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pro vyhledávání: '"Chechin, George"'
Autor:
Chechin, George, Bezuglova, Galina
Intermode interactions in one-dimensional nonlinear periodic structures have been studied by many authors, starting with the classic work by Fermi, Pasta, and Ulam (FPU) in the middle of the last century. However, symmetry selection rules for the ene
Externí odkaz:
http://arxiv.org/abs/2212.12829
Autor:
Chechin, George, Ryabov, Denis
Intermode interactions in one-dimensional nonlinear periodic structures have been studied by many authors, starting with the classical work by Fermi, Pasta, and Ulam (FPU) in the middle of the last century. However, symmetry selection rules for the e
Externí odkaz:
http://arxiv.org/abs/2109.09101
Autor:
Chechin, George, Ryabov, Denis
The research group from the Rostov State University has been developing the theory of bushes of nonlinear normal modes (NNMs) in Hamiltonian systems with discrete symmetry since the late 90s of the last century. Group-theoretical methods for studying
Externí odkaz:
http://arxiv.org/abs/2005.13343
Autor:
Chechin, George, Bezuglova, Galina
Publikováno v:
In Communications in Nonlinear Science and Numerical Simulation November 2023 126
Autor:
Chechin, George, Lapina, Victoria
We discuss bi-structures with one or two long bonds in the central part of the strained monoatomic chains appearing abruptly as a result of hard bifurcations of the static form with increasing strain above some critical value. Structures of this type
Externí odkaz:
http://arxiv.org/abs/1910.03326
Autor:
Chechin, George, Lapina, Victoria
We proved earlier that in the strained monoatomic chains with Lennard-Jones potential there can exist an equilibrium static bi-structure, which corresponds to N - 1 equal short interatomic bonds and one long bond with inversion in its center (N is th
Externí odkaz:
http://arxiv.org/abs/1903.05423
Autor:
Chechin, George, Ryabov, Denis
Publikováno v:
In Communications in Nonlinear Science and Numerical Simulation June 2023 120
Symmetry-determined nonlinear normal modes, which describe large-amplitude vibrations of diamond lattice, are studied by specific group-theoretical methods. For two of these modes, corresponding to vibrational state with and without multiplication of
Externí odkaz:
http://arxiv.org/abs/1811.06260
A group-theoretical approach for studying localized periodic and quasiperiodic vibrations in 2D and 3D lattice dynamical models is developed. This approach is demonstrated for the scalar models on the plane square lattice. The symmetry-determined inv
Externí odkaz:
http://arxiv.org/abs/1106.1757
In this tutorial we address the existence and stability of periodic and quasiperiodic orbits in N degree of freedom Hamiltonian systems and their connection with discrete symmetries. Of primary importance in our study are the nonlinear normal modes (
Externí odkaz:
http://arxiv.org/abs/1005.4308