Viscosity of Colloidal Suspensions

Simple expressions are given for the Newtonian viscosity $\eta_N(\phi)$ as well as the viscoelastic behavior of the viscosity $\eta(\phi,\omega)$ of neutral monodisperse hard sphere colloidal suspensions as a function of volume fraction $\phi$ and frequency $\omega$ over the entire fluid range, i.e., for volume fractions $0 < \phi < 0.55$. These expressions are based on an approximate theory which considers the viscosity as composed as the sum of two relevant physical processes: $\eta (\phi,\omega) = \eta_{\infty}(\phi) + \eta_{cd}(\phi,\omega)$, where $\eta_{\infty}(\phi) = \eta_0 \chi(\phi)$ is the infinite frequency (or very short time) viscosity, with $\eta_0$ the solvent viscosity, $\chi(\phi)$ the equilibrium hard sphere radial distribution function at contact, and $\eta_{cd}(\phi,\omega)$ the contribution due to the diffusion of the colloidal particles out of cages formed by their neighbors, on the P\'{e}clet time scale $\tau_P$, the dominant physical process in concentrated colloidal suspensions. The Newtonian viscosity $\eta_N(\phi) = \eta(\phi,\omega = 0)$ agrees very well with the extensive experiments of Van der Werff et al and others. Also, the asymptotic behavior for large $\omega$ is of the form $\eta_{\infty}(\phi) + A(\phi)(\omega \tau_P)^{-1/2}$, in agreement with these experiments, but the theoretical coefficient $A(\phi)$ differs by a constant factor $2/\chi(\phi)$ from the exact coefficient, computed from the Green-Kubo formula for $\eta(\phi,\omega)$. This still enables us to predict for practical purposes the visco-elastic behavior of monodisperse spherical colloidal suspensions for all volume fractions by a simple time rescaling.Comment: 51 page

Sound-propagation gap in fluid mixtures

We discuss the behavior of the extended sound modes of a dense binary hard-sphere mixture. In a dense simple hard-sphere fluid the Enskog theory predicts a gap in the sound propagation at large wave vectors. In a binary mixture the gap is only present for low concentrations of one of the two species. At intermediate concentrations sound modes are always propagating. This behavior is not affected by the mass difference of the two species, but it only depends on the packing fractions. The gap is absent when the packing fractions are comparable and the mixture structurally resembles a metallic glass.Comment: Published; withdrawn since ordering in archive gives misleading impression of new publicatio

Bounds for present value functions with stochastic interest rates and stochastic volatility.

The distribution of the present value of a series of cash flows under stochastic interest rates has been investigated by many researchers. One of the main problems in this context is the fact that the calculation of exact analytical results for this type of distributions turns out to be rather complicated, and is known only for special cases. An interesting solution to this difficulty consists of determining computable upper bounds, as close as possible to the real distribution.In the present contribution, we want to show how it is possible to compute such bounds for the present value of cash flows when not only the interest rates but also volatilities are stochastic. We derive results for the stop loss premium and distribution of these bounds.Distribution; Value; Cash flow; Interest rates; Researchers; Problems;

Dynamic structure factors of a dense mixture

We compute the dynamic structure factors of a dense binary liquid mixture. These describe dynamics on molecular length scales, where structural relaxation is important. We find that the presence of a few large particles in a dense fluid of small particles slows down the dynamics considerably. We also observe a deep narrowing of the spectrum for a disordered mixture composed of a nearly equal packing of the two species. In contrast, a few small particles diffuse easily in the background of a dense fluid of large particles. We expect our results to describe neutron scattering from a dense mixture

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

Parameterized Complexity of Weighted Multicut in Trees

The Edge Multicut problem is a classical cut problem where given anundirected graph $G$, a set of pairs of vertices $\mathcal{P}$, and a budget$k$, the goal is to determine if there is a set $S$ of at most $k$ edges suchthat for each $(s,t) \in \mathcal{P}$, $G-S$ has no path from $s$ to $t$. EdgeMulticut has been relatively recently shown to be fixed-parameter tractable(FPT), parameterized by $k$, by Marx and Razgon [SICOMP 2014], andindependently by Bousquet et al. [SICOMP 2018]. In the weighted version of theproblem, called Weighted Edge Multicut one is additionally given a weightfunction $\mathtt{wt} : E(G) \to \mathbb{N}$ and a weight bound $w$, and thegoal is to determine if there is a solution of size at most $k$ and weight atmost $w$. Both the FPT algorithms for Edge Multicut by Marx et al. and Bousquetet al. fail to generalize to the weighted setting. In fact, the weightedproblem is non-trivial even on trees and determining whether Weighted EdgeMulticut on trees is FPT was explicitly posed as an open problem by Bousquet etal. [STACS 2009]. In this article, we answer this question positively bydesigning an algorithm which uses a very recent result by Kim et al. [STOC2022] about directed flow augmentation as subroutine. We also study a variant of this problem where there is no bound on the sizeof the solution, but the parameter is a structural property of the input, forexample, the number of leaves of the tree. We strengthen our results by statingthem for the more general vertex deletion version.<br

Theorem on the Distribution of Short-Time Particle Displacements with Physical Applications

The distribution of the initial short-time displacements of particles is considered for a class of classical systems under rather general conditions on the dynamics and with Gaussian initial velocity distributions, while the positions could have an arbitrary distribution. This class of systems contains canonical equilibrium of a Hamiltonian system as a special case. We prove that for this class of systems the nth order cumulants of the initial short-time displacements behave as the 2n-th power of time for all n>2, rather than exhibiting an nth power scaling. This has direct applications to the initial short-time behavior of the Van Hove self-correlation function, to its non-equilibrium generalizations the Green's functions for mass transport, and to the non-Gaussian parameters used in supercooled liquids and glasses.Comment: A less ambiguous mathematical notation for cumulants was adopted and several passages were reformulated and clarified. 40 pages, 1 figure. Accepted by J. Stat. Phy