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Computational Nonlinear Physics

When dynamics result in unpredictable patterns and formations and when collective behaviors of systems cannot be simply or linearly described by accumulating the impacts of individual components, nonlinearity occurs. Computational nonlinear physics, in this sense, allows researchers to develop numerical models and simulations to understand complex nonlinear patterns and behaviors, which can be exemplified as turbulence, pattern formation and chaotic systems.

Computational nonlinear physics, having the integration of physics, mathematics and computer science, makes use of computational methods for the examination of nonlinear systems. Nonlinearity emerges through the collective behavior of systems, and interactions among their components which result in emergent phenomena like solitons, fractals and chaos. As the dynamics that may result in can be unpredictable, non-equilibrium pattern formation could be the outcomes. When the collective behaviors of systems cannot be simply or linearly described by adding up the effects of individual components, nonlinearity is said to occur. Computational nonlinear physics, in this regard, enable researchers to develop simulations and numerical models for understanding nonlinear and complex patterns as well as behaviors, which can be illustrated as pattern formation, turbulence and chaotic systems. In addition, means such as physics-informed neural networks (PINNs) are employed for the aim of solving nonlinear partial differential equations. To sum up, computational nonlinear physics proves to be beneficial in exploring the intricate phenomena that go beyond linear approximations, which may help with the generation of adopting new angles into natural as well as engineered systems.

Consequently, the relevant topical areas can be considered as the following points:

  • Non-linear optics and photonics
  • Dynamic systems in electronic circuits
  • Chaos and non-linearity
  • Fluid dynamics, modeling turbulent flows and vortex dynamics
  • Materials science and phase transitions
  • Biophysics and simulation of biological processes and / or neural networks
  • Climate modeling, climate patterns and currents.
  • Pattern formation and self-organization in nonlinear systems
  • Nonsmooth dynamics, systems with time and/or space delays
  • Nonlinear circuits, neural circuits, memristor and Josephson junctions
  • Micro/nanosystems, nanomaterials, multi-sensors, multi-actuators, nonlinear data fusion
  • Composite/nanocomposites, adaptive, multifunctional, metamaterial, morphing structures
  • Rigid/flexible multibody system dynamics, impact and contact
  • Reduced-order modeling
  • Fluid/structure interaction
  • Multi-scale/multi-physics dynamics
  • Nonlinear resonances, modal interactions, stochastic resonance, coherence resonance, noise and stochastic disturbance
  • Nonlinear control systems, synchronization
  • Nonlinear wave propagation in discrete/continuous media, pattern formation/selection in spatio-temporal systems
  • Computational techniques, perturbation methods, local/global methods, efficient algorithms, parallel processing, computational intelligence
  • Nonlinear dynamics for design

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