Inelastic Collapse of Three Particles

A system of three particles undergoing inelastic collisions in arbitrary spatial dimensions is studied with the aim of establishing the domain of ``inelastic collapse''---an infinite number of collisions which take place in a finite time. Analytic and simulation results show that for a sufficiently small restitution coefficient, $0\leq r<7-4\sqrt{3}\approx 0.072$, collapse can occur. In one dimension, such a collapse is stable against small perturbations within this entire range. In higher dimensions, the collapse can be stable against small variations of initial conditions, within a smaller $r$ range, $0\leq r<9-4\sqrt{5}\approx 0.056$.Comment: 6 pages, figures on request, accepted by PR

Energy flows in vibrated granular media

We study vibrated granular media, investigating each of the three components of the energy flow: particle-particle dissipation, energy input at the vibrating wall, and particle-wall dissipation. Energy dissipated by interparticle collisions is well estimated by existing theories when the granular material is dilute, and these theories are extended to include rotational kinetic energy. When the granular material is dense, the observed particle-particle dissipation rate decreases to as little as 2/5 of the theoretical prediction. We observe that the rate of energy input is the weight of the granular material times an average vibration velocity times a function of the ratio of particle to vibration velocity. `Particle-wall' dissipation has been neglected in all theories up to now, but can play an important role when the granular material is dilute. The ratio between gravitational potential energy and kinetic energy can vary by as much as a factor of 3. Previous simulations and experiments have shown that E ~ V^delta, with delta=2 for dilute granular material, and delta ~ 1.5 for dense granular material. We relate this change in exponent to the departure of particle-particle dissipation from its theoretical value.Comment: 19 pages revtex, 10 embedded eps figures, accepted by PR

Homogeneous cooling of rough, dissipative particles: Theory and simulations

We investigate freely cooling systems of rough spheres in two and three dimensions. Simulations using an event driven algorithm are compared with results of an approximate kinetic theory, based on the assumption of a generalized homogeneous cooling state. For short times $t$, translational and rotational energy are found to change linearly with $t$. For large times both energies decay like $t^{-2}$ with a ratio independent of time, but not corresponding to equipartition. Good agreement is found between theory and simulations, as long as no clustering instability is observed. System parameters, i.e. density, particle size, and particle mass can be absorbed in a rescaled time, so that the decay of translational and rotational energy is solely determined by normal restitution and surface roughness.Comment: 10 pages, 10 eps-figure

Federation of Piling Specialists’ casing extraction review

During construction of rotary bored piles it is necessary to install a temporary casing to prevent the collapse of material into the open bore and provide edge protection. T he preferred method of removal for some contractors is by means of the handling crane. The Federation of Piling Specialists (2010) released guidance to predict the load developed in the removal of casings. This paper investigated whether the recommended constants applied to the overburden and clay terms were reasonable for various casing diameter s , embedment and depth of overburden. A series of five ce ntrifuge tests were conducted where loads were recorded as casings were extracted. Results showed that the FPS method over predicted the pull - out force and indicated that the adhesion factor, α , and angle of dilation between the casing and soil, tan δ , are not constant. This paper proposes a new method of predicting extraction forces which was found to predict forces to within ±10% of those measured in centrifuge tests

The energy flux into a fluidized granular medium at a vibrating wall

We study the power input of a vibrating wall into a fluidized granular medium, using event driven simulations of a model granular system. The system consists of inelastic hard disks contained between a stationary and a vibrating elastic wall, in the absence of gravity. Two scaling relations for the power input are found, both involving the pressure. The transition between the two occurs when waves generated at the moving wall can propagate across the system. Choosing an appropriate waveform for the vibrating wall removes one of these scalings and renders the second very simple.Comment: 5 pages, revtex, 7 postscript figure

