Measurements of niobium absorption spectra in plasmas with nearly full M-shell configurations

A systematic study has been carried out on the changes in the L-shell absorption structure of niobium as a result of changing the population of the n = 3 shell from full to having vacancies in the 3d level. The niobium spectra were measured in the 2–3 keV frequency range, which spanned the 2p-nd transitions where 3 ≤ n ≤ 11. In addition to the detailed structure in these arrays the data also show 2s-4p and 2p-4s transitions and the bound-free L edge. The frequencies and widths of transition arrays, transmission between arrays, and the absorption due to the bound-free edge, can be seen in the data. The sample conditions were found from a combination of two-dimensional radiation-hydrodynamics calculations using the AWE NYM code and flux measurements using X-ray diodes, measurements of 1s-2p absorption spectra in aluminium and mixed aluminium/niobium samples. The electron temperature error, inferred from the modelling, is ±2 eV, with a density error of 30%. The data were recorded over the temperature range from 28 to 45 eV and show marked changes in the spectra over this range.The data were compared to spectra predicted by the AWE CASSANDRA [B.J.B. Crowley, J.W.O. Harris, J. Quant. Spectrosc. Radiat. Transfer 71 (2000) p. 257] opacity code. The calculated spectra were able to reproduce the measurements reasonably well. However, there are some differences in line positions that cannot be accounted for by gradients and there are differences in the array structure in the prediction and the measurements, with additional structure predicted but not seen in the measurements. There is also lower transmission on the blue side of the 2p-3d transition arrays compared to prediction.     

A study of ambient upstream material properties using perpendicular laser driven radiative blast waves in atomic cluster gases

We report on the characterisation of the upstream medium ahead of a radiative cylindrical blast wave launched in an argon cluster gas with a 1 J, 1 ps, 1054 nm Nd:Glass laser system. By launching two perpendicular blast waves and introducing a time delay between the heating beams it is possible to determine the extent of the cluster medium by observing the high energy absorption region associated with clusters, as apposed to the low energy deposition in monatomic gas. It was found that argon ions launched from the initial laser driven cluster ionisation created a ballistic ion wave which sweeps out ahead of the hydrodynamic blast wave at an initial velocity of 1000 kms⁻¹. This ballistic wave disassembles the clusters ahead of the blast wave into a neutral gas medium before the arrival of a radiative precursor. This observation gives us confidence that the dynamics of a radiative blast wave in cluster based experiments is determined primarily by the properties of an upstream atomic gas, and is not significantly influenced by cluster affects on energy transport or other material properties.     

Variational Average-Atom in Quantum Plasmas (VAAQP) – Recent progress, virial theorem and applications to the equation-of-state of warm dense Be

The Variational Average-Atom in Quantum Plasmas (VAAQP) code is based on a fully variational theory of dense plasmas in equilibrium in which the neutrality of the Wigner-Seitz ion sphere is not required, contrary to the Inferno model. We report on some recent progress in the VAAQP model and numerical code. Three important points of the virial theorem derivation are emphasized and explained. The virial theorem is also used as an important tool allowing us to check the formulas and numerical methods used in the code. Applications of the VAAQP code are shown using as an example the equation-of-state of beryllium in the warm dense matter regime. Comparisons with the Inferno model, and with available experimental data on the principal Hugoniot are also presented.     

Fundamental problems in brittle fracture: unstable cracks and delayed breaking

This presents a short review on two problems where brittle fracture is involved. In the first one, a hot glass plate is subject to a local stress when drowned into a cold bath. In the region of transition between the cold and hot side, large stresses build up, that can be related accurately to the various coefficients typical of the plate material, heat dilation coefficient, heat conductivity, Young's modulus, etc. Thanks to thais, one can compare well the experimental results and the theoretical predictions based on the Griffith criterion for the propagation of a straight crack, and for its instability against an undulating mode. In the other problem, one looks at the delay before a bent 2D crystal breaks: this (very long) delay is interpreted as the time required for homogeneous nucleation of a critical Griffith nucleus in a region of the crystal under extension. Although it agrees fairly well with some experimental data, other experimental facts are required to complicate the model by considering a multistep nucleation process. To cite this article: Y. Pomeau, C. R. Mecanique 330 (2002) 249–257.     

Density effects in plasmas: Detailed atomic calculations and analytical expressions

In warm dense plasmas, the free-electron and ion spatial distribution may strongly affect atomic structure. To account for such effects we have implemented a potential correction based on the uniform electron gas model in the Flexible Atomic Code (FAC). This code has been applied to obtain energies, wave-functions and radiative rates modified by the plasma environment. In hydrogen-like ions, these numerical results have been successfully compared to an analytical calculation based on first-order perturbation theory. In the case of multi-electron ions, we observe level crossings in agreement with another recent model calculation.     

Bifurcations and chaos in vibrating microcantilevers of tapping mode atomic force microscopy

We study the dynamics of a microcantilever in tapping mode atomic force microscopy when it is close to the sample surface and the van der Waals force has an important influence. Utilizing the averaging method, the extended version of the subharmonic Melnikov method and the homoclinic Melnikov method, we show that abundant bifurcation behavior and chaotic motions occur in vibrations of the microcantilever. In particular, in the subharmonic Melnikov analyses, a degenerate resonance is treated appropriately. Necessary computations for the subharmonic and homoclinic Melnikov methods are performed numerically. Numerical bifurcation analyses and numerical simulations are also given to demonstrate the theoretical results.     

A combined first principles and analytical determination of the modulus of cohesion,surface energy,and the additional constants in the second strain gradient elasticity

Mindlin’s (1965) second strain gradient theory due to its competency in capturing the effects of edges, corners, and surfaces is of particular interest. Formulation in this framework, in addition to the usual Lamé constants, requires the knowledge of sixteen additional materials constants. To date, there are no successful experimental techniques for measuring these material parameters which reflect the discrete nature of matter. The present work gives an accurate remedy for the atomistic calculations of these parameters by utilizing the first principles density functional theory (DFT) for the calculations of the atomic force constants combined with an analytical formulation. It will be shown that writing the consistency conditions obtained from the equivalency between the atomistic crystal lattice dynamics of the bulk material and its counterpart in the second strain gradient elasticity is insufficient for the calculations of all the additional constants. As it will be discussed, there are two missing conditions which are then provided by consideration of the free standing film problem that bring the surface effect into account. As a consequence of surface effect consideration, the modulus of cohesion which is one of the important additional constants is calculated. Moreover, an analytical expression for the surface energy in terms of the modulus of cohesion, Lamé constants, materials characteristic lengths, and the film thickness is presented. If the film thickness is much bigger than the magnitude of the characteristic lengths of the material, then the surface energy would no longer depend on the film thickness.     

An analytical method for solving internal forces and deformations of bar-system structure in space

In this paper, based on the idea of finite element method, the initial parametric method in bending problem of a beam is extended to analyse the bar-system structure by employing Dirac function and Heaviside step function.Then a new method for analysing the internal forces and deformations of bar-system structure in space is suggested by improving the mixed method in statically indeterminate structure.The inferred process and obtained answer will be more succinct and accurate when the problem of internal forces and deformations of bar-system structure is analysed by using the new method provided in this paper.