12,715 research outputs found

    Non-Universality of Density and Disorder in Jammed Sphere Packings

    Full text link
    We show for the first time that collectively jammed disordered packings of three-dimensional monodisperse frictionless hard spheres can be produced and tuned using a novel numerical protocol with packing density ϕ\phi as low as 0.6. This is well below the value of 0.64 associated with the maximally random jammed state and entirely unrelated to the ill-defined ``random loose packing'' state density. Specifically, collectively jammed packings are generated with a very narrow distribution centered at any density ϕ\phi over a wide density range ϕ∈[0.6, 0.74048…]\phi \in [0.6,~0.74048\ldots] with variable disorder. Our results support the view that there is no universal jamming point that is distinguishable based on the packing density and frequency of occurence. Our jammed packings are mapped onto a density-order-metric plane, which provides a broader characterization of packings than density alone. Other packing characteristics, such as the pair correlation function, average contact number and fraction of rattlers are quantified and discussed.Comment: 19 pages, 4 figure

    Universal Estimation of Directed Information

    Full text link
    Four estimators of the directed information rate between a pair of jointly stationary ergodic finite-alphabet processes are proposed, based on universal probability assignments. The first one is a Shannon--McMillan--Breiman type estimator, similar to those used by Verd\'u (2005) and Cai, Kulkarni, and Verd\'u (2006) for estimation of other information measures. We show the almost sure and L1L_1 convergence properties of the estimator for any underlying universal probability assignment. The other three estimators map universal probability assignments to different functionals, each exhibiting relative merits such as smoothness, nonnegativity, and boundedness. We establish the consistency of these estimators in almost sure and L1L_1 senses, and derive near-optimal rates of convergence in the minimax sense under mild conditions. These estimators carry over directly to estimating other information measures of stationary ergodic finite-alphabet processes, such as entropy rate and mutual information rate, with near-optimal performance and provide alternatives to classical approaches in the existing literature. Guided by these theoretical results, the proposed estimators are implemented using the context-tree weighting algorithm as the universal probability assignment. Experiments on synthetic and real data are presented, demonstrating the potential of the proposed schemes in practice and the utility of directed information estimation in detecting and measuring causal influence and delay.Comment: 23 pages, 10 figures, to appear in IEEE Transactions on Information Theor

    Analytical studies of groundwater-head fluctuation in a coastal confined aquifer overlain by a semi-permeable layer with storage

    Get PDF
    Analytical studies are carried out to investigate groundwater-head changes in a coastal aquifer system in response to tidal fluctuations. The system consists of an unconfined aquifer, a semi-confined aquifer and a semi-permeable confining unit between them. An exact analytical solution is derived to investigate the influences of both leakage and storage of the semi-permeable layer on the tide-induced groundwater-head fluctuation in the semi-confined aquifer. This solution is a generalization of the solution obtained by Jiao and Tang (Water Resource Research 35 (1999) 747-751) which ignored the storage of the semi-confining unit. The analytical solution indicates that both storage and leakage of the semi-permeable layer play an important role in the groundwater-head fluctuation in the confined aquifer. While leakage is generally more important than storage, the impact of storage on groundwater-head fluctuations changes with leakage. With the increase of leakage the fluctuation of groundwater-head in the confined aquifer will be controlled mainly by leakage. The study also demonstrates that the influence of storativity of the semi-permeable layer on groundwater-head fluctuation is negligible only when the storativity of the semi-permeable layer is comparable to or smaller than that of the confined aquifer. However, for aquifer systems with semi-permeable layer composed of thick, soft sedimentary materials, the storativity of the semi-permeable layer is usually much greater than that of the aquifer and its influence should be considered. © 2001 Elsevier Science Ltd. All rights reserved.postprin

    Airflow induced by pumping tests in unconfined aquifer with a low-permeability cap

    Get PDF
    Most analytical and numerical models developed to analyze pumping test data focus on saturated flow below the water table. Traditionally the soil above the initial water table prior to pumping has been thought to have little influence on the test results and has usually been ignored. It is hypothesized that, if the unsaturated zone is capped by low-permeability soil, airflow in the unsaturated zone may be developed during pumping and may have impact on the drawdown in the aquifer. A transient, three-dimensional and variably saturated flow model is employed to simulate the pumping-induced air and groundwater flows in both the saturated zone and unsaturated zone with a low-permeability layer. The results demonstrate that negative pressure in the unsaturated zone can be generated by pumping. The negative pressure begins to appear as the drawdown rate increases to a maximum, approaches a peak before the drawdown rate becomes zero, and then gradually disappears. Drawdown obtained from the capped aquifer is much greater because the water in the pores in the unsaturated zone is sucked by the negative pressure and the gravity drainage from the pores is hampered. Consequently, the drawdown versus time curve does not conform to the traditional S-shaped curve for an unconfined aquifer but is similar to that of a confined aquifer. If the airflow caused by the low-permeability cap is ignored, the error in estimated drawdown could be over 80% for the specific parameters and aquifer configuration used in the study. The possible errors in parameter estimation when airflow is ignored are explored. Overall, the hydraulic conductivity of the aquifer can be overestimated and the specific yield of the aquifer underestimated if airflow is ignored. The estimation error for specific yield tends to be greater than that in hydraulic conductivity. Copyright 2009 by the American Geophysical Union.published_or_final_versio
    • …
    corecore