DEVELOPMENT OF A STOCHASTIC MODEL TO EVALUATE PLANT GROWERS' ENTERPRISE BUDGETS

Increased domestic concentration and international competition in the floricultural industry are forcing growers to improve resource management efficiency. Cost management and cost accounting methods are becoming key tools as growers attempt to reduce costs. These tools allow growers to allocate costs for each crop, increasing their greenhouse planning abilities. Growers have a relative high degree of risk due to potential crop and market failure. Individual growers have different tolerance for risk and risk bearing capacity. Growers need a cost accounting system that incorporates production and market risk, a system that allows them to make informed business decisions. The research reported in this paper developed a greenhouse budgeting model that incorporated risk to allow growers to compare production costs for flowers with different genetics and production technologies. This enables greenhouse growers to make production management decisions that incorporate production and market risk. The model gives growers the option of imputing their own production data to evaluate how various yield and price assumptions influence income and expense projections, and ultimately, profit. The model allows growers to compare total production cost and revenue varying grower type, production time, geographical location, operation size, and cost structure. The model evaluates budgets for growers who market to mass-market retail operations or wholesale intermediaries who sell to merchandisers or flower shops distribution channels. The model was demonstrated with sample data to illustrate how incorporating risk analysis into a grower's greenhouse budget model effects resource allocation and production decisions as compare to a budget model that does not incorporate risk. Deterministic and stochastic models were used to demonstrate differences in production decisions under various assumptions. The stochastic model introduced prices and flowering characteristics variability. The @Risk software was used to generate the random number simulation of the stochastic model, and stochastic dominance analysis was used to rank the alternatives. The result for both the deterministic and stochastic models identified the same cultivar as most profitable. However, there were differences in crop profits levels and rankings for subsequent cultivars that could influence growers' production choice decisions. The grower's risk aversion level influenced his/her choice of the most profitable cultivars in the stochastic model. The model summarizes the sources of variability that affect cost and revenue. The model enables the grower to measure effects that change in productivity might have on profit. Growers can identify items in their budget that have a greater effect on profitability, and make adjustments. The model can be used to allocate cost across activities, so the grower would be able to measure the economic impact of an item on the budget.Crop Production/Industries,

The Detectability of AGN Cavities in Cooling-Flow Clusters

Chandra X-ray Observatory has revealed X-ray cavities in many nearby cooling flow clusters. The cavities trace feedback from the central active galactic nulceus (AGN) on the intracluster medium (ICM), an important ingredient in stabilizing cooling flows and in the process of galaxy formation and evolution. But, the prevalence and duty cycle of such AGN outbursts is not well understood. To this end, we study how the cooling is balanced by the cavity heating for a complete sample of clusters (the Brightest 55 clusters of galaxies, hereafter B55). In the B55, we found 33 cooling flow clusters, 20 of which have detected X-ray bubbles in their ICM. Among the remaining 13, all except Ophiuchus could have significant cavity power yet remain undetected in existing images. This implies that the duty cycle of AGN outbursts with significant heating potential in cooling flow clusters is at least 60 % and could approach 100 %, but deeper data is required to constrain this further.Comment: 4 pages, 2 figures; to appear in the proceedings of "The Monsters' Fiery Breath", Madison, Wisconsin 1-5 June 2009, Eds. Sebastian Heinz & Eric Wilcots; added annotation to the figur

Metaplectic Ice

Spherical Whittaker functions on the metaplectic n-fold cover of GL(r+1) over a nonarchimedean local field containing n distinct n-th roots of unity may be expressed as the partition functions of statistical mechanical systems that are variants of the six-vertex model. If n=1 then in view of the Casselman-Shalika formula this fact is related to Tokuyama's deformation of the Weyl character formula. It is shown that various properties of these Whittaker functions may be expressed in terms of the commutativity of row transfer matrices for the system. Potentially these properties (which are already proved by other methods, but very nontrivial) are amenable to proof by the Yang-Baxter equation

XMM-Newton view of MS0735+7421: the most energetic AGN outburst in a galaxy cluster

We discuss the possible cosmological effects of powerful AGN outbursts in galaxy clusters by starting from the results of an XMM-Newton observation of the supercavity cluster MS0735+7421.Comment: 6 pages, 5 figures. To appear in the Proceedings of "Heating vs. Cooling in Galaxies and Clusters of Galaxies", August 2006, Garching (Germany

Jet Interactions with the Hot Halos of Clusters and Galaxies

X-ray observations of cavities and shock fronts produced by jets streaming through hot halos have significantly advanced our understanding of the energetics and dynamics of extragalactic radio sources. Radio sources at the centers of clusters have dynamical ages between ten and several hundred million years. They liberate between 1E58-1E62 erg per outburst, which is enough energy to regulate cooling of hot halos from galaxies to the richest clusters. Jet power scales approximately with the radio synchrotron luminosity to the one half power. However, the synchrotron efficiency varies widely from nearly unity to one part in 10,000, such that relatively feeble radio source can have quasar-like mechanical power. The synchrotron ages of cluster radio sources are decoupled from their dynamical ages, which tend to be factors of several to orders of magnitude older. Magnetic fields and particles in the lobes tend to be out of equipartition. The lobes may be maintained by heavy particles (e.g., protons), low energy electrons, a hot, diffuse thermal gas, or possibly magnetic (Poynting) stresses. Sensitive X-ray images of shock fronts and cavities can be used to study the dynamics of extragalactic radio sources.Comment: 10 pages, 3 figures, invited review, "Extragalactic Jets: Theory and Observation from Radio to Gamma Ray, held in Girdwood, Alaska, U.S.A. 21-24 May, 2007, minor text changes; one added referenc