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  • 1
    Electronic Resource
    Electronic Resource
    Testing the thermodynamic approach to granular matter with a numerical model of a decisive experiment (2002)
    [s.l.] : Macmillian Magazines Ltd.
    Nature 415 (2002), S. 614-617 
    Details
    ISSN: 1476-4687
    Source: Nature Archives 1869 - 2009
    Topics: Biology , Chemistry and Pharmacology , Medicine , Natural Sciences in General , Physics
    Notes: [Auszug] Edwards has proposed a thermodynamic description of dense, slowly flowing granular matter, in which the grains (the ‘atoms’ of the system) interact with inelastic forces and enduring contacts. In Edwards' ensemble—one of the very few generalizations of standard statistical ...
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1038/415614a
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    Paper (German National Licenses)
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  • 2
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    Fluctuation distributions of energy minima in complex landscapes (2021)
    Details
    Publication Date: 2023-01-06
    Description: We discuss the properties of the distributions of energies of minima obtained by gradient descent in complex energy landscapes. We find strikingly similar phenomenology across several prototypical models. We particularly focus on the distribution of energies of minima in the analytically well-understood p-spin-interaction spin-glass model. We numerically find non-Gaussian distributions that resemble the Tracy-Widom distributions often found in problems of random correlated variables, and nontrivial finite-size scaling. Based on this, we propose a picture of gradient-descent dynamics that highlights the importance of a first-passage process in the eigenvalues of the Hessian. This picture provides a concrete link to problems in which the Tracy-Widom distribution is established. Aspects of this first-passage view of gradient-descent dynamics are generic for nonconvex complex landscapes, rationalizing the commonality that we find across models.
    Language: English
    Type: article , doc-type:article
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