Friction and the oscillatory motion of granular flows

This contribution reports on numerical simulations of 2D granular flows on erodible beds. The broad aim is to investigate whether simple flows of model granular matter exhibits spontaneous oscillatory motion in generic flow conditions, and in this case, whether the frictional properties of the contacts between grains may affect the existence or the characteristics of this oscillatory motion. The analysis of different series of simulations show that the flow develops an oscillatory motion with a well-defined frequency which increases like the inverse of the velocity's square root. We show that the oscillation is essentially a surface phenomena. The amplitude of the oscillation is higher for lower volume fractions, and can thus be related to the flow velocity and grains friction properties. The study of the influence of the periodic geometry of the simulation cell shows no significant effect. These results are discussed in relation to sonic sands.Comment: 7 pages, 8 figure

Study of the collapse of granular columns using DEM numerical simulation

Numerical simulations of the collapse and spreading of granular columns onto an horizontal plane using the Contact Dynamics method are presented. The final shape of the deposit seems to depend only on the aspect ratio $a$ of the columns; these results are in good agreement with previous experimental work. In particular, the renormalised runout distance shows a power law dependence on the aspect ratio $a$, which is incompatible with a simple friction model. The dynamics of the collapse is shown to be mostly controlled by the free fall of the column. The energy dissipation at the base of the column can be described simply by a coefficient of restitution. Hence the energy available for the sideways flow is proportional to the initial potential energy $E_0$. The dissipation process within the flow is well approximated by basal friction, contrary to the behaviour of the runout distance. The mass ejected sideways is showned to play a determining role in the spreading process. As $a$ increases, the same fraction of initial potential energy $E_0$ drives more mass against friction. This additional dissipation give a possible explanation for power-law dependence of the runout distance on $a$. Beyond the frictional properties of the material, we show that the flow characteristics strongly depend on the early dynamics of the collapse. We propose a new scaling for the runout distance that matches the data well, is compatible with a friction model, and provide a qualitative explanation to the column collapse phenomenology.Comment: 15 pages, 22 Figure

Friction vs Texture at the Approach of a Granular Avalanche

We perform a novel analysis of the granular texture of a granular bed close to stability limit. Our analysis is based on a unique criterion of friction mobilisation in a simulated two-dimensional packing. In this way, we recover the bimodal character of granular texture, and the coexistence of weak and strong phases in the sense of distinct contacts populations. Moreover, we show the existence of a well-defined subset of contacts within the weak contact network. These contacts are characterized by their important friction, and form a highly coherent population in terms of fabric. They play an antagonistic role with respect to force chains. We are thus able to discriminate between incoherent contacts and coherent contacts in the weak phase, and to specify the role that the latter plays in the destabilisation process.Comment: 4 pages, 6 figure

Continuum simulation of the discharge of the granular silo: a validation test for the mu(I)-visco-plastic flow law

Using both a continuum Navier-Stokes solver, with the mu(I)-flow-law implemented to model the viscous behavior, and the discrete Contact Dynamics algorithm, the discharge of granular silos is simulated in two dimensions from the early stages of the discharge until complete release of the material. In both cases, the Beverloo scaling is recovered. We first do not attempt quantitative comparison, but focus on the qualitative behavior of velocity and pressure at different locations in the flow. A good agreement is obtained in the regions of rapid flows, while areas of slow creep are not entirely captured by the continuum model. The pressure field shows a general good agreement. The evolution of the free surface implies differences, however, the bulk deformation is essentially identical in both approaches. The influence of the parameters of the mu(I)-flow-law is systematically investigated, showing the importance of the dependence on the inertial number I to achieve quantitative agreement between continuum and discrete discharge. The general ability of the continuum model to reproduce qualitatively the granular behavior is found to be very encouraging.Comment: 12 pages, 15 figure

Les Hors nature i La Jongleuse autorstwa Rachilde: między realistycznym przedstawieniem a zobrazowaniem niemożliwego

