up to two-loop order, and for a variety of graphs in higher order, thus indicating that the result might hold in general. From the explicit calculation of the two-loop approximation we extract the first model-dependent corrections to the $q\overline{q}$ potential or the Casimir effect. The importance of dilation transformations for the properties of the renormalization procedure are investigated. We prove that under certain conditions, forced by symmetry properties, the association of finite values to divergent series is unique, independent of the regularization procedure.

Phenazine free E2P-TCNQ, C28H22N6, Mr = 442.53 is monoclinic, P21/c, a = 10.875(3), b = 14.679(4), c = 14.526(2) Å, β = 90.90(2)°, V = 2321.9 Å3 , Z = 4, dc = 1.27 Mgm-3 , the compound doped with 50% phenazine, E2P-P-(TCNQ)2 C52H34N12, Mr = 826.93, is triclinic, P1̅, a = 7.739(3), b = 15.899(6), c = 17.037(7) Å, α = 83.44(3), β = 88.34(3), γ = 83.19(3)°, V = 2067.7 Å, Z = 2, dc= 1.33 Mgm-3. E2P-TCNQ was refined to R = 0.066 for 1880 reflections. It consists of planar TCNQ anions and bent E2P cations (dihedral angle 17.7° along the line N-N) arranged in regular mixed stacks along c. The structure of E2P-P-(TCNQ)2 could be solved principally, but did not refine well (R = 0.165 for 1206 reflections). Regular segregated stacks of the phenazine and the TCNQ moieties are formed, and along the cationic stack the E2P+ cations and the neutral phenazine molecules alternate.

Relativistic and non-relativistic mean-field theories are discussed in the framework of quantum electrodynamics. g-Hartree mean-fields are derived using methods of the steepest descent which yields semi-classical expansions as a generalisation of asymptotic expansions of classical analysis. Our applications of the g-Hartree theory of atoms show that, in the examples considered, correlations are efficiently suppressed.

We discuss general notions of the regularisation and renormalisation of ground-state observables in quantum field theory. We evoke a theorem by Ramanujan to introduce the concept of the cut-off independent parts of vacuum observables and discuss their measurement and methods for their calculation. The role of Atiyah-Patodi-Singer spectral invariants in determining the vacuum structure of relativistic matter fields is illustrated.

We discuss non-perturbative aspects of the Floquet picture for the interaction of single mode strong laser fields with electrons. In numerical studies we show that this system stays adiabatic to a surprising degree: for smooth pulses, adiabaticity holds even for very short pulse-length (down to the order of 10 cycles) except for transitions at avoided crossings sharply located in time. The latter are seen to act as interferometers, a non-adiabatic pumping mechanism is proposed. Non-perturbative aspects of multi-photon transitions are clarified.

The authors analyse the atomic many-body effects associated with single-electron excitations within the g-Hartree framework: g values are determined which exactly reproduce inner- and outer-shell ionisation energies for the whole periodic table. Average g values are then used to compute physical observables for several channels within a mean-field analysis. The results obtained, particularly for large-Z atoms, give excellent agreement with experiment.

The general significance of adiabatic motion on quasi-energy surfaces for microwave ionisation of excited hydrogen atoms is investigated. It is shown that non-monotonic structures in the ionisation signal can be traced to near-degeneracies of coarse-grained quasi-energy surfaces of a few effective states. Further experimental implications are discussed.

Brillouin-Wigner perturbation theory, formulated in the Schrodinger picture of quantum field theory, is employed to derive a perturbative scheme for the scattering matrix for photoionisation and electron scattering reactions on atoms. It is important to note that the intermediate states appearing in this series are physical, i.e. fully correlated, eigenstates of the total Hamiltonian. The scheme is amenable to numerical analysis: The key point is the use of an “energy-optimised”g-Hartree basis which yields an efficient treatment of atomic correlations and makes Brillouin-Wigner and Rayleigh-Schrodinger perturbation theories coincide.

Generalising previous work on static strong Coulomb fields to the time-dependent case, we propose an alternative e+e--pair production mechanism relying on avoided crossing transitions between positive and negative energy states. The resulting essential independence on the details of the collision process nicely matches experimental findings.

It is pointed out that generalized Atiyah-Patodi-Singer η-invariants naturally appear in the thermodynamic potential describing the equilibrium properties of a localized system of relativistic interacting fermions. Under circumstances to be specified, externalU(1) gauge fields induce oscillating charge distributions which should be experimentally detectable for strong Coulomb fields produced by highly stripped large-Z atoms. Casimir energy shifts result be the same mechanism.

Two variational approaches are employed to attack the bound-state problem of a charged scalar field interacting with an Abelian gauge field. The resulting variational equations allow for a qualitative discussion of all possible physical situations. Boundary conditions play a crucial role in their interpretation. A specially developed perturbation scheme yields hydrogenlike spectra. ''Self-trapping'' solutions and configurations with complete screening of the long-range force are discussed and are shown not to be obtainable by perturbation for small coupling. Metastable states appear for strong coupling. (AIP)

Hydrogen-like energy levels of scalar and spinor QED are calculated using a Euclidean functional approach. The matter field is integrated over. Stationary points of the resulting effective action already yield a hydrogen like level structure for the energy. There is an interesting difference between the scalar and the spinor case. Whereas for spinors the conventional results are reproduced, the calculation for scalars yields a fine structure which is opposite in sign to the conventional one and has no critical singularity at Zα=1/2. The crucial structural difference between the two cases is that, for scalars, minima for the gauge invariant energy are not extrema of the action, even for time independent fields.

