Structure in cohesive powders studied with spin-echo small angle\ud neutron scattering

Extracting structure and ordering information from the bulk of granular materials is a challenging task. Here we present Spin-Echo Small Angle Neutron Scattering Measurements in combination with computer simulations on a fine powder of silica, before and after uniaxial compression. The cohesive powder packing is modeled by using molecular dynamics simulations and the structure, in terms of the density–density correlation function, is calculated from the simulation and compared with experiment. In the dense case, both quantitative and qualitative agreement between measurement and simulations is observed, thus creating the desired link between experiment and computer simulation. Further simulations with appropriate attractive potentials and adequate preparation procedures are needed in order to capture the very loose-packed cohesive powders.\u

Long time diffusion in suspensions of interacting charged colloids

A new expression is given for the long time diffusion coefficient DL(k) of charged interacting colloidal spheres in suspension, as a function of the wavenumber k, near k = km, where the static structure factor has a maximum. The expression is based on a physical analogy between a mode description of the behaviour of atomic fluids (as observed in neutron scattering) and of colloids (as observed in light scattering). Use of this expresssion in conjunction with a hard-sphere model yields good agreement with extant data on colloids

Introductory clifford analysis

In this chapter an introduction is given to Clifford analysis and the underlying Clifford algebras. The functions under consideration are defined on Euclidean space and take values in the universal real or complex Clifford algebra, the structure and properties of which are also recalled in detail. The function theory is centered around the notion of a monogenic function, which is a null solution of a generalized Cauchy–Riemann operator, which is rotation invariant and factorizes the Laplace operator. In this way, Clifford analysis may be considered as both a generalization to higher dimension of the theory of holomorphic functions in the complex plane and a refinement of classical harmonic analysis. A notion of monogenicity may also be associated with the vectorial part of the Cauchy–Riemann operator, which is called the Dirac operator; some attention is paid to the intimate relation between both notions. Since a product of monogenic functions is, in general, no longer monogenic, it is crucial to possess some tools for generating monogenic functions: such tools are provided by Fueter’s theorem on one hand and the Cauchy–Kovalevskaya extension theorem on the other hand. A corner stone in this function theory is the Cauchy integral formula for representation of a monogenic function in the interior of its domain of monogenicity. Starting from this representation formula and related integral formulae, it is possible to consider integral transforms such as Cauchy, Hilbert, and Radon transforms, which are important both within the theoretical framework and in view of possible applications

Unified description of long-time tails and long-range correlation functions for sheared granular liquids

Unified description on the long-time tail of velocity autocorrelation function and the long-range correlation for the equal-time spatial correlation functions is developed based on the generalized fluctuating hydrodynamics. The cross-over of the long-time tail from $t^{-3/2}$ to $t^{-5/2}$ is predicted independent of the density, and the equal-time spatial density correlation function and the equal-time spatial velocity correlation function respectively satisfy $r^{-11/3}$ and $r^{-5/3}$ for large $r$ limit.Comment: 10 pages. to be published in Euro. Phys. J.

Inelastic X-ray scattering study of the collective dynamics in liquid sodium

Inelastic X-ray scattering data have been collected for liquid sodium at T=390 K, i.e. slightly above the melting point. Owing to the very high instrumental resolution, pushed up to 1.5 meV, it has been possible to determine accurately the dynamic structure factor, $S(Q,\omega)$, in a wide wavevector range, $1.5 \div 15$ nm$^{-1}$, and to investigate on the dynamical processes underlying the collective dynamics. A detailed analysis of the lineshape of $S(Q,\omega)$, similarly to other liquid metals, reveals the co-existence of two different relaxation processes with slow and fast characteristic timescales respectively. The present data lead to the conclusion that: i) the picture of the relaxation mechanism based on a simple viscoelastic model fails; ii) although the comparison with other liquid metals reveals similar behavior, the data do not exhibit an exact scaling law as the principle of corresponding state would predict.Comment: RevTex, 7 pages, 6 eps figures. Accepted by Phys. Rev.

Self-diffusion beyond Fick's law

The Van Hove self-correlation function, the intermediate incoherent scattering function and its Laplace transform are determined asymptotically for a one component fluid in equilibrium, using the mode coupling theory. The results reproduce in the hydrodynamic limit the predictions from Fick's law. The corrections to Fick's law are consistent with a long time tail in the velocity correlation function and with a diverging super Burnett coefficient in the linear diffusion equation

The nonexistence of the linear diffusion equation beyond Fick's law

The self-diffusion of a tagged particle in a 3-dimensional fluid of identical particles cannot be described by a linear diffusion equation which contains corrections to Fick's law proportional to 4n, 6n, … For long times a t divergence is found for the super-Burnett coefficient, the proportionality coefficient of the 4-term, both from the mode-mode coupling theory and the kinetic theory of hard spheres. Furthermore, higher asymptotic corrections of the form t-2+2-n (n = 2, 3, …) to the t--time tail of the velocity autocorrelation function are calculated from both theories and the results are compared

Kinetic theory of the eigenmodes of classical fluids and neutron scattering

The lowest lying eigenmodes of a classical fluid have been approximately determined for a wide range of densities and wavenumbers. The most important eigenmodes are direct extensions of the three hydrodynamic heat and sound modes to much larger wavenumbers. A new and consistent interpretation of neutron spectra and related molecular dynamics simulations in terms of these modes is made. Also experimental predictions are discussed, some of which seem particularly suitable for investigating with spillation sources