Study on autonomous satellite navigation from SHAR observations

This paper uses two navigation schemes to prove the potential of a novel autonomous orbit determination with stellar horizon atmospheric refraction measurements. Scheme one needs a single processor and uses an extended Kalman filter. The second scheme needs two parallel processors. One processor uses a hatched leastsquare initial state estimator and a high-precision dynamic state propagator. The other processor uses a real-time orbit predictor. Simulations have been executed respectively for three types （low/medial/high） of satellite orbits on which various numbers of stars are observed. The results show both schemes can autonomously determine the orbits with a considerable performance. The second scheme in general performs a little better than the first scheme.

On the mean field limit of the Random Batch Method for interacting particle systems

The Random Batch Method proposed in our previous work(Jin et al.J Comput Phys,2020)is not only a numerical method for interacting particle systems and its mean-field limit,but also can be viewed as a model of the particle system in which particles interact,at discrete time,with randomly selected mini-batch of particles.In this paper,we investigate the mean-field limit of this model as the number of particles N→∞.Unlike the classical mean field limit for interacting particle systems where the law of large numbers plays the role and the chaos is propagated to later times,the mean field limit now does not rely on the law of large numbers and the chaos is imposed at every discrete time.Despite this,we will not only justify this mean-field limit(discrete in time)but will also show that the limit,as the discrete time intervalτ→0,approaches to the solution of a nonlinear Fokker-Planck equation arising as the mean-field limit of the original interacting particle system in the Wasserstein distance.

THE RANDOM BATCH METHOD FOR N-BODY QUANTUM DYNAMICS

This paper discusses a numerical method for computing the evolution of large interacting system of quantum particles.The idea of the random batch method is to replace the total interaction of each particle with the N−1 other particles by the interaction with p≪N particles chosen at random at each time step,multiplied by(N−1)/p.This reduces the computational cost of computing the interaction potential per time step from O(N^(2))to O(N).For simplicity,we consider only in this work the case p=1—in other words,we assume that N is even,and that at each time step,the N particles are organized in N/2 pairs,with a random reshuffling of the pairs at the beginning of each time step.We obtain a convergence estimate for the Wigner transform of the single-particle reduced density matrix of the particle system at time t that is both uniform in N>1 and independent of the Planck constant h̵.The key idea is to use a new type of distance on the set of quantum states that is reminiscent of the Wasserstein distance of exponent 1(or Monge-Kantorovich-Rubinstein distance)on the set of Borel probability measures on Rd used in the context of optimal transport.

Random Batch Particle Methods for the Homogeneous Landau Equation

We consider in this paper randombatch particlemethods for efficiently solving the homogeneous Landau equation in plasma physics.The methods are stochastic variations of the particle methods proposed by Carrillo et al.[J.Comput.Phys.:X 7:100066,2020]using the random batch strategy.The collisions only take place inside the small but randomly selected batches so that the computational cost is reduced to O(N)per time step.Meanwhile,our methods can preserve the conservation of mass,momentum,energy and the decay of entropy.Several numerical examples are performed to validate our methods.

Temporal variation in modal properties of a base-isolated building during an earthquake

Temporal variation of dynamical modal properties of a base-isolated building is investigated using earthquake records in the building. A batch processing least-squares estimation method is applied to segment-wise time-series data. To construct an input-output system,an auto-regressive model with exogenous input (ARX) of second-order including a forgetting coefficient as a weighting coefficient is used for the estimation of modal parameters. The fundamental and second natural frequencies and the damping ratios of the fundamental and second natural modes of the base-isolated building are identified in the time domain. The identified results are consistent with the results obtained from the micro-tremor vibration data,forced-vibration test data and earthquake records in the present base-isolated building in the case of taking into account the amplitude-dependency of the isolators and viscous dampers. It is finally pointed out that several factors,e.g.,amplitude dependency of the isolator and damper system and special characteristics of the series-type viscous damper system,may be related complicatedly with the temporal variation in modal properties of the above-mentioned system.