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For problems in astrophysics, planetary science and beyond, numerical simulations are often limited to simulating fewer particles than in the real system. To model collisions, the simulated particles (aka superparticles) need to be inflated to represent a collectively large collisional cross section of real particles. Here we develop a superparticle-based method that replicates the kinetic energy loss during real-world collisions, implement it in an $N$-body code and test it. The tests provide interesting insights into dynamics of self gravitating collisional systems. They show how particle systems evolve over several free fall timescales to form central concentrations and equilibrated outer shells. The superparticle method can be extended to account for the accretional growth of objects during inelastic mergers.
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The dynamics of planetesimals plays an important role in planet formation, because their velocity distribution sets the growth rate to larger bodies. When planetesimals form in protoplanetary discs, their orbits are nearly circular and planar due to the effect of gas drag. However, mutual close encounters of the planetesimals increase eccentricities and inclinations until an equilibrium between stirring and damping is reached. After disc dissipation, there is no more gas drag and mutual close encounters as well as encounters with planets stir the orbits again. The high number of planetesimals in protoplanetary discs renders it difficult to simulate their dynamics by means of direct N-body simulations of planet formation. Therefore, we developed a novel method for the dynamical evolution of planetesimals that is based on following close encounters between planetesimal-mass bodies and gravitational stirring by planet-mass bodies. To separate the orbital motion from the close encounters, we employ a Hamiltonian splitting scheme as used in symplectic N-body integrators. Close encounters are identified using a cell algorithm with linear scaling in the number of bodies. A grouping algorithm is used to create small groups of interacting bodies which are integrated separately. Our method allows simulating a high number of planetesimals interacting through gravity and collisions with low computational cost. The typical computational time is of the order of minutes or hours, up to a few days for more complex simulations, as compared to several hours or even weeks for the same setup with full N-body. The dynamical evolution of the bodies is sufficiently well reproduced. This will make it possible to study the growth of planetesimals through collisions and pebble accretion coupled to their dynamics for a much higher number of bodies than previously accessible with full N-body simulations.
We propose a new model for treating solid-phase photoprocesses in interstellar ice analogues. In this approach, photoionization and photoexcitation are included in more detail, and the production of electronically-excited (suprathermal) species is explicitly considered. In addition, we have included non-thermal, non-diffusive chemistry to account for the low-temperature characteristic of cold cores. As an initial test of our method, we have simulated two previous experimental studies involving the UV irradiation of pure solid O$_2$. In contrast to previous solid-state astrochemical model calculations which have used gas-phase photoabsorption cross-sections, we have employed solid-state cross-sections in our calculations. This method allows the model to be tested using well-constrained experiments rather than poorly constrained gas-phase abundances in ISM regions. Our results indicate that inclusion of non-thermal reactions and suprathermal species allows for reproduction of low-temperature solid-phase photoprocessing that simulate interstellar ices within cold ($sim$ 10 K) dense cores such as TMC-1.
Central stages in the evolution of rocky, potentially habitable planets may play out under atmospheric conditions with a large inventory of non-dilute condensable components. Variations in condensate retention and accompanying changes in local lapse rate may substantially affect planetary climate and surface conditions, but there is currently no general theory to effectively describe such atmospheres. In this article, expanding on the work by Li et al. (2018), we generalize the single-component moist pseudoadiabat derivation in Pierrehumbert (2010) to allow for multiple condensing components of arbitrary diluteness and retained condensate fraction. The introduction of a freely tunable retained condensate fraction allows for a flexible, self-consistent treatment of atmospheres with non-dilute condensable components. To test the pseudoadiabats capabilities for simulating a diverse range of climates, we apply the formula to planetary atmospheres with compositions, surface pressures, and temperatures representing important stages with condensable-rich atmospheres in the evolution of terrestrial planets: a magma ocean planet in a runaway greenhouse state; a post-impact, late veneer-analogue planet with a complex atmospheric composition; and an Archean Earth-like planet near the outer edge of the classical circumstellar habitable zone. We find that variations in the retention of multiple non-dilute condensable species can significantly affect the lapse rate and in turn outgoing radiation and the spectral signatures of planetary atmospheres. The presented formulation allows for a more comprehensive treatment of the climate evolution of rocky exoplanets and early Earth analogues.
We develop a highly efficient numerical method to simulate small-amplitude flapping propulsion by a flexible wing in a nearly inviscid fluid. We allow the wings elastic modulus and mass density to vary arbitrarily, with an eye towards optimizing these distributions for propulsive performance. The method to determine the wing kinematics is based on Chebyshev collocation of the 1D beam equation as coupled to the surrounding 2D fluid flow. Through small-amplitude analysis of the Euler equations (with trailing-edge vortex shedding), the complete hydrodynamics can be represented by a nonlocal operator that acts on the 1D wing kinematics. A class of semi-analytical solutions permits fast evaluation of this operator with $O(N log N)$ operations, where $N$ is the number of collocation points on the wing. This is in contrast to the minimum $O(N^2)$ operations required by a direct 2D fluid solver. The coupled wing-fluid problem is thus recast as a PDE with nonlocal operator, which we solve using a preconditioned iterative method. These techniques yield a solver of near-optimal complexity, $O(N log N)$, allowing one to rapidly search the infinite-dimensional parameter space of all possible material distributions and even perform optimization over this space.
We generalize solid-state tight-binding techniques for the spectral analysis of large superconducting circuits. We find that tight-binding states can be better suited for approximating the low-energy excitations than charge-basis states, as illustrated for the interesting example of the current-mirror circuit. The use of tight binding can dramatically lower the Hilbert space dimension required for convergence to the true spectrum, and allows for the accurate simulation of larger circuits that are out of reach of charge basis diagonalization.
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