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In this thesis, we propose model order reduction techniques for high-dimensional PDEs that preserve structures of the original problems and develop a closure modeling framework leveraging the Mori-Zwanzig formalism and recurrent neural networks. Since high ...
We present a fully Hamiltonian and computationally efficient scheme to include the electrostatic effects due to the classical environment in a Car-Parrinello mixed quantum mechanics/mol. mechanics (QM/MM) method. The polarization due to the MM atoms close ...
Atomistic simulations are a bottom up approach that predict properties
of materials by modelling the quantum mechanical behaviour of all electrons
and nuclei present in a system. These simulations, however, routinely assume
nuclei to be classical particles ...
The theory of discrete variational mechanics has its roots in the optimal control literature of the 1960's. The past ten years have seen a major development of discrete variational mechanics and corresponding numerical integrators, due largely to pioneerin ...
We study some mechanical problems in which a friction force is acting on a system. Using the fundamental concepts of state, time evolution and energy conservation, we explain how to extend Newtonian mechanics to thermodynamics. We arrive at the two laws of ...
The free energy plays a fundamental role in theories of phase transformations and microstructure evolution. It encodes the thermodynamic coupling between different fields, such as mechanics and chemistry, within continuum descriptions of non-equilibrium ma ...
We examine the correspondence between a quantum system and its classical analogue. We consider the wedge billiard which shows a wide variety of behaviors ranging from integrable to strongly chaotic. Angle-action coordinates are provided for the flow and fo ...
The Monge problem [23], [27], as reformulated by Kantorovich [19], [20] is that of the transportation, at a minimum "cost", of a given mass distribu- tion from an initial to a final position during a given time interval. It is an optimal transport problem ...
The goal of this short presentation is to introduce Geometric Mechanics as well as Asynchronous Variational Integrators (AVI). The geometric point of view in mechanics combined with solid analysis has been a phenomenal success in linking various diverse ar ...
The most classic approach to the dynamics of an n-dimensional mechanical system constrained by d independent holonomic constraints is to pick explicitly a new set of (n - d) curvilinear coordinatesparametrizingthe manifold of configurations satisfying the ...
