Contribution of particle-particle,hole-hole and particle-hole ring diagrams to the binding energies of finite nuclei

Two classes of diagrams, namely particle-particle, hole-hole (pp, hh) and particle-hole (ph) ring diagrams are summed for the nuclei ¹⁶O and ⁴⁰Ca, and their contributions to the ground-state energy shift ΔE of these nuclei is calculated. We find that hh and mixed diagrams (involving both pp and hh interactions) are not less important than the usual pp ladder diagrams which are summed in the standard Brueckner approach. We also study the convergence of these two classes of diagrams as the dimension of the model space involved is increased, and as a function of the residual interaction used. In evaluating these diagrams a transition-amplitude method is used. This is compared to the quasi-boson correlation expression for the ground-state energy due to particle-hole excitations and to an analogous correlation expression resulting from particle-particle and hole-hole excitations. Additionally we derive expressions for, and evaluate a subclass of these diagrams namely “TDA” ring diagrams, where unlike the usual pp, hh and ph diagrams, backward-folding graphs are excluded. We find that the backward-folding graphs are negligible for pp, hh ring diagrams and small for ph graphs. In the smallest model space considered for ⁴⁰Ca we also obtained the TDA ring diagram contributions via matrix inversion techniques which additionally allow us to study the relative importance of ph exchange graphs neglected in the ring-diagram formalism, and of cross TDA diagrams (i.e. TDA ring diagrams where both pp, hh, and ph interactions are allowed). Finally we study the uncertainties spurious effects introduce in ring-diagram calculations.     

A simple method for evaluating Goldstone diagrams in an angular momentum coupled representation

A simple and convenient method is derived for evaluating linked Goldstone diagrams in an angular momentum coupled representation. Our method is general, and can be used to evaluate any effective interaction and/or effective operator diagrams for both closed-shell nuclei (vacuum to vacuum linked diagrams) and open-shell nuclei (valence linked diagrams). The techniques of decomposing diagrams into ladder diagrams, cutting open internal lines and cutting of one-body insertions are introduced. These enable us to determine angular momentum factors associated with diagrams in the coupled representation directly, without the need for carrying out complicated angular momentum algebra. A summary of diagram rules is given.     

An algorithm for generating Goldstone and Bloch-Brandow diagrams

An algorithm for the automatic generation of Goldstone and Bloch-Brandow diagrams, needed for diagrammatic perturbation expansions, is described (the Bloch-Brandow diagrams are required for degenerate perturbations). Diagrams are produced in sets, each set consisting of members related by exchanges about interaction lines. Only distinct connected diagrams are generated. Applications are described.     

Protein crystal growth: An approach based on phase diagram determination

There is an increasing need to rationalize protein crystal growth, mostly carried out so far by trial-and-error. The phase rule gives the number of conditions necessary to specify the state of protein crystallization in equilibrium. Unsaturated and supersaturated regions are distinguished in phase diagrams. Examples of such diagrams for protein crystals are tabulated. To determine the phase diagrams reliably, the following items are discussed: (1) proper crystallization methods, (2) the length of time needed for establishing equilibrium, and (3) the importance of specifying the kind of solid state. Various crystallization methods are compared as to their effect on the solution system by using the phase diagrams, and the potential usefulness of the diagrams for crystallizing new proteins is discussed.     

Diagrammatic techniques in the Martin-Schwinger-Puff many-body theory

In an attempt to understand the connection between the Martin-Schwinger-Puff Green's function approach to the many-body problem and the diagrammatic approach of Brueckner and Goldstone, the perturbation expansion of the Green's function theory is studied. This expansion leads naturally to a representation of the theory by two sets of time-dependent diagrams—the kinetic energy diagrams and the potential energy diagrams. Rules are given for writing each time-dependent diagram as a sum of time-independent diagrams. Complications arise in the application of these rules to bubble diagrams. A special simple treatment of these diagrams is then proposed. There exists a simple relation between families of kinetic diagrams and potential diagrams. This relation stems from a rather general thermodynamic identity. Both the relation and its thermodynamic origin are described. As a consequence of these studies, some connections between the Brueckner-Goldstone theory and the Green's function theory are made.     

