An Improved Coordinate Registration for Over-the-Horizon Radar Using Reference Sources

In the target localization of skywave over-the-horizon radar (OTHR), the error of the ionospheric parameters is one main error source. To reduce the error of ionospheric parameters, a method using both the information of reference sources (e.g., terrain features, ADS-B) in ground coordinates and the corresponding OTHR measurements is proposed to estimate the ionospheric parameters. Describing the ionospheric electron density profile by the quasi-parabolic model, the estimation of the ionospheric parameters is formulated as an inverse problem, and is solved by a Markov chain Monte Carlo method due to the complicated ray path equations. Simulation results show that, comparing with using the a prior value of the ionospheric parameters, using the estimated ionospheric parameters based on four airliners in OTHR coordinate registration process, the ground range RMSE of interested targets is reduced from 2.86 to 1.13 km and the corresponding improvement ratio is up to 60.39%. This illustrates that the proposed method using reference sources is able to significantly improve the accuracy of target localization.

Zero inertia limit of incompressible Qian–Sheng model

The Qian–Sheng model is a system describing the hydrodynamics of nematic liquid crystals in the Q-tensor framework. When the inertial effect is included, it is a hyperbolic-type system involving a second-order material derivative coupling with forced incompressible Navier–Stokes equations. If formally letting the inertial constant [Formula: see text] go to zero, the resulting system is the corresponding parabolic model. We provide the result on the rigorous justification of this limit in [Formula: see text] with small initial data, which validates mathematically the parabolic Qian–Sheng model. To achieve this, an initial layer is introduced to not only overcome the disparity of the initial conditions between the hyperbolic and parabolic models, but also make the convergence rate optimal. Moreover, a novel [Formula: see text]-dependent energy norm is carefully designed, which is non-negative only when [Formula: see text] is small enough, and handles the difficulty brought by the second-order material derivative.

High order Anderson parabolic model driven by rough noise in space

In this paper, we concern the fourth parabolic model on [Formula: see text] driven by a multiplicative Gaussian noise which behaves like fractional Brownian motion in time and space with Hurst index [Formula: see text] and [Formula: see text], respectively. The existence and uniqueness of mild solution in Skorohod sense are proved, and the weak intermittency is obtained by estimating [Formula: see text]th ([Formula: see text]) moment of the solution. Moreover, the Hölder continuity can be obtained for the time and space variable.

Global existence and asymptotic behaviour of solutions for a hyperbolic-parabolic model of chemotaxis on network

In this paper, we discuss a hyperbolic-parabolic system modeling biological phenomena evolving on a network. The global existence of the is obtained by using energy estimates with suitable the transmission conditions at interior. Moreover, for the case of acyclic network, the existence and uniqueness of stationary solution to the system is proposed and it is proved that these ones are asymptotic profiles for a class of global solutions