Examinando por Autor "Burdzy, Krzysztof"

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    A Lower Bound for the Number of Elastic Collisions
    (Springer New York LLC, 2019-12) Burdzy, Krzysztof; Duarte, Mauricio
    We prove by example that the number of elastic collisions of n balls of equal mass and equal size ind-dimensional space can be greater than n3/27 for n≥ 3 and d≥ 2. The previously known lower bound was of order n2. © 2019, Springer-Verlag GmbH Germany, part of Springer Nature.
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    Fermi acceleration in rotating drums
    (American Institute of Physics Inc., 2022-06-01) Burdzy, Krzysztof; Duarte, Mauricio; Gauthier, Carl-Erik; Graham, C. Robin; San Martin, Jaime
    Consider hard balls in a bounded rotating drum. If there is no gravitation, then there is no Fermi acceleration, i.e., the energy of the balls remains bounded forever. If there is gravitation, Fermi acceleration may arise. A number of explicit formulas for the system without gravitation are given. Some of these are based on an explicit realization, which we derive, of the well-known microcanonical ensemble measure. © 2022 Author(s).
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    On the number of hard ball collisions
    (John Wiley and Sons Ltd., 2020-02) Burdzy, Krzysztof; Duarte, Mauricio
    We give a new and elementary proof that the number of elastic collisions of a finite number of balls in the Euclidean space is finite. We show that if there are (Formula presented.) balls of equal masses and radii 1, and at the time of a collision between any two balls the distance between any other pair of balls is greater than (Formula presented.), then the total number of collisions is bounded by (Formula presented.), for any fixed (Formula presented.) and large (Formula presented.). We also show that if there is a number of collisions larger than (Formula presented.) for an appropriate (Formula presented.), then a large number of these collisions occur within a subfamily of balls that form a very tight configuration. © 2019 London Mathematical Society