The Rise of Linear Borders

Since roughly the late 19th century, international borders have generally been characterized by linearity, or the appearance as a series of one-dimensional points, connected by straight lines. Prior to this, various kinds of frontiers existed globally, some of them being more linear than others, but most included some kind of formal ambiguity. International relations (IR) often takes for granted the historical process which brought about the global linearization of borders, culminating in the late 19th century and still ongoing in ocean spaces and in outer space. But because cross-border relations are the main substance of inquiry in IR, many theories and areas of study in IR contain some perspective on that process, at least implicitly.

On the System Entropy and Energy Dissipativity of Stochastic Systems and Their Application in Biological Systems

This study discusses the relationship between the entropy and the dissipativity of stochastic systems under the background of biological systems. First, measurement methods of the system entropy and energy dissipativity of linear stochastic biological systems are introduced. We found that the system entropy is negatively proportional to the energy dissipativity in logarithmic scale. Some opposite effects between system entropy and energy dissipativity are also discussed and compared based on their measured values to get insight into the understanding of the system mechanisms and the system characteristics. We found that the intrinsic random fluctuation and the enhancement of the system robust stability both can increase the system entropy but decrease the system dissipativity. The system entropy and the energy dissipativity of nonlinear stochastic biological systems are also discussed and compared based on a global linearization method. Computation methods are also provided. Finally, two numerical examples are demonstrated to verify theoretical prediction.

Nonlinear Multigrid for Reservoir Simulation

Summary A feasibility study is presented on the effectiveness of applying nonlinear multigrid methods for efficient reservoir simulation of subsurface flow in porous media. A conventional strategy modeled after global linearization by means of Newton’s method is compared with an alternative strategy modeled after local linearization, leading to a nonlinear multigrid method in the form of the full-approximation scheme (FAS). It is demonstrated through numerical experiments that, without loss of robustness, the FAS method can outperform the conventional techniques in terms of algorithmic and numerical efficiency for a black-oil model. Furthermore, the use of the FAS method enables a significant reduction in memory usage compared with conventional techniques, which suggests new possibilities for improved large-scale reservoir simulation and numerical efficiency. Last, nonlinear multilevel preconditioning in the form of a hybrid-FAS/Newton strategy is demonstrated to increase robustness and efficiency.

A Novel Dissipativity-Based Control for Inexact Nonlinearity Cancellation Problems

When dealing with linear systems feedback interconnected with memoryless nonlinearities, a natural control strategy is making the overall dynamics linear at first and then designing a linear controller for the remaining linear dynamics. By canceling the original nonlinearity via a first feedback loop, global linearization can be achieved. However, when the controller is not capable of exactly canceling the nonlinearity, such control strategy may provide unsatisfactory performance or even induce instability. Here, the interplay between accuracy of nonlinearity approximation, quality of state estimation, and robustness of linear controller is investigated and explicit conditions for stability are derived. An alternative controller design based on such conditions is proposed and its effectiveness is compared with standard methods on a benchmark system.

Spacecraft Autonomous GPS Navigation based on Polytopic Linear Differential Inclusion

Aiming at improving the poor real-time performance of existing nonlinear filtering algorithms applied to spacecraft autonomous navigation based on Global Positioning System (GPS) measurements and simplifying the algorithm design of navigation algorithms, a spacecraft autonomous navigation algorithm based on polytopic linear differential inclusion is proposed in this paper. Firstly, it is demonstrated that the nonlinear estimation error system of spacecraft autonomous navigation can be modelled as a polytopic linear differential inclusion system model according to the idea of global linearization. Thus, the filtering of a nonlinear system simplified to a filtering of a polytopic linear system with coefficients. Secondly, Tensor-Product (TP) model transformation is applied to determine the polytopic linear differential inclusion system model. The model error introduced by global linearization is reduced and the compromise between computational complexity and modelling accuracy is realised. Finally, a spacecraft autonomous navigation algorithm based on polytopic linear differential inclusion is designed by combining multi-model Kalman filtering with data fusion. Compared with an Extended Kalman Filter (EKF), the proposed algorithm is simpler and easier to implement since it need not update the Jacobian matrices online. Simulation results demonstrate the same estimation accuracy of the proposed algorithm to that of EKF.