Quadratic Relationship

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George B. Benedek - One of the best experts on this subject based on the ideXlab platform.

  • Thickness–radius Relationship and spring constants of cholesterol helical ribbons
    Proceedings of the National Academy of Sciences of the United States of America, 2009
    Co-Authors: Boris Khaykovich, Natalia Kozlova, Wonshik Choi, Aleksey Lomakin, Chintan Hossain, Yongjin Sung, Ramachandra R. Dasari, Michael S. Feld, George B. Benedek
    Abstract:

    Using quantitative phase microscopy, we have discovered a Quadratic Relationship between the radius R and the thickness t of helical ribbons that form spontaneously in multicomponent cholesterol–surfactant mixtures. These helical ribbons may serve as mesoscopic springs to measure or to exert forces on nanoscale biological objects. The spring constants of these helices depend on their submicroscopic thickness. The Quadratic Relationship (R ∝ t2) between radius and thickness is a consequence of the crystal structure of the ribbons and enables a determination of the spring constant of any of our helices solely in terms of its observable geometrical dimensions.

Sandra Gordon - One of the best experts on this subject based on the ideXlab platform.

  • Improved models of the effects of winter chilling on blackcurrant (Ribes nigrum L.) show cultivar specific sensitivity to warm winters
    Agricultural and Forest Meteorology, 2020
    Co-Authors: Katharine F. Preedy, Rex M. Brennan, Hamlyn G. Jones, Sandra Gordon
    Abstract:

    Abstract Sufficient chilling in winter is essential for many perennial crops to start growing in spring and to produce good yields. Using blackcurrants as an example we have developed improved models which can help identify varieties resilient to the variable winters expected as the climate warms. Controlled temperature experiments were used to calibrate 3 proposed models of chilling accumulation requirements for a number of commercial blackcurrant cultivars. The first model assumed a linear Relationship between bud break and chilling accumulation, the second a Quadratic Relationship which allows for the possibility of over-chilling and the third, an asymmetric Quadratic Relationship in which the maximum achievable effectiveness is temperature dependent. The models were then applied to data on selected cultivars gathered from blackcurrant growers across the United Kingdom and the third model was found to provide the best fit for the data, suggesting that long warm winters do not have the same effect as short cold winters in terms of the satisfaction of chilling requirement. Further, the degree to which temperature affects maximum bud break varies by cultivar. We discuss the potential effects of differing timing of chill on the applicability of the models presented.

Boris Khaykovich - One of the best experts on this subject based on the ideXlab platform.

  • Thickness–radius Relationship and spring constants of cholesterol helical ribbons
    Proceedings of the National Academy of Sciences of the United States of America, 2009
    Co-Authors: Boris Khaykovich, Natalia Kozlova, Wonshik Choi, Aleksey Lomakin, Chintan Hossain, Yongjin Sung, Ramachandra R. Dasari, Michael S. Feld, George B. Benedek
    Abstract:

    Using quantitative phase microscopy, we have discovered a Quadratic Relationship between the radius R and the thickness t of helical ribbons that form spontaneously in multicomponent cholesterol–surfactant mixtures. These helical ribbons may serve as mesoscopic springs to measure or to exert forces on nanoscale biological objects. The spring constants of these helices depend on their submicroscopic thickness. The Quadratic Relationship (R ∝ t2) between radius and thickness is a consequence of the crystal structure of the ribbons and enables a determination of the spring constant of any of our helices solely in terms of its observable geometrical dimensions.

Ian C. Ward - One of the best experts on this subject based on the ideXlab platform.

  • Air flow through cracks
    Building and Environment, 2003
    Co-Authors: P. H. Baker, Steve Sharples, Ian C. Ward
    Abstract:

    The pressure flow characteristics of a number of full-scale model cracks, representative of real leakage paths, have been measured. The crack flow equations developed by Etheridge [1] have been verified over a wider range of parameters. The authors suggest a Quadratic Relationship: ΔP = A·Q+B·Q2 which follows from the same flow theory as the Etheridge solution, to replace the ubiquitous power law as a practical fit to pressurisation data. Unlike the power law, the Quadratic coefficients A and B can be directly related to crack parameters, and a simple graphical method is given to enable the prediction of crack leakage areas.

Michael S. Feld - One of the best experts on this subject based on the ideXlab platform.

  • Thickness–radius Relationship and spring constants of cholesterol helical ribbons
    Proceedings of the National Academy of Sciences of the United States of America, 2009
    Co-Authors: Boris Khaykovich, Natalia Kozlova, Wonshik Choi, Aleksey Lomakin, Chintan Hossain, Yongjin Sung, Ramachandra R. Dasari, Michael S. Feld, George B. Benedek
    Abstract:

    Using quantitative phase microscopy, we have discovered a Quadratic Relationship between the radius R and the thickness t of helical ribbons that form spontaneously in multicomponent cholesterol–surfactant mixtures. These helical ribbons may serve as mesoscopic springs to measure or to exert forces on nanoscale biological objects. The spring constants of these helices depend on their submicroscopic thickness. The Quadratic Relationship (R ∝ t2) between radius and thickness is a consequence of the crystal structure of the ribbons and enables a determination of the spring constant of any of our helices solely in terms of its observable geometrical dimensions.