Testing Dirac-Brueckner models in collective flow of heavy-ion collisions

We investigate differential in-plane and out-of-plane flow observables in heavy-ion reactions at intermediate energies from 0.2-2 AGeV within the framework of relativistic BUU transport calculations. The mean field is based on microscopic Dirac-Brueckner-Hartree-Fock (DB) calculations. We apply two different sets of DB predictions, those of ter Haar and Malfliet and more recent ones from the Tübingen group, which are similar in general but differ in details. The latter DB calculations exclude spurious contributions from the negative-energy sector to the mean field which results in a slightly softer equation of state and a less repulsive momentum dependence of the nucleon-nucleus potential at high densities and high momenta. For the application to heavy-ion collisions in both cases non-equilibrium features of the phase space are taken into account on the level of the effective interaction. The systematic comparison to experimental data favours the less repulsive and softer model. Relative to non-relativistic approaches one obtains larger values of the effective nucleon mass. This produces a sufficient amount of repulsion to describe the differential flow data reasonably well. Received: 8 January 2001 / Accepted: 12 November 2001     

Directed and elliptic flow in 197Au+197Au at intermediate energies

Directed and elliptic flow for the ¹⁹⁷Au+¹⁹⁷Au system at incident energies between 40 and 150 MeV per nucleon has been measured using the INDRA 4π multi-detector. For semi-central collisions, the excitation function of elliptic flow shows a transition from in-plane to out-of-plane emission at around 100 MeV per nucleon. The directed flow changes sign at a bombarding energy between 50 and 60 MeV per nucleon and remains negative at lower energies. Molecular dynamics calculations (CHIMERA) indicate sensitivity of the global squeeze-out transition on the σ _NN and demonstrate the importance of angular momentum conservation in transport codes at low energies.     

Baryon flow at SIS energies and beyond

We calculate the baryon flow P_x/A(y) in the energy range from 0.25 to 4.0A GeV in a relativistic transport model for Ni + Ni and Au + Au collisions employing various models for the baryon self-energies. We find that to describe the flow data of the FOPI Collaboration above 1A GeV the strength of the vector potential has to be reduced at high relative momentum or at high density. The latter phenomenon leads to a softening of the nuclear equation of state at high density.     

Out-of-plane emission of nuclear matter in Au+Au collisions between 100 and 800 AMeV

We present new experimental results concerning the azimuthal distributions of proton-likes, light and intermediate mass fragments at midrapidity for Au(100–800 A MeV) +Au collisions measured with the FOPI phase-I detector at GSI in Darmstadt. The azimuthal distributions are investigated as a function of the collision centrality, the incident energy, the fragment charge and transverse momentum. The azimuthal anisotropy is maximum for impact parameters around 7 fm. Intermediate mass fragments present a stronger out-of-plane emission signal than light fragments and a saturation is reached for Z ⩾ 4. The azimuthal anisotropy increases with the fragment transverse momentum and decreases as the incident energy increases. The azimuthal anisotropy of Z = 2 particles investigated as a function of the scaled fragment transverse momentum follows an universal curve for bombarding energies between 250–800 A MeV. A signature for a transition from in-plane to out-of-plane emission is evidenced at the lowest beam energies.     

Proton emission in α-induced reactions at 43 MeVnucleon

Inclusive proton spectra and proton-proton correlations have been measured from α + ⁵⁸Ni and α + ¹⁹⁷Au reactions at energies E_α = 100 MeV and 172 MeV. The inclusive spectra are compared to results of a simple model assuming local equilibration of the energy transferred to the target nucleons. This model describes the energy and angular dependence sufficiently well at angles ? 40°. Due to finite number effects, it also explains the occurrence of differences between in-plane to out-of-plane pp correlations. In addition, the measured coincidences indicate contributions from quasifree pp scattering.     

Many-body approximation scheme beyond GW

We explore the combination of the extended dynamical mean field theory (EDMFT) with the GW approximation (GWA); the former sums the local contributions to the self-energies to infinite order in closed form and the latter handles the nonlocal ones to lowest order. We investigate the different levels of self-consistency that can be implemented within this method by comparing to the exact quantum Monte Carlo solution of a finite-size model Hamiltonian. We find that using the EDMFT solution for the local self-energies as input to the GWA for the nonlocal self-energies gives the best result.     

