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Register a new userInvestigating the use of field solvers for simulating classical systems
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We explore the use of field solvers as approximations of classical Vlasov-Poisson systems. This correspondence is investigated in both electrostatic and gravitational contexts. We demonstrate the ability of field solvers to be excellent approximations of problems with cold initial condition into the non linear regime. We also investigate extensions of the Schrodinger-Poisson system that employ multiple stacked cold streams, and the von Neumann-Poisson equation as methods that can successfully reproduce the classical evolution of warm initial conditions. We then discuss how appropriate simulation parameters need to be chosen to avoid interference terms, aliasing, and wave behavior in the field solver solutions. We present a series of criteria clarifying how parameters need to be chosen in order to effectively approximate classical solutions.
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We introduce a numerical method and python package, https://github.com/andillio/CHiMES, that simulates quantum systems initially well approximated by mean field theory using a second order extension of the classical field approach. We call this the field moment expansion method. In this way, we can accurately approximate the evolution of first and second field moments beyond where the mean field theory breaks down. This allows us to estimate the quantum breaktime of a classical approximation without any calculations external to the theory. We investigate the accuracy of the field moment expansion using a number of well studied quantum test problems. Interacting Bosonic systems similar to scalar field dark matter are chosen as test problems. We find that successful application of this method depends on two conditions: the quantum system must initially be well described by the classical theory, and that the growth of the higher order moments be hierarchical.
Recently, a family of models that couple multifluid systems to the full Maxwell equations draw a lot of attention in laboratory, space, and astrophysical plasma modeling. These models are more complete descriptions of the plasma than reduced models like magnetohydrodynamic (MHD) since they naturally retain non-ideal effects like electron inertia, Hall term, pressure anisotropy/nongyrotropy, etc. One obstacle to broader application of these model is that an explicit treatment of their source terms leads to the need to resolve rapid kinetic processes like plasma oscillation and electron cyclotron motion, even when they are not important. In this paper, we suggest two ways to address this issue. First, we derive the analytic forms solutions to the source update equations, which can be implemented as a practical, but less generic solver. We then develop a time-centered, locally implicit algorithm to update the source terms, allowing stepping over the fast kinetic time-scales. For a plasma with $S$ species, the locally implict algorithm involves inverting a local $3S+3$ matrix only, thus is very efficient. The performance can be further elevated by using the direct update formulas to skip null calculations. Benchmarks illustrated the exact energy-conservation of the locally implicit solver, as well as its efficiency and robustness for both small-scale, idealized problems and large-scale, complex systems. The locally implicit algorithm can be also easily extended to include other local sources, like collisions and ionization, which are difficult to solve analytically.
We explore higher-dimensional generalizations of the Runge-Kutta-Wentzel-Kramers-Brillouin method for integrating coupled systems of first-order ordinary differential equations with highly oscillatory solutions. Such methods could improve the performance and adaptability of the codes which are used to compute numerical solutions to the Einstein-Boltzmann equations. We test Magnus expansion-based methods on the Einstein-Boltzmann equations for a simple universe model dominated by photons with a small amount of cold dark matter. The Magnus expansion methods achieve an increase in run speed of about 50% compared to a standard Runge-Kutta integration method. A comparison of approximate solutions derived from the Magnus expansion and the Wentzel-Kramers-Brillouin (WKB) method implies the two are distinct mathematical approaches. Simple Magnus expansion solutions show inferior long range accuracy compared to WKB. However we also demonstrate how one can improve on the standard Magnus approach to obtain a new Jordan-Magnus method. This has a WKB-like performance on simple two-dimensional systems, although its higher-dimensional generalization remains elusive.
The solution of problems in physics is often facilitated by a change of variables. In this work we present neural transformations to learn symmetries of Hamiltonian mechanical systems. Maintaining the Hamiltonian structure requires novel network architectures that parametrize symplectic transformations. We demonstrate the utility of these architectures by learning the structure of integrable models. Our work exemplifies the adaptation of neural transformations to a family constrained by more than the condition of invertibility, which we expect to be a common feature of applications of these methods.
Optical resonators are widely used in modern photonics. Their spectral response and temporal dynamics are fundamentally driven by their natural resonances, the so-called quasinormal modes (QNMs), with complex frequencies. For optical resonators made of dispersive materials, the QNM computation requires solving a nonlinear eigenvalue problem. This rises a difficulty that is only scarcely documented in the literature. We review our recent efforts for implementing efficient and accurate QNM-solvers for computing and normalizing the QNMs of micro- and nano-resonators made of highly-dispersive materials. We benchmark several methods for three geometries, a two-dimensional plasmonic crystal, a two-dimensional metal grating, and a three-dimensional nanopatch antenna on a metal substrate, in the perspective to elaborate standards for the computation of resonance modes.
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