Related papers: Asynchronous Variational Integration of Interactio…
An asynchronous, variational method for simulating elastica in complex contact and impact scenarios is developed. Asynchronous Variational Integrators (AVIs) are extended to handle contact forces by associating different time steps to…
The phase field approach is widely used to model fracture behaviors due to the absence of the need to track the crack topology and the ability to predict crack nucleation and branching. In this work, the asynchronous variational integrators…
Dynamic simulation of elastic bodies is a longstanding task in engineering and computer graphics. In graphics, numerical integrators like implicit Euler and BDF2 are preferred due to their stability at large time steps, but they tend to…
Symplectic integration algorithms have become popular in recent years in long-term orbital integrations because these algorithms enforce certain conservation laws that are intrinsic to Hamiltonian systems. For problems with large variations…
The simulation of multi-body systems with frictional contacts is a fundamental tool for many fields, such as robotics, computer graphics, and mechanics. Hard frictional contacts are particularly troublesome to simulate because they make the…
Symplectic integrators are widely used for long-term integration of conservative astrophysical problems due to their ability to preserve the constants of motion; however, they cannot in general be applied in the presence of nonconservative…
A fixed time-step variational integrator cannot preserve momentum, energy, and symplectic form simultaneously for nonintegrable systems. This barrier can be overcome by treating time as a discrete dynamic variable and deriving adaptive…
A new approach is developed to integrate numerically the equations of motion for systems of interacting rigid polyatomic molecules. With the aid of a leapfrog framework, we directly involve principal angular velocities into the integration,…
A general model covering a large variety of the so-called adhesive or cohesive, possibly also frictional, contact interfaces between visco-elastic bodies with inertia considered in a thermodynamical context is presented. A semi-implicit…
Molecular dynamics simulations provide a versatile framework to study interfacial heat transport, but their accuracy remains limited by the accuracy of available interatomic potentials. In the past, researchers have adopted the use of…
Multibody dynamics simulators are an important tool in many fields, including learning and control for robotics. However, many existing dynamics simulators suffer from inaccuracies when dealing with constrained mechanical systems due to…
Simple models for spherical particles with a soft shell have been shown to self-assemble into numerous crystal phases and even quasicrystals. However, most of these models rely on a simple pairwise interaction, which is usually a valid…
Numerical methods that preserve geometric invariants of the system, such as energy, momentum or the symplectic form, are called geometric integrators. Variational integrators are an important class of geometric integrators. The general idea…
The interaction of fluid membranes with a scaffold, which can be a planar surface or a more complex structure, is intrinsic to a number of systems - from artificial supported bilayers and vesicles to cellular membranes. In principle, these…
We present a novel theory of the adhesive contact of linear viscoelastic materials against rigid substrates moving at constant velocity. Despite the non-conservative behavior of the system, the closure equation of the contact problem can be…
Research on Multi-rotor Aerial Vehicles (MAVs) has experienced remarkable advancements over the past two decades, propelling the field forward at an accelerated pace. Through the implementation of motion control and the integration of…
In the framework of the recently developed asymptotic models for tibio-femoral contact incorporating frictionless elliptical contact interaction between thin elastic, viscoelastic, or biphasic cartilage layers, we apply an asymptotic…
We discuss a novel approach that allows to obtain effective potentials from ab initio trajectories. Our method consists in fitting the weighted radial distribution functions obtained from the ab initio data with the ones obtained from…
Structure-preserving integrators are in the focus of ongoing research because of their distinguished features of robustness and long time stability. In particular, their formulation for coupled problems that include dissipative mechanisms…
We use a variational wave function to calculate the energy of the interaction between external charges in the compact Abelian gauge theory in 2+1 dimensions with mixed action. Our variational wave functions preserve the compact gauge…