The basic parameters of the Joint European Torus (JET) machine are presented together with the reasons that guided their choice. The design principles followed during the conceptual phase are also described. Existing technology and modular design were used as far as possible, with a view to reducing the technological risk and to make the machine easily maintained. For each of the main components of the machine, the design and manufacturing techniques are reviewed. The operating history of the vacuum vessel and associated systems, such as the pumping and bakeout systems, is presented.

By explicitly introducing degrees of freedom for the electromagnetic field into the Hamiltonian for an N-electron system, we propose a variational procedure leading to mean fields different from the Hartree-Fock field. We show that g-Hartree equations result if the electromagnetic field is assumed to be in a coherent state. Since the solutions of these equations, the g-Hartree orbitals, are derived from a variational ansatz more general than the Hartree-Fock functional, we expect them to be particularly suitable to furnish a single-particle basis set for fast converging configuration interaction (CI) calculations. We report configuration interaction studies on the water molecule in a double zeta basis set employing various single-particle basis set transformations for the construction of the configuration state functions and investigate the convergence behaviour of the CI expansion explicitly. We find that the expansion in terms of g-Hartree orbitals receives substantially larger fractions of the total correlation energy in the case considered, if single excitations with respect to the mean field configuration are retained in the CI procedure.

A novel many-body approach, developed recently for atoms (the g-Hartree method), has been applied to the critical double-well problem in Ba+. A significant improvement over earlier ab initio approaches is demonstrated and correlations are shown to have a large effect. A correct choice of g leads to simultaneous agreement between theory and experiment for three different classes of data, namely, quantum defects, intensity variation and the spin-orbit splitting.

For pt.II see ibid., vol.15, p.4315 (1982). Relativistic and non-relativistic g-Hartree calculations of correlation energies for first-row atoms are presented. A discussion of the connection of various mean-field approaches is given.

summary A summary of P. D. En'ko's contributions to the theory of epidemics is presented. This work appeared 1889 in Russian in St. Petersburg. En'ko actually fitted his discrete time model to several epidemics of measles which he observed in boarding-schools in St. Petersburg. His remarkable contribution predates the Reed-Frost model by nearly forty years.

For pt.I see ibid., vol.15, no.23, p.4293 (1982). The one-parameter non-uniqueness of stationary electron configurations in atoms can be used to single out a mean-field equation yielding the exact total energy. This equation is Hartree-like and contains exchange terms with a strength parametrising electron correlations, radiative corrections and further perturbative contributions. A numerical study of this equation is presented for the relativistic case.

For pt.IV see Physica, vol.131, A, p.363 (1985). The g-Hartree method is adapted to the direct ab initio calculation of transition energies in atoms. For the elements He (Z=2), Li (Z=3), Be (Z=4), Ne (Z=10), Mg (Z=12) and Ar (Z=18) all ionisation energies have been computed and found to agree with available experimental data within the computational errors. The systematic aspect (which is a truly second-order determination of the optimal mean field and contains no semi-phenomenological partial-summation prescriptions such as the self-energy summations in the Schwinger-Dyson approach) is emphasised and is shown to match experimental data significantly better than second-order (in the same strict sense) Brueckner-Hartree-Fock calculations. A detailed comparison of the method with other published approximation schemes shows a systematic improvement over the results obtained in conventional many body theories.

The equilibrium properties of an inhomogeneous gas of interacting fermions are derived using methods of finite temperature quantum field theory. A Landau-type quasiparticle spectrum yielding the exact ground state energy or, at finite temperatures, the exact thermodynamic potential is constructed from the g-Hartree equations. The heat kernel expansion of Schrodinger operators is then used to express the Hohenberg-Kohn density functional as a series in the quasiparticle density which is asymptotic in the Thomas-Fermi limit. This series is systematically derived from the microscopic action and incorporates boundary effects in an unambiguous manner. The methods developed apply to a large class of field-theoretical models encompassing theories with Yukawa interactions.

Confidence in the extrapolation of animal toxicity data to humans can be enhanced by the application of pharmacokinetic concepts integrated with chronic toxicity data and knowledge of a chemical's mechanism(s) of toxicity. Basic pharmacokinetic concepts (including dose-dependent or Michaelis-Menten kinetics) and their relationship to the risk estimation process are discussed using vinyl chloride and styrene as specific examples. Species differences in metabolic rates must be considered in order to arrive at realistic estimates of human risk to vinyl chloride-induced liver angiosarcomas utilizing vinyl chloride toxicity data observed in rats. Because small animal species generally metabolize chemicals more rapidly than larger species on a body surface area basis, small animals should be more sensitive to chemicals (such as vinyl chloride) that exert their toxicities via the metabolic formation of toxic products. Inhaled styrene is a chemical whose clearance from the blood at low exposure levels in both rats and humans follows first-order kinetics. However, at higher exposure levels, the pharmacokinetic fate of styrene in rats is dose-dependent, suggesting a saturation of styrene metabolism. These data indicate that any extrapolation of observable toxicity at elevated exposure levels in rats to anticipated responses at lower levels in either rats or humans may be invalid. An integration of the foregoing concepts provides a sound scientific basis for the use of experimental animal data to predict the risk to humans from chemical exposure.