Investigation of the helicity of magnetic fields on the Sun within the Parker dynamo model

Construction of the butterfly diagrams for the magnetic helicity in several approximations of a Parker dynamo has been carried out. The diagrams are constructed both for the cases of efficient generation of the magnetic field (large dynamo numbers) and for the weak generation (a small dynamo number). The corresponding asymptotic solution to the solar dynamo is used in the first case. The butterfly diagrams for different values of the meridional circulation were studied due to this solution. The butterfly diagrams are constructed and based on the few-mode approximation, which is valid for moderate dynamo numbers. The issue of which butterfly diagram features are common in all these approximations and can be compared with observational data is discussed.     

A probabilistic analysis of the Walker-Vause model for liquid binary mixtures

A simple method to calculate the probability distribution for a binary fluid mixture is presented. The method is applid to the Walker-Vause binary liquid model and different temperature vs composition phase diagrams are obtained. These diagrams are obtained using catastrophe theory methods. Comparison with some experimental data are also discussed and a simplified model leading to closed-loop phase diagrams is considered.     

A FOLDED DIAGRAM METHOD FOR DERIVING AN ENERGY-INDEPENDENT NUCLEON-NUCLEON N-N POTENTIAL FROM MESON EXCHANGES (Ⅰ) THEORY

In this paper, a folded diagram method for deriving an energy-independent nucleon-nucleon (N-N) potential from meson exchanges is proposed. The potential obtained by this method contains not only the irreducible diagrams but also the mesonic folded diagrams. And it is proved that all stretched diagrams are not contained in this potential.     

Phase diagrams on an unsignalized intersection for the cases of different maximum velocities of vehicles

Using the cellular automaton traffic flow model, we investigate an unsignalized intersection which consists of two perpendicular one-lane roads. Both the roads cross at a point and the intersecting roads are cyclic. Each vehicle may pass or occupy the intersection where all the vehicles on both roads are not allowed to turn. Different from Ishibashi and Fukui’s studies in which the update is carried out for both roads in turn, the parallel update is proposed and its detailed rules are presented in our model. In this work, the cases of different maximum vehicle velocities on both roads are considered. Based on simulation results and the principle for constructing phase diagrams, phase diagrams are mapped out and their specific flow formulas for all the regions in the phase diagrams are obtained for various vehicle densities, which are seldom done in previous studies. One also finds that the topology of phase diagrams depends on the update rules of eastbound and northbound roads and their maximum velocities of vehicles.     

Dynamic properties of phase diagram in cylindrical ferroelectric nanotubes

The dynamic properties of phase diagrams in cylindrical ferroelectric nanotubes were investigated by utilizing the effective-field theory with correlations. Three different structure mechanisms are discussed by performing three different interaction functions. Effects of structure factors of the ferroelectric nanotubes are shown in phase diagrams. A linear relation between the crossover value of transverse field in inner-layer of nanotube and the exchange interaction are revealed. Moreover, for the first time, the phase transition characteristics are shown both in 2-D and 3-D phase diagrams by comparing the variations of the ferroelectric region and the morphology vividly. In comparison, results of the usual mean-field approximation are also presented in some phase diagrams, it suggest that the differential operator technique with correlations reduces some extent of the ferroelectric features of the ferroelectric nanotube.     

Construction of free-energy diagrams of amorphous alloys

Summary Free-energy diagrams of amorphous alloys are constructed using Miedema's semiempirical model of heats of formation. These diagrams account for the experimental glass-forming concentration range in binary alloys of transition metals. One of the main factors controlling glass formation is the elastic contribution to the heat of mixing of the solid solution phase. Free-energy diagrams of this kind are also useful for interpreting some characteristic processes occurring in amorphous systems, such as the spontaneous vitrification observed by Von Allmen and coworkers in several Ti-based and Nb-based alloys. The authors have agreed not to receive proofs for correction.     

