Related papers: On the accuracy of symplectic integrators for secu…
We report on an ongoing investigation into a seismic calibration of solar models designed for estimating the main-sequence age and a measure of the chemical abundances of the Sun. Only modes of low degree are employed, so that with…
Although analytical studies on the secular motion of the irregular satellites have been published recently, these theories have not yet been satisfactorily reconciled with the results of direct numerical integrations. These discrepancies…
We provide new existence and uniqueness results for the discrete-time Hamilton (DTH) equations of a symplectic-energy-momentum (SEM) integrator. In particular, we identify points in extended-phase space where the DTH equations of SEM…
Cosmological parameter estimation from forthcoming experiments promise to reach much greater precision than current constraints. As statistical errors shrink, the required control over systematic errors increases. Therefore, models or…
Error correction of sequenced reads remains a difficult task, especially in single-cell sequencing projects with extremely non-uniform coverage. While existing error correction tools designed for standard (multi-cell) sequencing data…
Time-symmetric integration schemes share with symplectic schemes the property that their energy errors show a much better behavior than is the case for generic integration schemes. Allowing adaptive time steps typically leads to a loss of…
Many astronomers have speculated that the solar system contains undiscovered massive planets or a distant stellar companion. The acceleration of the solar system barycenter can constrain the mass and position of the putative companion. In…
An error analysis of trigonometric integrators (or exponential integrators) applied to spatial semi-discretizations of semilinear wave equations with periodic boundary conditions in one space dimension is given. In particular, optimal…
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…
Adiabatic modeling of solar-like oscillations cannot exceed a certain level of precision for fitting individual frequencies. This is known as the problem of near surface effects on the mode physics. We present a theoretical study which…
Ensuring a satisfactory statistical convergence of anharmonic thermodynamic properties requires sampling of many atomic configurations, however the methods to obtain those necessarily produce correlated samples, thereby reducing the…
Ptolemy-s planetary model is an ancient geocentric astronomical model, describing the observed motion of the Sun and the planets. Ptolemy accounted for the deviations of planetary orbits from perfect circles by introducing two small and…
The long-term variations in the orbit of the Earth govern the insolation on its surface and hence its climate. The use of the astronomical signal, whose imprint has been recovered in the geological records, has revolutionized the…
We construct a secular theory of a coplanar system of N-planets not involved in strong mean motion resonances, and which are far from collision zones. Besides the point-to-point Newtonian mutual interactions, we consider the general…
We present a non-canonically symplectic integration scheme tailored to numerically computing the post-Newtonian motion of a spinning black-hole binary. Using a splitting approach we combine the flows of orbital and spin contributions. In…
Modified Hamiltonians are used in the field of geometric numerical integration to show that symplectic schemes for Hamiltonian systems are accurate over long times. For nonlinear systems the series defining the modified Hamiltonian usually…
Stochastic methods offer an effective way to suppress coherent errors in quantum simulation. In particular, the randomized compilation protocol may reduce circuit depth by randomly sampling Hamiltonian terms rather than following the…
We reconsider the variational derivation of symplectic partitioned Runge-Kutta schemes. Such type of variational integrators are of great importance since they integrate mechanical systems with high order accuracy while preserving the…
Spin-orbit coupling of planetary systems plays an important role in the dynamics and habitability of planets. However, symplectic integrators that can accurately simulate not only how orbit affects spin but also how spin affects orbit have…
We construct a symplectic, globally defined, minimal-coordinate, equivariant integrator on products of 2-spheres. Examples of corresponding Hamiltonian systems, called spin systems, include the reduced free rigid body, the motion of point…