Related papers: Optimized Verlet-like algorithms for molecular dyn…

In this paper we propose a time-splitting finite-element scheme for approximating solutions of the Ericksen-Leslie equations governing the flow of nematic liquid crystals. These equations are to be solved for a velocity vector field and a…

We present an algorithm for safe robot navigation in complex dynamic environments using a variant of model predictive equilibrium point control. We use an optimization formulation to navigate robots gracefully in dynamic environments by…

A new algorithm has been developed to compute low Mach Numbers supercritical fluid flows. The algorithm is applied using a finite volume method based on the SIMPLER algorithm. Its main advantages are to decrease significantly the CPU time,…

A thermodynamically consistent particle-based model for fluid dynamics with continuous velocities and a non-ideal equation of state is presented. Excluded volume interactions are modeled by means of biased stochastic multiparticle…

This paper proposes a low order geometrically exact flexible beam formulation based on the utilisation of generic beam shape functions to approximate distributed kinematic properties of the deformed structure. The proposed nonlinear beam…

Event-driven molecular dynamics is a valuable tool in condensed and soft matter physics when particles can be modeled as hard objects or more generally if their interaction potential can be modeled in a stepwise fashion. Hard spheres model…

Vertex functions are a crucial ingredient of several forefront many-body algorithms in condensed matter physics. However, the full treatment of their frequency and momentum dependence severely restricts numerical calculations. A significant…

Stable computational algorithms for the approximate solution of the Cauchy problem for nonstationary problems are based on implicit time approximations. Computational costs for boundary value problems for systems of coupled multidimensional…

This paper presents a randomized algorithm for computing the near-optimal low-rank dynamic mode decomposition (DMD). Randomized algorithms are emerging techniques to compute low-rank matrix approximations at a fraction of the cost of…

We provide a unifying framework for $\mathcal{L}_2$-optimal reduced-order modeling for linear time-invariant dynamical systems and stationary parametric problems. Using parameter-separable forms of the reduced-model quantities, we derive…

We introduce a modified model of random walk, and then develop two novel clustering algorithms based on it. In the algorithms, each data point in a dataset is considered as a particle which can move at random in space according to the…

We exploit analogies between first-order algorithms for constrained optimization and non-smooth dynamical systems to design a new class of accelerated first-order algorithms for constrained optimization. Unlike Frank-Wolfe or projected…

Gradient descent and its variants are widely used in machine learning. However, oracle access of gradient may not be available in many applications, limiting the direct use of gradient descent. This paper proposes a method of estimating…

The authors present a new molecular dynamics algorithm for sampling the isothermal-isobaric ensemble. In this approach the velocities of all particles and volume degrees of freedom are rescaled by a properly chosen random factor. The…

This is the final paper in a series that introduces geodesic molecular dynamics at constant potential energy. This dynamics is entitled NVU dynamics in analogy to standard energy-conserving Newtonian NVE dynamics. In the first two papers…

In this paper we propose a high-order accurate scheme for image segmentation based on the level-set method. In this approach, the curve evolution is described as the 0-level set of a representation function but we modify the velocity that…

This paper transfers the concept of moment matching to nonlinear structural systems and further provides a simulation-free reduction scheme for such nonlinear second-order models. After first presenting the steady-state interpretation of…

The optimal conversion of a continuous inter-particle potential to a discrete equivalent is considered here. Existing and novel algorithms are evaluated to determine the best technique for creating accurate discrete forms using the minimum…

A class of second-order algorithms is proposed for minimizing smooth nonconvex functions that alternates between regularized Newton and negative curvature steps in an iteration-dependent subspace. In most cases, the Hessian matrix is…

This paper concerns models and convergence principles for dealing with stochasticity in a wide range of algorithms arising in nonlinear analysis and optimization in Hilbert spaces. It proposes a flexible geometric framework within which…