Related papers: On a large-stepsize integrator for charged-particl…
A system of reduced equations is proposed for the electron motion in the strongly-radiation dominated regime for an arbitrary electromagnetic field configuration. The developed approach is used to analyze various scenarios of an electron…
Likelihood-based inference in stochastic non-linear dynamical systems, such as those found in chemical reaction networks and biological clock systems, is inherently complex and has largely been limited to small and unrealistically simple…
This paper proposes an iterative methodology to integrate large-scale behavioral activity-based models with dynamic traffic assignment models. The main novelty of the proposed approach is the decoupling of the two parts, allowing the…
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…
This paper is concerned with an efficient numerical method for solving the 1D stationary Schr\"odinger equation in the highly oscillatory regime. Being a hybrid, analytical-numerical approach it does not have to resolve each oscillation, in…
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,…
Estimating the number of components is a fundamental challenge in unsupervised learning, particularly when dealing with high-dimensional data with many components or severely imbalanced component sizes. This paper addresses this challenge…
Immersed boundary methods have attracted substantial interest in the last decades due to their potential for computations involving complex geometries. Often these cannot be efficiently discretized using boundary-fitted finite elements.…
We investigate the sensing capacity of non-equilibrium dynamics in quantum systems exhibiting Bloch oscillations. By focusing on the resource efficiency of the probe, quantified by quantum Fisher information, we find different scaling…
We develop two classes of composite moment-free numerical quadratures for computing highly oscillatory integrals having integrable singularities and stationary points. The first class of the quadrature rules has a polynomial order of…
We describe an algorithm for the numerical solution of second order linear differential equations in the highly-oscillatory regime. It is founded on the recent observation that the solutions of equations of this type can be accurately…
For trigonometric and modified trigonometric integrators applied to oscillatory Hamiltonian differential equations with one or several constant high frequencies, near-conservation of the total and oscillatory energies are shown over time…
A common way to evaluate electronic integrals for polyatomic molecules is to use Becke's partitioning scheme [J. Chem. Phys.88, 2547 (1988)] in conjunction with overlapping grids centered at each atomic site. The Becke scheme was designed…
In this paper, we extend several time reversible numerical integrators to solve the Lorentz force equations from second order accuracy to higher order accuracy for relativistic charged particle tracking in electromagnetic fields. A fourth…
Despite significant advances in particle imaging technologies over the past two decades, few advances have been made in particle tracking, i.e. linking individual particle positions across time series data. The state-of-the-art tracking…
Developing particle-in-cell (PIC) methods using finite element basis sets, and without auxiliary divergence cleaning methods, was a long standing problem until recently. It was shown that if consistent spatial basis functions are used, one…
The objective of this work is the introduction and investigation of favourable time integration methods for the Gross--Pitaevskii equation with rotation term. Employing a reformulation in rotating Lagrangian coordinates, the equation takes…
Symplectic schemes are powerful methods for numerically integrating Hamiltonian systems, and their long-term accuracy and fidelity have been proved both theoretically and numerically. However direct applications of standard symplectic…
By implementing the exact density matrix for the rotating anisotropic harmonic trap, we derive a class of very fast and accurate fourth order algorithms for evolving the Gross-Pitaevskii equation in imaginary time. Such fourth order…
We derive a formalism, the separation method, for the efficient and accurate calculation of two-body matrix elements for a Gaussian potential in the cylindrical harmonic-oscillator basis. This formalism is of critical importance for…