High accuracy measurement of unsteady flows using digital particle image velocimetry

The analysis of digital PIV data, either derived from CCD technology or through film and then scanned, typically involves two quantization steps: spatial and intensity quantization. The all-optical systems do not introduce these sources of error. For systems which make use of digital technology however, it is of crucial importance to have reliable error bounds and a sufficiently accurate estimate of particle position, taking into consideration both types of quantization. The accuracy demanded by aerodynamicists from PIV has been a major barrier to its practical application in the past. The more recent approach of using the Gaussian profile of the particle images to yield sub-pixel accurate position estimates has resulted in robust measurements being taken to an accuracy of 1/10th pixel and 1% in velocity for the in-plane velocity, in hostile industrial environments. A major problem for 3D PIV estimation has historically been that the out-of-plane velocity error was of the order of 3–4 times larger than in-plane. The out-of-plane velocity estimate can be derived from the change in the ratio of amplitude to variance—known as the depth factor—of the Gaussian form, as a particle traverses the beam profile. However, such measurements are crucially dependent not only on an accurate position estimate but also on an equally accurate estimate of the amplitude and variance. The accuracy of the Gaussian profile fit using a Nelder–Meade optimisation method as developed until now however, is not capable of providing the required accuracies. Therefore, this paper presents a development of the “locales” approach to position estimation to achieve the desired objective of high accuracy PIV measurements. This approach makes use of the fact that by considering all the possible digital representations of the Gaussian particle profile, regions of indistinguishable position can be derived. These positions are referred to as “locales”. By considering the density, distribution, and shape of these locales, the available precision can be estimated and an accurate (no worse than 0.5% error for a typical PIV image) in-plane velocity, accuracy can be obtained; while at the same time providing estimates of the depth factor with an error of approximately 0.8%. This paper describes the implementation of an efficient algorithm to provide velocity estimates to an accuracy of at least 0.5% in-plane, together with a discussion of the required constraints imposed on the imaging. The method was validated by creating a synthetic PIV image with CCD-type noise. The flow being analysed is that of flow past the near wake of a cylinder at a Reynolds Number of 140,000. This image was then analysed with the new method and the velocity estimates compared to the CFD data for a range of signal-to-noise ratios (SNR). For a realistic SNR of 5, the accuracy of the method is confirmed as being at least 0.5% in-plane. Finally, the algorithm was used to map an experimental transonic flow field of the stator trailing edge region of a full-size annular cascade with an estimated error of 0.5%. The experimental results are found to be in good agreement with a previously reported steady state viscous calculation and PIV mapping.     

SUPER AND COMBINATORIAL HARMONIC RESPONSE OF FLEXIBLE ELASTIC CABLES WITH SMALL SAG

The paper deals with the analysis of cables in stayed bridges and TV-towers, where the excitation is caused by harmonically varying in-plane motions of the upper support point with the amplitude U. Such cables are characterized by a sag-to-chord-length ratio below &0uml;02, which means that the lowest circular eigenfrequencies for in-plane and out-of-plane eigenvibrations, ω₁and ω₂, are closely separated. The dynamic analysis is performed by a two-degree-of-freedom modal decomposition in the lowest in-plane and out-of-plane eigenmodes. Modal parameters are evaluated based on the eigenmodes for the parabolic approximation to the equilibrium suspension. Superharmonic components of the ordern , supported by the parametric terms of the excitation and the non-linear coupling terms, are registered in the response for circular frequency ω?ω₁/n. At moderate U, the cable response takes place entirely in the static equilibrium plane. At larger amplitudes the in-plane response becomes unstable and a coupled whirling superharmonic component occurs. In the paper a first order perturbation solution to the superharmonic response is performed based on the averaging method. For ω?(m/n)ω₁, m<n, the geometrical non-linear restoring forces gives rise to a substantial combinatorial harmonic component with the circular frequency (n/m)ω. Both entirely in-plane and coupled in-plane and out-of-plane responses occur. Based on an initial frequency analysis of the response, an analytical model for these vibrations is formulated with emphasis on superharmonics of the order n=3 and combinatorial harmonics of the order (n, m)=(3,2). All analytical solutions have been verified by direct numerical integration of the modal equations of motion.     

