This paper aims at reviewing nonlinear methods for model order reduction in structures with
geometric nonlinearity, with a special emphasis on the techniques based on invariant …

The author attempts to portray the ideas and general principles of the theory of materials
within the framework of phenomenological continuum mechanics. It is a well-written rigorous …

The prediction of extreme events, from avalanches and droughts to tsunamis and epidemics,
depends on the formulation and analysis of relevant, complex dynamical systems. Such …

Fifteen years have elapsed after the second edition of Practical Bifurcation and Stability
Analysis was published. During that time period the? eld of computational bifurcation has …

This book aims to bridge the gap between practising mathematicians and the practitioners of
turbulence theory. It presents the mathematical theory of turbulence to engineers and …

Many industrial processes belong to distributed parameter systems (DPS) that have strong
spatial–temporal dynamics. Modeling of DPS is difficult but essential to simulation, control …

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In data-driven modeling of spatiotemporal phenomena careful consideration is needed in
capturing the dynamics of the high wavenumbers. This problem becomes especially …

This paper introduces a methodology for the synthesis of nonlinear finite-dimensional output
feedback controllers for systems of quasi-linear parabolic partial differential equations …

We evaluate several alternative methods for the approximation of inertial manifolds for the
one-dimensional Kuramoto-Sivashinsky equation (KSE). A method motivated by the …