Why Do Granular Materials Stiffen with Shear Rate? : Test of Novel Stress-Based Statistics

Peer reviewedPublisher PD

Critical jamming of frictional grains in the generalized isostaticity picture

While frictionless spheres at jamming are isostatic, frictional spheres at jamming are not. As a result, frictional spheres near jamming do not necessarily exhibit an excess of soft modes. However, a generalized form of isostaticity can be introduced if fully mobilized contacts at the Coulomb friction threshold are considered as slipping contacts. We show here that, in this framework, the vibrational density of states (DOS) of frictional discs exhibits a plateau when the generalized isostaticity line is approached. The crossover frequency to elastic behavior scales linearly with the distance from this line. Moreover, we show that the frictionless limit, which appears singular when fully mobilized contacts are treated elastically, becomes smooth when fully mobilized contacts are allowed to slip.Comment: 4 pages, 4 figures, submitted to PR

Frictional Rigidity Percolation : A New Universality Class and Its Superuniversal Connections through Minimal Rigidity Proliferation

18 pages, 16 figuresPeer reviewedPublisher PD

Entropy and Temperature of a Static Granular Assembly

Granular matter is comprised of a large number of particles whose collective behavior determines macroscopic properties such as flow and mechanical strength. A comprehensive theory of the properties of granular matter, therefore, requires a statistical framework. In molecular matter, equilibrium statistical mechanics, which is founded on the principle of conservation of energy, provides this framework. Grains, however, are small but macroscopic objects whose interactions are dissipative since energy can be lost through excitations of the internal degrees of freedom. In this work, we construct a statistical framework for static, mechanically stable packings of grains, which parallels that of equilibrium statistical mechanics but with conservation of energy replaced by the conservation of a function related to the mechanical stress tensor. Our analysis demonstrates the existence of a state function that has all the attributes of entropy. In particular, maximizing this state function leads to a well-defined granular temperature for these systems. Predictions of the ensemble are verified against simulated packings of frictionless, deformable disks. Our demonstration that a statistical ensemble can be constructed through the identification of conserved quantities other than energy is a new approach that is expected to open up avenues for statistical descriptions of other non-equilibrium systems.Comment: 5 pages, 4 figure

Numerical simulation of roll waves in pipelines using the two-fluid model

A finite volume discretization of the incompressible two-fluid model in four-equation form is proposed for simulating roll waves appearing in multiphase pipelines. The new formulation has two important advantages compared to existing roll wave simulators: (i) it is conservative by construction, meaning that the correct shock magnitude is obtained at the hydraulic jump, and (ii) it can be more easily extended with additional physics (e.g. Compressibility, axial diffusion, surface tension), without rederiving the model equations. A simple, robust, first-order upwind discretization of the four-equation model is able to capture the roll wave profiles, although a fine grid is needed to achieve converged results. The four-equation model leads to new roll wave solutions that differ from existing analytical and numerical results. Our solutions are believed to be physically more correct because the shock relations satisfy physically conserved quantities

Pseudomonas fluorescens CHA0 maintains carbon delivery to Fusarium graminearum-infected roots and prevents reduction in biomass of barley shoots through systemic interactions

Soil bacteria such as pseudomonads may reduce pathogen pressure for plants, both by activating plant defence mechanisms and by inhibiting pathogens directly due to the production of antibiotics. These effects are hard to distinguish under field conditions, impairing estimations of their relative contributions to plant health. A split-root system was set up with barley to quantify systemic and local effects of pre-inoculation with Pseudomonas fluorescens on the subsequent infection process by the fungal pathogen Fusarium graminearum. One root half was inoculated with F. graminearum in combination with P. fluorescens strain CHA0 or its isogenic antibiotic-deficient mutant CHA19. Bacteria were inoculated either together with the fungal pathogen or in separate halves of the root system to separate local and systemic effects. The short-term plant response to fungal infection was followed by using the short-lived isotopic tracer 11CO2 to track the delivery of recent photoassimilates to each root half. In the absence of bacteria, fungal infection diverted carbon from the shoot to healthy roots, rather than to infected roots, although the overall partitioning from the shoot to the entire root system was not modified. Both local and systemic pre-inoculation with P. fluorescens CHA0 prevented the diversion of carbon as well as preventing a reduction in plant biomass in response to F. graminearum infection, whereas the non-antibiotic-producing mutant CHA19 lacked this ability. The results suggest that the activation of plant defences is a central feature of biocontrol bacteria which may even surpass the effects of direct pathogen inhibition

Energy-stable discretization of the one-dimensional two-fluid model

In this paper we present a complete framework for the energy-stable simulation of stratified incompressible flow in channels, using the one-dimensional two-fluid model. Building on earlier energy-conserving work on the basic two-fluid model, our new framework includes diffusion, friction, and surface tension. We show that surface tension can be added in an energy-conserving manner, and that diffusion and friction have a strictly dissipative effect on the energy. We then propose spatial discretizations for these terms such that a semi-discrete model is obtained that has the same conservation properties as the continuous model. Additionally, we propose a new energy-stable advective flux scheme that is energy-conserving in smooth regions of the flow and strictly dissipative where sharp gradients appear. This is obtained by combining, using flux limiters, a previously developed energy-conserving advective flux with a novel first-order upwind scheme that is shown to be strictly dissipative. The complete framework, with diffusion, surface tension, and a bounded energy, is linearly stable to short wavelength perturbations, and exhibits nonlinear damping near shocks. The model yields smoothly converging numerical solutions, even under conditions for which the basic two-fluid model is ill-posed. With our explicit expressions for the dissipation rates, we are able to attribute the nonlinear damping to the different dissipation mechanisms, and compare their effects

Spring 1974

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