Dynamics of a monolayer of nitrogen physisorbed on graphite

The dynamics of a crystalline monolayer of molecular nitrogen physisorbed on the basal plane of graphite, which was assumed to be rigid, has been studied by means of lattice and molecular dynamics. The study focusses mainly on the registered solid in which the centres of mass adopt the √3 × √3 R30° structure, but some results are also reported for denser monlayers, including one where the centre-of-mass lattice is non-triangular. Harmonic dispersion curves are reported for two models of the N₂-N₂ interaction combined with Steele's representation of the molecule-surface interaction. The one-phonon density of states is given for one of the models. Molecular dynamics results for the same model at two temperatures, 5 and 17 K, are analysed in terms of the dynamical structure factor, and one-phonon approximation to it, and the out-of-plane motions are treated in a manner similar to the one-phonon approximation. In-plane and out-of-plane motions are largely decoupled in all cases studied, and the in-plane motions show evidence of marked anharmonicity. The out-of-plane motions appear to exhibit Fermi-Pasta-Ulam type recurrences, although this is not analysed in detail.     

Thickness dependence of magnetic anisotropic properties of FeCoNd films

The magnetic FeCoNd films with thickness (t) from 50 to 166 nm were fabricated by RF magnetron co-sputtering at ambient condition. The amorphous structures of all of the films were investigated by X-ray diffraction and transmission electron microscopy. A spin reorientation transition from in-plane single domain state to out-of-plane stripe domain state was observed as a function of t. When t is below a critical thickness, magnetic moments lie in the film plane corresponding to in-plane single domain state because of the strong demagnetization energy. However, when t is increased, out-of-plane stripe domain structure was developed due to a dominated perpendicular magnetic anisotropy. Scanning electron microscopy data indicate that the perpendicular anisotropy, which is responsible for the formation of stripe domains, may result from the shape effect of the columnar growth of the FeCo grains.     

Transport theory for quantum crystals

A correlation function approach is developed to treat non-equilibrium phenomena of quantum crystals at low frequency and long wavelength within the renormalized harmonic approximation (RHA). The derivation of the transport equations is carried out by studying the hierarchy of equations of motion for the retarded Green's functions of a pure, nonprimitive, nonionic, anharmonic lattice. Using a factorization technique to take into account the most important terms due to the particle fluctuations and the leading contributions to the hydrodynamic singularities of the phonon self-energy, we find a differential equation for the displacement field and a generalized transport equation for the phonon gas. The microscopic RHA expressions for the local temperature, the local heat density and the energy current are derived; the quasiparticle parameters (elastic constants, generalized Grüneisen parameters, quasiparticle interaction) entering the equations of motion are shown to be consistent with the RHA. In the hydrodynamic regime the general equations are reduced to two coupled differential equations for the lattice deformations and for the local temperature. Then only the displacement-displacement, the displacement-energy density and the energy density-energy density correlation functions show macroscopic fluctuations; for these functions thermodynamical sum-rules are derived.     

Elliptic flow in an integrated (3+1)d microscopic + macroscopic approach with fluctuating initial conditions

The elliptic flow excitation function calculated in a Boltzmann approach with an intermediate hydrodynamic stage for heavy-ion reactions from GSI-SIS to the highest CERN-SPS energies is discussed in the context of the experimental data. The specific setup with initial conditions and freeze-out from a non-equilibrium transport model allows for a direct comparison between ideal fluid dynamics and hadronic transport simulations. At higher SPS energies, where the pure transport calculation cannot account for the high elliptic flow values, the smaller mean free path in the hydrodynamic evolution leads to higher elliptic flow values. The lower mean free path leads to higher pressure gradients in the early stage and as a consequence to higher elliptic flow values even without a phase transition. Special emphasis is put on the influence of the initial conditions on the results of the hybrid model calculation. Event-by-event fluctuations are directly taken into account via event-wise non-equilibrium initial conditions generated by the primary collisions and string fragmentations in the microscopic UrQMD model. This leads to non-trivial velocity and energy density distributions for the hydrodynamical initial conditions. Due to the more realistic initial conditions and the incorporated hadronic rescattering the results are in line with the experimental data almost over the whole energy range from E _lab=2–160A GeV.     

