2,513,331 research outputs found

    On the non-integrability of the Popowicz peakon system

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    We consider a coupled system of Hamiltonian partial differential equations introduced by Popowicz, which has the appearance of a two-field coupling between the Camassa-Holm and Degasperis-Procesi equations. The latter equations are both known to be integrable, and admit peaked soliton (peakon) solutions with discontinuous derivatives at the peaks. A combination of a reciprocal transformation with Painlev\'e analysis provides strong evidence that the Popowicz system is non-integrable. Nevertheless, we are able to construct exact travelling wave solutions in terms of an elliptic integral, together with a degenerate travelling wave corresponding to a single peakon. We also describe the dynamics of N-peakon solutions, which is given in terms of an Hamiltonian system on a phase space of dimension 3N.Comment: 8 pages, AIMS class file. Proceedings of AIMS conference on Dynamical Systems, Differential Equations and Applications, Arlington, Texas, 200

    Relaxation rate, diffusion approximation and Fick's law for inelastic scattering Boltzmann models

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    We consider the linear dissipative Boltzmann equation describing inelastic interactions of particles with a fixed background. For the simplified model of Maxwell molecules first, we give a complete spectral analysis, and deduce from it the optimal rate of exponential convergence to equilibrium. Moreover we show the convergence to the heat equation in the diffusive limit and compute explicitely the diffusivity. Then for the physical model of hard spheres we use a suitable entropy functional for which we prove explicit inequality between the relative entropy and the production of entropy to get exponential convergence to equilibrium with explicit rate. The proof is based on inequalities between the entropy production functional for hard spheres and Maxwell molecules. Mathematical proof of the convergence to some heat equation in the diffusive limit is also given. From the last two points we deduce the first explicit estimates on the diffusive coefficient in the Fick's law for (inelastic hard-spheres) dissipative gases.Comment: 25 page

    Manuscript Collections

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    Edwin C. Graber Poetry Collection

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    Edwin C. Graber is from Freeman, Hutchinson County, South Dakota. The collection is composed of chapbooks of his poetry

    Lonita Gustad Corothers Papers

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    Lonita Gustad Corothers was a student in the Division of Pharmacy at South Dakota State College starting in September of 1946 and graduating in the spring of 1950. Her graduating class was comprised of eight women and 56 men. Her minor was in chemistry. She began keeping a diary in 1945 when she was 17 years old and realized that she was living in momentous times. The collection is composed of her diaries from 1946 through 2010, excerpts from and a timeline index of the diaries, correspondence with Tom Corothers written primarily during their courtship, a grief notebook written after her husband died, and her original writings and poetry

    Valerian Three Irons American Indian Oral Histories Microfiche

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    Valerian Three Irons, was an American Indian Studies professor and Diversity Association at South Dakota State University from 1997 to 2011. He donated the Listen to Indians microfiche to the Archives in 2004. The “Listening to Indians” project which was planned executed, and directed by Mr. Samuel I. Meyers as part of the New York Times Oral History Program. The project was funded by the New York Times Oral History Program and completed in 1978. Members of many American Indian tribes are represented

    Quiet City, trumpet manuscript

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    Trumpet part for Aaron Copland's "Quiet City", copied out and annotated by Roger Voisin for use in performance. Top right corner signed by Copland: "For Roger Voisin who plays this like a dream. A Copland 1957"

    Clark S. Thomas Student Expense Notebook

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    Notebook of Clark S. Thomas documenting his personal expenses while attending South Dakota State College

    Incredible Gladys Pyle Collection

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    This collection is a small representation of the research that Jeanette Kinyon and Jean Walz gathered for biography of Gladys Pyle, titled The Incredible Gladys Pyle. Pyle was a South Dakota politician and the first woman elected to the United States Senate without having previously been appointed to her position; she was also the first female senator to serve as a Republican and the first female senator from South Dakota
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