Invariant forms and control dimensional parameters in complexity quantification
نویسندگان
چکیده
Non-equilibrium dynamics is omnipresent in nature and technology can exhibit symmetries order. In idealistic systems this universality well-captured by traditional models of dynamical systems. Realistic processes are often more complex. This work considers two paradigmatic complexities—canonical Kolmogorov turbulence interfacial Rayleigh-Taylor mixing. We employ invariant forms to assess very different properties characteristics these processes. inter-link, for the first time, our knowledge, scaling laws spectral shapes reveal decisive role control dimensional parameters their respective dynamics. find that provide key insights into attributes non-equilibrium dynamics, thus expanding range applicability well-beyond frameworks.
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translation invariant surfaces in the 3-dimensional heisenberg group
in this paper, we study translation invariant surfaces in the 3-dimensional heisenberg group $rm nil_3$. in particular, we completely classify translation invariant surfaces in $rm nil_3$ whose position vector $x$ satisfies the equation $delta x = ax$, where $delta$ is the laplacian operator of the surface and $a$ is a $3 times 3$-real matrix.
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ژورنال
عنوان ژورنال: Frontiers in Applied Mathematics and Statistics
سال: 2023
ISSN: ['2297-4687']
DOI: https://doi.org/10.3389/fams.2023.1201043