Abstract. Numerical simulations of ice sheets rely on the momentum balance to determine how ice velocities change as the geometry of the system evolves. Ice is generally assumed to follow a Stokes flow with a nonlinear viscosity. Several approximations have been proposed in order to lower the computational cost of a full-Stokes stress balance. A popular option is the Blatter–Pattyn or higher-order model (HO), which consists of a three-dimensional set of equations that solves the horizontal velocities only. However, it still remains computationally expensive for long transient simulations. Here we present a depth-integrated formulation of the HO model, which can be solved on a two-dimensional mesh in the horizontal plane. We employ a specific polynomial function to describe the vertical variation in the velocity, which allows us to integrate the vertical dimension using a semi-analytic integration. We assess the performance of this MOno-Layer Higher-Order (MOLHO) model to compute ice velocities and simulate grounding line dynamics on standard benchmarks (ISMIP-HOM and MISMIP3D). We compare MOLHO results to the ones obtained with the original three-dimensional HO model. We also compare the time performance of both models in time-dependent runs. Our results show that the ice velocities and grounding line positions obtained with MOLHO are in very good agreement with the ones from HO. In terms of computing time, MOLHO requires less than 10 % of the computational time of a typical HO model, for the same simulations. These results suggest that the MOno-Layer Higher-Order formulation provides improved computational time performance and a comparable accuracy compared to the HO formulation, which opens the door to higher-order paleo simulations.
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The Reachable Set of a Drone: Exploring the Position Isochrones for a Quadcopter
Quadcopters are increasingly popular for robotics applications. Being able to efficiently calculate the set of positions reachable by a quadcopter within a time budget enables collision avoidance and pursuit-evasion strategies.This paper examines the set of positions reachable by a quadcopter within a specified time limit using a simplified 2D model for quadcopter dynamics. This popular model is used to determine the set of candidate optimal control sequences to build the full 3D reachable set. We calculate the analytic equations that exactly bound the set of positions reachable in a given time horizon for all initial conditions. To further increase calculation speed, we use these equations to derive tight upper and lower spherical bounds on the reachable set.
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- NSF-PAR ID:
- 10318015
- Date Published:
- Journal Name:
- 2021 IEEE International Conference on Robotics and Automation (ICRA)
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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ABSTRACT We detail a method to measure the correspondence between dark matter (DM) models and observations of stellar populations within Local Group dwarf spheroidal galaxies (LG dSphs) that assumes no parametric stellar distribution. Solving the spherical or cylindrical Jeans equations, we calculate the consistency of DM and stellar kinematic models with stellar positions and line-of-sight velocities. Our method can be used to search for signals of standard and exotic DM distributions. Applying our methodology to the Fornax LG dSph and using statistical bootstrapping, we find: (i) that oblate or prolate cored DM haloes match the stellar data, respectively, ≃60 or ≃370 times better than oblate or prolate cusped DM haloes for isotropic and isothermal stellar velocity dispersions, (ii) that cusped spherical DM haloes and cored spherical DM haloes match the Fornax data similarly well for isotropic stellar velocity dispersions, (iii) that the semiminor to semimajor axial ratio of spheroidal DM haloes are more extreme than 80 per cent of those predicted by Lambda cold dark matter with baryon simulations, (iv) that oblate cored or cusped DM haloes are, respectively, ≃5 or ≃30 times better matches to Fornax than prolate cored or cusped DM haloes, and (v) that Fornax shows no evidence of a disc-like structure with more than two per cent of the total DM mass. We further note that the best-fitting cusped haloes universally favour the largest mass and size fit parameters. If these extreme limits are decreased, the cusped halo likelihoods decrease relative to those of cored haloes.
- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Conference Paper:
- https://doi.org/10.1109/ICRA48506.2021.9561715
