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We derive a new criterion for estimating characteristic dynamical timescales in N-body simulations. The criterion uses the second, third, and fourth derivatives of particle positions: acceleration, jerk, and snap. It can be used for…
An approach is proposed to improve the efficiency of fourth-order algorithms for numerical integration of the equations of motion in molecular dynamics simulations. The approach is based on an extension of the decomposition scheme by…
We review the implementation of individual particle time-stepping for N-body dynamics. We present a class of integrators derived from second order Hamiltonian splitting. In contrast to the usual implementation of individual time-stepping,…
Topology optimization is a powerful tool utilized in various fields for structural design. However, its application has primarily been restricted to static or passively moving objects, mainly focusing on hard materials with limited…
We present a new implicit asymptotic preserving time integration scheme for charged-particle orbit computation in arbitrary electromagnetic fields. The scheme is built on the Crank-Nicolson integrator and continues to recover full-orbit…
A new approach for integration of motion in many-body systems of interacting polyatomic molecules is proposed. It is based on splitting time propagation of pseudo-variables in a modified phase space, while the real translational and…
Time distributed optimization is an implementation strategy that can significantly reduce the computational burden of model predictive control by exploiting its robustness to incomplete optimization. When using this strategy, optimization…
We propose a novel unifying scheme for parallel implementation of articulated robot dynamics algorithms. It is based on a unified Lie group notation for deriving the equations of motion of articulated robots, where various well-known…
A wide range of implicit time integration methods, including multi-step, implicit Runge-Kutta, and Galerkin finite-time element schemes, is evaluated in the context of chaotic dynamical systems. The schemes are applied to solve the Lorenz…
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,…
This work introduces novel unconditionally stable operator splitting methods for solving the time dependent nonlinear Poisson-Boltzmann (NPB) equation for the electrostatic analysis of solvated biomolecules. In a pseudo-transient…
Recent advances in deep learning have allowed neural networks (NNs) to successfully replace traditional numerical solvers in many applications, thus enabling impressive computing gains. One such application is time domain simulation, which…
We present a new method for developing time step controllers based on a technique from the field of machine learning. This method is applicable to stable time integrators that have an embedded scheme, i.e., that have local error estimation…
Optimizing problems in a distributed manner is critical for systems involving multiple agents with private data. Despite substantial interest, a unified method for analyzing the convergence rates of distributed optimization algorithms is…
This work introduces a time-adaptive strategy that uses a refinement estimator based on the first Frenet curvature. In dynamics, a time-adaptive strategy is a mechanism that interactively proposes changes to the time step used in iterative…
Robotic manipulation and locomotion often entail nearly-simultaneous collisions -- such as heel and toe strikes during a foot step -- with outcomes that are extremely sensitive to the order in which impacts occur. Robotic simulators…
A single-step high-order implicit time integration scheme with controllable numerical dissipation at high frequencies is presented for the transient analysis of structural dynamic problems. The amount of numerical dissipation is controlled…
We investigate a high-order, fully explicit, asymptotic-preserving scheme for a kinetic equation with linear relaxation, both in the hydrodynamic and diffusive scalings in which a hyperbolic, resp. parabolic, limiting equation exists. The…
It has previously been shown that varying the numerical timestep during a symplectic orbital integration leads to a random walk in energy and angular momentum, destroying the phase space-conserving property of symplectic integrators. Here…
The method of choice for integrating the equations of motion of the general N-body problem has been to use an individual time step scheme. For the sake of efficiency, block time steps have been the most popular, where all time step sizes…