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Two specialized algorithms for the numerical integration of the equations of motion of a Brownian walker obeying detailed balance are introduced. The algorithms become symplectic in the appropriate limits, and reproduce the equilibrium…
Variational quantum algorithms are promising applications of noisy intermediate-scale quantum (NISQ) computers. These algorithms consist of a number of separate prepare-and-measure experiments that estimate terms in a Hamiltonian. The…
This paper proposes several explicit and implicit multistep frequency response optimized integrators considering first or second order derivative. A prediction-based method aiming at accelerating a novel power system transient simulation…
We study a classical reparametrization-invariant system, in which ``time'' is not a priori defined. It consists of a nonrelativistic particle moving in five dimensions, two of which are compactified to form a torus. There, assuming a…
Variational integrators are well-suited for simulation of mechanical systems because they preserve mechanical quantities about a system such as momentum, or its change if external forcing is involved, and holonomic constraints. While they…
We present two types of meta-algorithm that can greatly improve the accuracy of existing algorithms for integrating the equations of motion of dynamical systems. The first meta-algorithm takes an integrator that is time-symmetric only for…
A recently introduced particle-based model for fluid dynamics with effective excluded volume interactions is analyzed in detail. The interactions are modeled by means of stochastic multiparticle collisions which are biased and depend on…
We investigate the response of large inertial particle to turbulent fluctuations in a inhomogeneous and anisotropic flow. We conduct a Lagrangian study using particles both heavier and lighter than the surrounding fluid, and whose diameters…
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…
Recently, the spectral manipulation of single photons has been achieved through spatial-temporal modulation of the optical refractive index. Here, we generalize this mechanism to massive particles, i.e. realizing the acceleration or…
The schooling behavior of fish can be studied through simulations involving a large number of interacting particles. In such systems, each individual particle is guided by behavior rules, which include aggregation towards a centroid,…
In the framework of a Particle-In-Cell scheme for some 1D Vlasov-Poisson system depending on a small parameter, we propose a time-stepping method which is numerically uniformly accurate when the parameter goes to zero. Based on an…
Universal fault-tolerant quantum computers will require error-free execution of long sequences of quantum gate operations, which is expected to involve millions of physical qubits. Before the full power of such machines will be available,…
Numerical methods that preserves geometric invariants of the system such as energy, momentum and symplectic form, are called geometric integrators. These include variational integrators as an important subclass of geometric integrators. The…
In this paper, we present different types of integrators for electro-magnetic particle-in-cell (PIC) methods. While the integrator is an important tool of the PIC methods, it is necessary to characterize the different conservation…
We propose and analyse a numerical integrator that computes a low-rank approximation to large time-dependent matrices that are either given explicitly via their increments or are the unknown solution to a matrix differential equation.…
We formulate a finite-size particle numerical model of strongly magnetized plasmas in the drift-kinetic approximation. We use the phase space action as an alternative to previous variational formulations based on Low's Lagrangian or on a…
In the era of noisy intermediate-scale quantum computers, variational quantum algorithms are promising approaches for solving optimization tasks by training parameterized quantum circuits with the aid of classical routines informed by…
A procedure to numerically integrate non-autonomous linear delay differential equations is presented. It is based on the use of an spectral discretization of the delayed part to transform the original problem into a matrix linear ordinary…
Geometric integrators of the Schr\"{o}dinger equation conserve exactly many invariants of the exact solution. Among these integrators, the split-operator algorithm is explicit and easy to implement, but, unfortunately, is restricted to…