Equations of structural relaxation

In the mode coupling theory of the liquid to glass transition the long time structural relaxation follows from equations solely determined by equilibrium structural parameters. The present extension of these structural relaxation equations to arbitrarily short times on the one hand allows calculations unaffected by model assumptions about the microscopic dynamics and on the other hand supplies new starting points for analytical studies. As a first application, power-law like structural relaxation at a glass-transition singularity is explicitly proven for a special schematic MCT model.Comment: 11 pages, 3 figures; talk given at the Seventh international Workshop on disordered Systems, Molveno, Italy, March 199

Tagged-particle dynamics in a hard-sphere system: mode-coupling theory analysis

The predictions of the mode-coupling theory of the glass transition (MCT) for the tagged-particle density-correlation functions and the mean-squared displacement curves are compared quantitatively and in detail to results from Newtonian- and Brownian-dynamics simulations of a polydisperse quasi-hard-sphere system close to the glass transition. After correcting for a 17% error in the dynamical length scale and for a smaller error in the transition density, good agreement is found over a wide range of wave numbers and up to five orders of magnitude in time. Deviations are found at the highest densities studied, and for small wave vectors and the mean-squared displacement. Possible error sources not related to MCT are discussed in detail, thereby identifying more clearly the issues arising from the MCT approximation itself. The range of applicability of MCT for the different types of short-time dynamics is established through asymptotic analyses of the relaxation curves, examining the wave-number and density-dependent characteristic parameters. Approximations made in the description of the equilibrium static structure are shown to have a remarkable effect on the predicted numerical value for the glass-transition density. Effects of small polydispersity are also investigated, and shown to be negligible.Comment: 20 pages, 23 figure

Structural relaxation of polydisperse hard spheres: comparison of the mode-coupling theory to a Langevin dynamics simulation

We analyze the slow, glassy structural relaxation as measured through collective and tagged-particle density correlation functions obtained from Brownian dynamics simulations for a polydisperse system of quasi-hard spheres in the framework of the mode-coupling theory of the glass transition (MCT). Asymptotic analyses show good agreement for the collective dynamics when polydispersity effects are taken into account in a multi-component calculation, but qualitative disagreement at small $q$ when the system is treated as effectively monodisperse. The origin of the different small-$q$ behaviour is attributed to the interplay between interdiffusion processes and structural relaxation. Numerical solutions of the MCT equations are obtained taking properly binned partial static structure factors from the simulations as input. Accounting for a shift in the critical density, the collective density correlation functions are well described by the theory at all densities investigated in the simulations, with quantitative agreement best around the maxima of the static structure factor, and worst around its minima. A parameter-free comparison of the tagged-particle dynamics however reveals large quantiative errors for small wave numbers that are connected to the well-known decoupling of self-diffusion from structural relaxation and to dynamical heterogeneities. While deviations from MCT behaviour are clearly seen in the tagged-particle quantities for densities close to and on the liquid side of the MCT glass transition, no such deviations are seen in the collective dynamics.Comment: 23 pages, 26 figure

A reason for fusion rules to be even

We show that certain tensor product multiplicities in semisimple braided sovereign tensor categories must be even. The quantity governing this behavior is the Frobenius-Schur indicator. The result applies in particular to the representation categories of large classes of groups, Lie algebras, Hopf algebras and vertex algebras.Comment: 6 pages, LaTe

From Equilibrium to Steady State: The Transient Dynamics of Colloidal Liquids under Shear

We investigate stresses and particle motion during the start up of flow in a colloidal dispersion close to arrest into a glassy state. A combination of molecular dynamics simulation, mode coupling theory and confocal microscopy experiment is used to investigate the origins of the widely observed stress overshoot and (previously not reported) super-diffusive motion in the transient dynamics. A link between the macro-rheological stress versus strain curves and the microscopic particle motion is established. Negative correlations in the transient auto-correlation function of the potential stresses are found responsible for both phenomena, and arise even for homogeneous flows and almost Gaussian particle displacements.Comment: 24 pages, 14 figures, J. Phys.: Condens. Matter, in pres

