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We present a differentiable dynamics solver that is able to handle frictional contact for rigid and deformable objects within a unified framework. Through a principled mollification of normal and tangential contact forces, our method…
We discuss in detail properties of trapped atomic condensates with anisotropic dipole interactions. A practical procedure for constructing anisotropic low energy pseudo potentials is proposed and justified by the agreement with results of…
The systematic errors due to the practical implementation of the Contact Dynamics method for simulation of dense granular media are examined. It is shown that, using the usual iterative solver to simulate a chain of rigid particles,…
Vlasov kinetic theory is the dynamics of a bunch of particles flowing according to symplectic Hamiltonian dynamics. More recently, this geometry has been extended to contact Hamiltonian dynamics. In this paper, we introduce geometric…
This paper presents a geometric-variational approach to continuous and discrete mechanics and field theories. Using multisymplectic geometry, we show that the existence of the fundamental geometric structures as well as their preservation…
We develop the equations of motion for full body models that describe the dynamics of rigid bodies, acting under their mutual gravity. The equations are derived using a variational approach where variations are defined on the Lie group of…
Long-range corrected (LC) hybrid functionals and asymptotically corrected (AC) model potentials are two distinct density functional methods with correct asymptotic behavior. They are known to be accurate for properties that are sensitive to…
In this work we introduce contact Hamiltonian mechanics, an extension of symplectic Hamiltonian mechanics, and show that it is a natural candidate for a geometric description of non-dissipative and dissipative systems. For this purpose we…
In this paper, we propose an integrated dynamical model of Connected and Automated Vehicles (CAVs) which incorporates CAV technologies and a microscopic car-following model to improve safety, efficiency and convenience. We rigorously…
In this lectures various methods which give a possibility to extend an area of applicability of perturbation series and hence to omit their local character are analysed. While applying asymptotic methods as a rule the following situation…
As roles for unmanned aerial vehicles (UAV) continue to diversify, the ability to sense and interact closely with the environment becomes increasingly important. Within this paper we report on the initial flight tests of a novel adaptive…
Variational integrators for Lagrangian dynamical systems provide a systematic way to derive geometric numerical methods. These methods preserve a discrete multisymplectic form as well as momenta associated to symmetries of the Lagrangian…
Common methods for learning robot dynamics assume motion is continuous, causing unrealistic model predictions for systems undergoing discontinuous impact and stiction behavior. In this work, we resolve this conflict with a smooth, implicit…
The molecular dynamics method is applied to simulate the recrystallization of an amorphous/crystalline silicon interface. The atomic structure of the amorphous material is constructed with the method of Wooten, Winer, and Weaire. The…
We present a new class of high-order variational integrators on Lie groups. We show that these integrators are symplectic, momentum preserving, and can be constructed to be of arbitrarily high-order, or can be made to converge…
Elastic interaction of pressurized spherical cavities embedded in a three-dimensional hyperelastic medium is computationally analyzed. Using finite element analysis across several positive and negative pressure scenarios, we calculate the…
This is the author's PhD Thesis (University of Cambridge, 2014) in its original form. In the first part, using an invariance result, we compute the symplectic homology of contact-type energy levels for magnetic systems on surfaces, provided…
In this paper we present an influence of discontinuous coupling on the dynamics of multistable systems. Our model consists of two periodically forced oscillators that can interact via soft impacts. The controlling parameters are the…
This paper presents a three-dimensional framework for simulating dynamic wetting phenomena using the volume of fluid (VOF) method, implemented in Basilisk. A geometric interpolation scheme is developed to obtain an accurate and reliable…
In intelligent manufacturing, robots are asked to dynamically adapt their behaviours without reducing productivity. Human teaching, where an operator physically interacts with the robot to demonstrate a new task, is a promising strategy to…