Multiphase chemical reactors with characteristic multiscale structures are intrinsically
discrete at the elemental scale. However, due to the lack of multiscale models and the …

Accurate numerical simulation of dynamical systems is essential in applications ranging
from particle physics to geophysical fluid flow to space hazard analysis. However, most …

This paper concerns heteroclinic connections and resonance transitions in the planar
circular restricted 3-body problem, with applications to the dynamics of comets and asteroids …

Discover How Geometric Integrators Preserve the Main Qualitative Properties of Continuous
Dynamical Systems A Concise Introduction to Geometric Numerical Integration presents the …

In this volume readers will find for the first time a detailed account of the theory of symplectic
reduction by stages, along with numerous illustrations of the theory. Special emphasis is …

Practical time steps in today's state-of-the-art simulators typically rely on Newton's method to
solve large systems of nonlinear equations. In practice, this works well for small time steps …

The paper provides an introduction and survey of conservative discretization methods for
Hamiltonian partial differential equations. The emphasis is on variational, symplectic and …

We develop an optimal transportation meshfree (OTM) method for simulating general solid
and fluid flows, including fluid–structure interaction. The method combines concepts from …

We introduce vertex block descent, a block coordinate descent solution for the variational
form of implicit Euler through vertex-level Gauss-Seidel iterations. It operates with local …

Fluid deformable surfaces are ubiquitous in cell and tissue biology, including lipid bilayers,
the actomyosin cortex or epithelial cell sheets. These interfaces exhibit a complex interplay …