Active and Nonlinear Microrheology in Dense Colloidal Suspensions

We present a first-principles theory for the active nonlinear microrheology of colloidal model systems: for constant external force on a spherical probe particle embedded in a dense host dispersion, neglecting hydrodynamic interactions, we derive an exact expression for the friction. Within mode-coupling theory (MCT), we discuss the threshold external force needed to delocalize the probe from a host glass, and its relation to strong nonlinear velocity-force curves in a host fluid. Experimental microrheology data and simulations, which we performed, are explained with a simplified model

Feasibility study concerning the actual implementation of a joint cross-border procurement procedure by public buyers from different Member States

Joint procurement refers to a situation in which two or more contracting authorities conduct a procurement procedure together. The key characteristic of this specific procedure is that only one tender is published on behalf of all participating contracting authorities. The notion of joint procurement does not automatically imply any cross-border element as such. Joint cross-border procurement refers to the particular procurement procedure which involves contracting authorities from different Member States conducting a common tender by bundling their demands and acting jointly in the award of the contract. There have already been some attempts to conduct JCBPP procedures in the European Union, despite the fact that until the implementation of Directive 2014/24/EU there were no explicit legal provisions to facilitate such forms of cooperation. Therefore contracting authorities faced both legal and practical difficulties, mostly due to conflicts between national public procurement rules and barriers preventing recourse to other Member States’ central purchasing body or the joint cross-border award of public contracts. Currently existing literature still offers only a few contributions describing the use and impact of JCBPP and the limited practical experience there is in conducting such procedures has not been presented in an aggregated form so far. This analysis is intended to help identify the best solutions for implementing JCBPP projects and offers concrete recommendations which should serve as a guideline for all interested stakeholders. The aim of the study is not to assess theoretical scenarios of JCBPP between contracting authorities in different Member States or to offer a legal analysis of factors that can influence the implementation of such projects. Its scope is to practically analyse projects that have been implemented in the past months or years and to highlight how they have been conducted, the obstacles or difficulties experienced by the participating contracting authorities and how they managed to overcome them. Centralised – and therefore “joint” – purchasing techniques are successfully used in most Member States and the idea of exploring a cross-border dimension is generating more and more interest as it facilitates cooperation between contracting authorities across Europe and at the same time enhances the benefits of the Internal Market by creating better business opportunities for economic operators. Thus, this feasibility study on the possible implementation of a JCBPP procedure consists of an analysis of relevant JCPPP projects, including a cost benefit analysis, and draws conclusions based on the main issues which need to be considered when conducting a JCBPP. The results of the feasibility study have allowed the drafting of recommendations for the implementation of JCBPP procedures. The feasibility study focuses on the legal, administrative and procedural aspects encountered in four selected JCBPP projects, taking into consideration country and sector-specific characteristics relevant to the implementation of such procedures

Vortex phase transformations probed by the local ac response of Bi_{2}Sr_{2}CaCu_{2}O_{8+\delta} single crystals with various doping

The linear ac response of the vortex system is measured locally in Bi-2212 single crystals at various doping, using a miniature two-coil mutual-inductance technique. It was found that a step-like change in the local ac response takes place exactly at the first-order transition (FOT) temperature T_{FOT}(H) determined by a global dc magnetization measurement. The T_{FOT}(H) line in the H-T phase diagram becomes steeper with increasing doping. In the higher-field region where the FOT is not observed, the local ac response still shows a broadened but distinct feature, which can be interpreted to mark the growth of a short-range order in the vortex system.Comment: 4 pages, including 5 eps figure

Dense colloidal suspensions under time-dependent shear

We consider the nonlinear rheology of dense colloidal suspensions under a time-dependent simple shear flow. Starting from the Smoluchowski equation for interacting Brownian particles advected by shearing (ignoring fluctuations in fluid velocity) we develop a formalism which enables the calculation of time-dependent, far-from-equilibrium averages. Taking shear-stress as an example we derive exactly a generalized Green-Kubo relation, and an equation of motion for the transient density correlator, involving a three-time memory function. Mode coupling approximations give a closed constitutive equation yielding the time-dependent stress for arbitrary shear rate history. We solve this equation numerically for the special case of a hard sphere glass subject to step-strain.Comment: 4 page