A novel approach to high-sensitivity grating interferometry

The authors propose a new approach for obtaining information about in-plane and out-of-plane displacements of an object tested using high-sensitivity grating interferometry. The interferences of each of the specimen grating diffraction orders with a reference beam are recorded separately. Computer addition and subtraction of the phase functions calculated from the interferograms give the in-plane and out-of-plane displacement values, respectively. The authors present their experimental work, and then compare their results with those obtained using a conventional grating interferometry approach.     

Components of collective flow and azimuthal distribution in40Ar+27Al collision with BUU method

The in-plane, out-of-plane and longitudinal components of the collective flow are extracted from the BUU simulation for⁴⁰Ar+²⁷Al collision in intermediate energy domain. It is found that the in-plane collective flow changes from a negative value to a positive value around 85 MeV/u. The flow angles are estimated by the in-plane and longitudinal components of the collective flow, and the rotational behavior in addition to the inplane flow is also found by the asymmetry of the azimuthal distribution in the calculation.     

Orthotropic material properties of the gerbil basilar membrane

In this paper, two sets of experimental results to extract the two effective elastic moduli, the effective shear modulus, and the effective Poisson's ratio for the gerbil cochlear partition are analyzed. In order to accomplish this, a geometrically nonlinear composite orthotropic plate model is employed. The model is used to predict both out-of-plane and in-plane motion of the partition under a static finite area distributed load. This loading condition models the small, but finite size, probe tips used in experiments. Both in-plane and out-of-plane motion are needed for comparison with recent experimental results. It is shown that the spatial decay rate (the space constant) for the in-plane deflection is different than for the out-of-plane deflection, which has a significant effect on the derived partition properties. The size of the probe tip is shown to have little influence on the results. Results are presented for two types of boundary conditions. Orthotropy ratios determined from the experimental data are found to vary with longitudinal position and choice of boundary conditions. Orthotropy ratios (the ratio of the two elastic moduli) are in the range of 65 close to the base to 10 in the upper middle turn of the cochlea.     

The ridge as a shadowing effect in hydrodynamics

The aim of this work is to clarify the origin of the in-plane/out-of-plane effect, in the two-particle correlation function, computed with the NexSPheRIO code, in Au + Au collisions at 200 AGeV. We show that such an effect can be understood in terms of the shadowing effect caused by a peripheral high-energydensity tube.     

Low-dimension self-interstitial diffusion in α-Zr

The mobility of self-interstitials in α-zirconium (α-Zr) is studied with molecular dynamic (MD) and molecular static (MS) simulations, using Ackland’s many-body inter-atomic potential. The basal crowdion configuration is found to be the ground state. Four types of diffusion jumps can be identified via MS, in-plane in-line, in-plane off-line, out-of-plane in-line and out-of-plane off-line. The in-plane migration is dominated by one-dimensional crowdion motion along the [110] directions, interrupted from time to time by off-line or out-of-plane jumps. Based on the MS results, the activation energies and pre-exponentials for the diffusion processes are determined by fits to the Arrhenius plots of D_c and D_a. The diffusional anisotropy factor D_c/D_a is also obtained, and compares well with experimental results. The mean frequency of each type of jumps is then found using Monte Carlo simulation, and is reported as a function of temperature. The mean lifetime and mean free path of the one-dimensional mobility are then obtained. The 1-D mean free path is found to be unimportant for sink separations involved under the usual irradiation damage conditions. Received: 4 March 2002 / Accepted: 4 April 2002 / Published online: 10 September 2002 RID="*" ID="*"Corresponding author. E-mail: Chung.Woo@polyu.edu.hk