Hydrodynamic Limit for an Evolutional Model of Two-Dimensional Young Diagrams

We construct dynamics of two-dimensional Young diagrams, which are naturally associated with their grandcanonical ensembles, by allowing the creation and annihilation of unit squares located at the boundary of the diagrams. The grandcanonical ensembles, which were introduced by Vershik [17], are uniform measures under conditioning on their size (or equivalently, area). We then show that, as the averaged size of the diagrams diverges, the corresponding height variable converges to a solution of a certain non-linear partial differential equation under a proper hydrodynamic scaling. Furthermore, the stationary solution of the limit equation is identified with the so-called Vershik curve. We discuss both uniform and restricted uniform statistics for the Young diagrams.     

Thermodynamics of binary solutions of the eutectic type with intermediate phases of constant composition

A consistent method is proposed for calculating the phase diagrams of binary solutions with intermediate phases of constant composition. The proposed method is based on the nonlinear transformations of the concentration axes and makes it possible to correctly reduce the calculation of the phase diagrams with intermediate phases to a sequence of phase diagrams of individual subsystems. The thermodynamics of binary solutions of the eutectic type with intermediate phases of constant composition is described using the proposed method within the framework of the generalized lattice model. The results of the calculations performed are compared with a number of phase diagrams of real binary systems.     

Bremsstrahlung contribution to deep inelastic electron-photon scattering

A comparison is made between the contributions of multiperipheral and bremsstrahlung diagrams to two-photon scattering in the deep inelastic regime. The bremsstrahlung diagrams are seen to dominate the cross section for high values of the scaling variable.     

Operator approach to analytical evaluation of Feynman diagrams

The operator approach to analytical evaluation of multiloop Feynman diagrams is proposed. We show that the known analytical methods of evaluation of massless Feynman integrals, such as the integration-by-parts method and the method of “uniqueness” (which is based on the star-triangle relation), can be drastically simplified by using this operator approach. To demonstrate the advantages of the operator method of analytical evaluation of multiloop Feynman diagrams, we calculate ladder diagrams for the massless ϕ ³ theory (analytical results for these diagrams are expressed in terms of multiple polylogarithms). It is shown how operator formalism can be applied to calculation of certain massive Feynman diagrams and investigation of the Lipatov integrable chain model. The text was submitted by the authors in English.     

Multi-loop Feynman integrals and conformal quantum mechanics

New algebraic approach to analytical calculations of D-dimensional integrals for multi-loop Feynman diagrams is proposed. We show that the known analytical methods of evaluation of multi-loop Feynman integrals, such as integration by parts and star-triangle relation methods, can be drastically simplified by using this algebraic approach. To demonstrate the advantages of the algebraic method of analytical evaluation of multi-loop Feynman diagrams, we calculate ladder diagrams for the massless φ³ theory. Using our algebraic approach we show that the problem of evaluation of special classes of Feynman diagrams reduces to the calculation of the Green functions for specific quantum mechanical problems. In particular, the integrals for ladder massless diagrams in the φ³ scalar field theory are given by the Green function for the conformal quantum mechanics.     

Padé approximants and realistic effective interactions

The convergence of the J = 0, T = 1 effective interaction for sd-shell nuclei is student in terms of separate summations of infinite subseries. It is suggested that first the subset of non-folded diagrams be separately summed to all orders and that the remaining, folded diagrams be grouped according to the number of folds and expressed in terms of the former sum of non-folded diagrams and its energy derivatives. The sum of non-folded diagrams is extrapolated from the lowest three orders using the Padé approximation, and encouraging results are obtained.     

Wave-vector diagrams for two-dimensional photonic crystals

Photonic crystals exhibit band gaps, meaning that electromagnetic fields cannot propagate in them for specific ranges of wavelengths and directions. The calculation of band structure diagrams has been intensively studied and is now well understood. In contrast to that, so-called wave-vector diagrams (i.e. dispersion surfaces, depicting the loci of all relevant wave vectors at a fixed wavelength) are less known and used. In principle, they show how the effective index of the structure depends on the direction of propagation. A method to calculate explicitly wave-vector diagrams for two-dimensional photonic crystals is derived which leads finally to quadratic eigenvalue problems. Results for square and triangular lattices are presented and some applications are discussed.