The style of Rachilde which abounds in picturesque comparison invites a reader to examine her use of hypotyposis. Two of her novels: Les Hors Nature and La Jongleuse offer particularly interesting examples of this figure, both of them mainly in erotically uninhibited scenes. Because of the bowdlerisation of the time, while impressing the reader's imagination with the power of images, Rachilde had to avoid clear wording and resort to suggestion. That’s why many rhetorical figures: ellipses, circumlocutions, metaphors blur the clarity of description, which according to Yves Le Bozec makes one of the formal features of hypotypose. The aim of this paper is to analyse the construction of this figure in Rachilde's literary output. — On the other hand, the scenes in question were designed to illustrate the concept of ideal love – the impossible one – that the novelist develops in her works. Crossing the limits of the theoretical discourse, the protagonists direct their own performances, watched by the stunned and outraged viewers. This way of presentation enhances the hypotypotique effect. The reactions of eyewitnesses replace the phrases designed to encourage the audience to observe the scene. Such phrases are common in theatrical hypotyposis. This interweaving is designed to impress the reader deeply. — However, the question arises whether Rachilde, despite her primary axiological intention, did not succumb to the temptation to provoke the public with shocking images, and whether the strength of her hypotyposis does not remain, in the end, one of her major achievements.Pełen obrazowych porównań styl Rachilde zachęca do przyjrzenia się występujących w jej powieściach hypotypozom. Ciekawe przykłady tej figury spotykamy w dwóch utworach: Les Hors nature i La Jongleuse. W obu przypadkach chodzi o sceny odważne erotycznie. Ze względu na cenzurę obyczajową Rachilde musi jednocześnie działać na wyobraźnię czytelnika siłą swoich obrazów, unikać jasnych sformułowań i uciekać się do sugestii. Liczne figury stylistyczne: elipsy, peryfrazy, metafory, zaburzają jasny przekaz, który, według Yves’a Le Bozeca, stanowi jeden ze składników hypotypozy. Artykuł stawia sobie zatem za cel omówienie budowy tej figury u Rachilde. — Z drugiej jednak strony wybrane sceny mają posłużyć jako demonstracja teorii miłości idealnej – niemożliwej – którą powieściopisarka zawarła w swoich powieściach. Wykraczając poza ramy teoretycznego dyskursu, bohaterowie reżyserują swoje wystąpienia na oczach zamarłych z oburzenia widzów. Ten rodzaj przestawienia teatralnego wzmacnia efekt hypotypozy, a reakcje świadków naocznych zastępują zwroty zachęcające do przyjrzenia się scenie, częste w hypotypozach teatralnych. Tego rodzaju połączenie ma głęboko wstrząsnąć czytelnikiem. — Ostatecznie warto się zastanowić, czy Rachilde, niezależnie od pierwotnych zamierzeń aksjologicznych, nie uległa pokusie prowokacji za pomocą szokujących obrazów i czy potęga stworzonych przez nią hypotypoz nie stanowi ostatecznie jednego z jej podstawowych osiągnięć

Pretzel knots of length three with unknotting number one

textThis thesis provides a partial classification of all 3-stranded pretzel knots K=P(p,q,r) with unknotting number one. Scharlemann-Thompson, and independently Kobayashi, have completely classified those knots with unknotting number one when p, q, and r are all odd. In the case where p=2m, we use the signature obstruction to greatly limit the number of 3-stranded pretzel knots which may have unknotting number one. In Chapter 3 we use Greene's strengthening of Donaldson's Diagonalization theorem to determine precisely which pretzel knots of the form P(2m,k,-k-2) have unknotting number one, where m is an integer, m>0, and k>0, k odd. In Chapter 4 we use Donaldson's Diagonalization theorem as well as an unknotting obstruction due to Ozsv\'ath and Szab\'o to partially classify which pretzel knots P(2,k,-k) have unknotting number one, where k>0, odd. The Ozsv\'ath-Szab\'o obstruction is a consequence of Heegaard Floer homology. Finally in Chapter 5 we explain why the techniques used in this paper cannot be used on the remaining cases.Mathematic

Free time activities of gifted adolescents at a residential high school

This study investigated the free time use of gifted juniors and seniors at a two-year residential public high school. This study was descriptive in nature and designed to explain life in this environment. The purpose of the study was to learn how students spent their free time and whether or not gender and grade affected activity preference. The sample included 181 students at the Greenhouse Institute. Eighty-two boys and 99 girls participated. Each of the participants completed a self-report survey about their use of free time. The students completed items that related to five different activity areas How Often , Before Dinner , Weekends , Schedule , and Where in Town . Survey responses were analyzed using frequencies and chi-square statistics. The results indicated that students spent much of their free time with friends and listening to music. The results also showed that free time preferences were affected by grade and gender. Taken together, many of the results were comparable to the activity preferences of students in non-residential public high schools but also included activities that were unique to a residential environment