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We revisit here the dynamics of an engineered dimer granular crystal under an external periodic drive in the presence of dissipation. Earlier findings included a saddle-node bifurcation, whose terminal point initiated the observation of chaos; the sy
Externí odkaz:
http://arxiv.org/abs/2407.19347
Autor:
Chapman, S. Jon, Kavousanakis, M., Charalampidis, E. G., Kevrekidis, I. G., Kevrekidis, P. G.
In the present work we revisit the problem of the generalized Korteweg-de Vries equation parametrically, as a function of the relevant nonlinearity exponent, to examine the emergence of blow-up solutions, as traveling waveforms lose their stability p
Externí odkaz:
http://arxiv.org/abs/2310.13770
Steady states are invaluable in the study of dynamical systems. High-dimensional dynamical systems, due to a separation of time-scales, often evolve towards a lower dimensional manifold $M$. We introduce an approach to locate saddle points (and other
Externí odkaz:
http://arxiv.org/abs/2309.16920
Autor:
Williams, M. O., Psarellis, Y. M., Pozharskiy, D., Chong, C., Li, F., Yang, J., Kevrekidis, P. G., Kevrekidis, I. G.
This chapter discusses the development and implementation of algorithms based on Equation-Free/Dynamic Data Driven Applications Systems (EF/DDDAS) protocols for the computer-assisted study of the bifurcation structure of complex dynamical systems, su
Externí odkaz:
http://arxiv.org/abs/2305.02404
Autor:
Chapman, S. J., Kavousanakis, M. E., Charalampidis, E. G., Kevrekidis, I. G., Kevrekidis, P. G.
The nonlinear Schroedinger model is a prototypical dispersive wave equation that features finite time blowup, either for supercritical exponents (for fixed dimension) or for supercritical dimensions (for fixed nonlinearity exponent). Upon identifying
Externí odkaz:
http://arxiv.org/abs/2201.13051
The Equation-Free approach to efficient multiscale numerical computation marries trusted micro-scale simulations to a framework for numerical macro-scale reduction -- the patch dynamics scheme. A recent novel patch scheme empowered the Equation-Free
Externí odkaz:
http://arxiv.org/abs/2108.11568
Publikováno v:
Phys. Rev. E 104, 044202 (2021)
The study of nonlinear waves that collapse in finite time is a theme of universal interest, e.g. within optical, atomic, plasma physics, and nonlinear dynamics. Here we revisit the quintessential example of the nonlinear Schrodinger equation and syst
Externí odkaz:
http://arxiv.org/abs/2008.08968
Equation-free macroscale modelling is a systematic and rigorous computational methodology for efficiently predicting the dynamics of a microscale system at a desired macroscale system level. In this scheme, the given microscale model is computed in s
Externí odkaz:
http://arxiv.org/abs/2007.06815
Scientists and engineers often create accurate, trustworthy, computational simulation schemes - but all too often these are too computationally expensive to execute over the time or spatial domain of interest. The equation-free approach is to marry s
Externí odkaz:
http://arxiv.org/abs/2002.11852
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