this study proposes a new linear approximation for solving the dynamic response equations of a rocking rigid block. linearization assumptions which have already been used by hounser and other researchers cannot be valid for all rocking blocks with various slenderness ratios and dimensions; hence, developing new methods which can result in better approximation of governing equations while keepin...

this study proposes a new linear approximation for solving the dynamic response equations of a rocking rigid block. linearization assumptions which have already been used by hounser and other researchers cannot be valid for all rocking blocks with various slenderness ratios and dimensions; hence, developing new methods which can result in better approximation of governing equations while keepin...

The objective of this note is to show how one can combine Polynomial Chaos Expansions (PCE) and adjoint theory to efficiently obtain sensitivities for robust optimal control. A non-intrusive PCE method is used to analyze the constraint equations for the state (which depends on uncertain inputs), namely the governing equations of the dynamical system. Adjoint solutions are constructed for each o...

Usage of fuzzy differential equations (FDEs) is a natural way to model dynamical systems under possibilistic uncertainty. We consider second order hybrid fuzzy differentia

We investigate nonlinear phenomena in dispersed two-phase systems under creeping-flow conditions. We consider nonlinear evolution of a single deformed drop and collective dynamics of arrays of hydrodynamically coupled particles. To explore physical mechanisms of system instabilities, chaotic drop evolution, and structural transitions in particle arrays we use simple models, such as small-deform...

We present a method for the generation of real-time dynamic autonomous agents in game environments. The method is based on the use of dynamical systems theory which allows us to express intelligent behaviors using systems of differential equations. These differential equations operate at two distinct levels. At one level, the differential equations governing movement comprise a carefully design...

A new class of integro-partial differential equation models is derived for the prediction of granular flow dynamics. These models are obtained using a novel limiting averaging method (inspired by techniques employed in the derivation of infinite-dimensional dynamical systems models) on the Newtonian equations of motion of a many-particle system incorporating widely used inelastic particle-parti...

We present an equation-free multi-scale approach to the computational study of the collective dynamics of the Kuramoto model [Chemical Oscillations, Waves, and Turbulence, Springer-Verlag (1984)], a prototype model for coupled oscillator populations. Our study takes place in a reduced phase space of coarse-grained “observables” of the system: the first few moments of the oscillator phase angle ...

The information detection of complex systems from data is currently undergoing a revolution, driven by the emergence big and machine learning methodology. Discovering governing equations quantifying dynamical properties are among central challenges. In this work, we devised nonparametric approach to relative entropy rate observations stochastic differential with different drift functions. estim...

We propose a sparse regression method capable of discovering the governing partial differential equation(s) of a given system by time series measurements in the spatial domain. The regression framework relies on sparsity-promoting techniques to select the nonlinear and partial derivative terms of the governing equations that most accurately represent the data, bypassing a combinatorially large ...