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Atmospheric systems incorporating thermal dynamics must be stable with respect to both energy and entropy. While energy conservation can be enforced via the preservation of the skew-symmetric structure of the Hamiltonian form of the…
Numerical algorithms based on variational and symplectic integrators exhibit special features that make them promising candidates for application to general relativity and other constrained Hamiltonian systems. This paper lays part of the…
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…
We study the motion of a particle in a 3-dimensional lattice in the presence of a Coulomb potential, but we demonstrate semiclassicaly that the trajectories will always remain in a plane which can be taken as a rectangular lattice. The…
Hamilton's equations of motion form a fundamental framework in various branches of physics, including astronomy, quantum mechanics, particle physics, and climate science. Classical numerical solvers are typically employed to compute the…
We derive energy-norm a posteriori error bounds for an Euler time-stepping method combined with various spatial discontinuous Galerkin schemes for linear parabolic problems. For accessibility, we address first the spatially semidiscrete…
In a recent study, (Jain et al 2007 Phys. Rev. Lett. 99 190601), a symmetric exclusion process with time-dependent hopping rates was introduced. Using simulations and a perturbation theory, it was shown that if the hopping rates at two…
A Hamiltonian formulation of generic many-particle systems with space-dependent balanced loss and gain coefficients is presented. It is shown that the balancing of loss and gain necessarily occurs in a pair-wise fashion. Further, using a…
There is a growing interest in the conservation of invariants when numerically solving a system of ordinary differential equations. Methods that exactly preserve these quantities in time are known as geometric integrators. In this paper we…
We provide topological obstructions to the existence of orbit cylinders of symmetric orbits, for mechanical systems preserved by antisymplectic involutions (e.g. the restricted three-body problem). Such cylinders induce continuous paths…
Time crystals are systems that spontaneously break time-translation symmetry, exhibiting repeating patterns in time. Recent work has shown that non-Hermitian Floquet systems can host a time crystalline phase with quasi-long-range order. In…
This paper presents an adaptive symplectic integrator, SQQ-PTQ, developed on the basis of the fixed-step symplectic integrator SQQ. To mitigate the Runge phenomenon, SQQ-PTQ employs Chebyshev interpolation for approximating the action,…
Discrete time crystals (DTC) have emerged as a significant phase of matter for out-of-equilibrium many-body systems. We study how long-range interactions and disorder contribute to the stability of the DTC phase. Generally, a stable DTC…
The largest part of any gravitational-wave inspiral of a compact binary can be understood as a slow, adiabatic drift between the trajectories of a certain referential conservative system. In many contexts, the phase space of this…
In most semiconductors and insulators the presence of a small density of charged impurities cannot be avoided, but their effect can be reduced by compensation doping, i.e. by introducing defects of opposite charge. Screening in such a…
Lagrangian displacement field $\Psi$ is the central object in Lagrangian perturbation theory (LPT). LPT is very successful at high redshifts, but it performs poorly at low redshifts due to severe shell crossing. To understand and quantify…
Using the Hubbard Hamiltonian for transition metal-3d and oxygen-2p states with perovskite geometry, we propose a new scaling procedure for a nontrivial extension of these systems to large spatial dimensions $D$. The scaling procedure is…
Symplectic tracking of beam particles using point magnets is achieved using a reference orbit made of circular arcs and straight lines that join smoothly with each other. For this choice of the reference orbit, results are given for the…
The effect of dynamical tide ``kicks" on eccentric binary orbits is considered using the orbital mapping method. It is demonstrated that when mode damping is negligible the mode amplitude will generically grow in time for all values of…
We propose new semi-implicit numerical methods for the integration of the stochastic Landau-Lifshitz equation with built-in angular momentum conservation. The performance of the proposed integrators is tested on the 1D Heisenberg chain. For…