Further development of discrete computational techniques for calculation of restricted diffusion propagators in porous media

Magnetic resonance is a well-established tool for structural characterisation of porous media. Features of pore-space morphology can be inferred from NMR diffusion-diffraction plots or the time-dependence of the apparent diffusion coefficient. Diffusion NMR signal attenuation can be computed from the restricted diffusion propagator, which describes the distribution of diffusing particles for a given starting position and diffusion time. We present two techniques for efficient evaluation of restricted diffusion propagators for use in NMR porous-media characterisation. The first is the Lattice Path Count (LPC). Its physical essence is that the restricted diffusion propagator connecting points A and B in time t is proportional to the number of distinct length-t paths from A to B. By using a discrete lattice, the number of such paths can be counted exactly. The second technique is the Markov transition matrix (MTM). The matrix represents the probabilities of jumps between every pair of lattice nodes within a single timestep. The propagator for an arbitrary diffusion time can be calculated as the appropriate matrix power. For periodic geometries, the transition matrix needs to be defined only for a single unit cell. This makes MTM ideally suited for periodic systems. Both LPC and MTM are closely related to existing computational techniques: LPC, to combinatorial techniques; and MTM, to the Fokker-Planck master equation. The relationship between LPC, MTM and other computational techniques is briefly discussed in the paper. Both LPC and MTM perform favourably compared to Monte Carlo sampling, yielding highly accurate and almost noiseless restricted diffusion propagators. Initial tests indicate that their computational performance is comparable to that of finite element methods. Both LPC and MTM can be applied to complicated pore-space geometries with no analytic solution. We discuss the new methods in the context of diffusion propagator calculation in porous materials and model biological tissues.

On the zeros of the Abelian integrals for a class of Liénard systems

A planar polynomial differential system has a finite number of limit cycles. However, finding the upper bound of the number of limit cycles is an open problem for the general nonlinear dynamical systems. In this paper, we investigated a class of Liénard systems of the form x'=y, y'=f(x)+y g(x) with deg f=5 and deg g=4. We proved that the related elliptic integrals of the Liénard systems have at most three zeros including multiple zeros, which implies that the number of limit cycles bifurcated from the periodic orbits of the unperturbed system is less than or equal to 3.

Markov modelling of the IEEE 802.11 DCF for real-time applications with periodic traffic

Popular wireless network standards, such as IEEE 802.11/15/16, are increasingly adopted in real-time control systems. However, they are not designed for real-time applications. Therefore, the performance of such wireless networks needs to be carefully evaluated before the systems are implemented and deployed. While efforts have been made to model general wireless networks with completely random traffic generation, there is a lack of theoretical investigations into the modelling of wireless networks with periodic real-time traffic. Considering the widely used IEEE 802.11 standard, with the focus on its distributed coordination function (DCF), for soft-real-time control applications, this paper develops an analytical Markov model to quantitatively evaluate the network quality-of-service (QoS) performance in periodic real-time traffic environments. Performance indices to be evaluated include throughput capacity, transmission delay and packet loss ratio, which are crucial for real-time QoS guarantee in real-time control applications. They are derived under the critical real-time traffic condition, which is formally defined in this paper to characterize the marginal satisfaction of real-time performance constraints.

Stability boundary analysis of the dynamic voltage restorer in weak systems with dynamic loads

In this contribution, a stability analysis for a dynamic voltage restorer (DVR) connected to a weak ac system containing a dynamic load is presented using continuation techniques and bifurcation theory. The system dynamics are explored through the continuation of periodic solutions of the associated dynamic equations. The switching process in the DVR converter is taken into account to trace the stability regions through a suitable mathematical representation of the DVR converter. The stability regions in the Thevenin equivalent plane are computed. In addition, the stability regions in the control gains space, as well as the contour lines for different Floquet multipliers, are computed. Besides, the DVR converter model employed in this contribution avoids the necessity of developing very complicated iterative map approaches as in the conventional bifurcation analysis of converters. The continuation method and the DVR model can take into account dynamics and nonlinear loads and any network topology since the analysis is carried out directly from the state space equations. The bifurcation approach is shown to be both computationally efficient and robust, since it eliminates the need for numerically critical and long-lasting transient simulations.

Natural convection and heat transfer in attics subject to periodic thermal forcing

The heat transfer through the attics of buildings under realistic thermal forcing has been considered in this study. A periodic temperature boundary condition is applied on the sloping walls of the attic to show the basic flow features in the attic space over diurnal cycles. The numerical results reveal that, during the daytime heating stage, the flow in the attic space is stratified; whereas at the night-time cooling stage, the flow becomes unstable. A symmetrical solution is seen for relatively low Rayleigh numbers. However, as the Ra gradually increases, a transition occurs at a critical value of Ra. Above this critical value, an asymmetrical solution exhibiting a pitchfork bifurcation arises at the night-time. It is also found that the calculated heat transfer rate at the night-time cooling stage is much higher than that during the daytime heating stage.

Natural convection in a triangular enclosure subject to periodic thermal forcing

The effects of periodic thermal forcing on the flow field and heat transfer through an attic space are examined numerically in this paper. We consider the case with a fixed aspect ratio of 0.5 and a fixed Grashof number of 1.33×106. The numerical results reveal that, during the daytime, the flow is stratified; whereas at the night-time, the flow becomes unstable. A number of regular plumes and vortices are observed in the contours of isotherms and stream functions respectively. Moreover, the flow appears to be symmetric during the daytime, and becomes asymmetric at the night-time. It is also found that the flow is weaker during the daytime than that at the night-time in the present case, and the calculated heat transfer rate at the night-time is approximately three times greater than the heat transfer rate during the daytime.

Guidance of aircraft in periodic inspection tasks

This paper presents a guidance approach for aircraft in periodic inspection tasks. The periodic inspection task involves flying to a series of desired fixed points of inspection with specified attitude requirements so that requirements for downward looking sensors, such as cameras, are achieved. We present a solution using a precision guidance law and a bank turn dynamics model. High fidelity simulation studies illustrate the effectiveness of this approach under both ideal (nil-wind) and non-ideal (wind) conditions.

A reliable real-time transport protocol for control systems over wireless networks

Deploying networked control systems (NCSs) over wireless networks is becoming more and more popular. However, the widely-used transport layer protocols, Transmission Control Protocol (TCP) and User Datagram Protocol (UDP), are not designed for real-time applications. Therefore, they may not be suitable for many NCS application scenarios because of their limitations on reliability and/or delay performance, which real-control systems concern. Considering a typical type of NCSs with periodic and sporadic real-time traffic, this paper proposes a highly reliable transport layer protocol featuring a packet loss-sensitive retransmission mechanism and a prioritized transmission mechanism. The packet loss-sensitive retransmission mechanism is designed to improve the reliability of all traffic flows. And the prioritized transmission mechanism offers differentiated services for periodic and sporadic flows. Simulation results show that the proposed protocol has better reliability than UDP and improved delay performance than TCP over wireless networks, particularly when channel errors and congestions occur.

A reliable real-time transport protocol for networked control systems over wireless networks

Deploying wireless networks in networked control systems (NCSs) has become more and more popular during the last few years. As a typical type of real-time control systems, an NCS is sensitive to long and nondeterministic time delay and packet losses. However, the nature of the wireless channel has the potential to degrade the performance of NCS networks in many aspects, particularly in time delay and packet losses. Transport layer protocols could play an important role in providing both reliable and fast transmission service to fulfill NCS’s real-time transmission requirements. Unfortunately, none of the existing transport protocols, including the Transport Control Protocol (TCP) and the User Datagram Protocol (UDP), was designed for real-time control applications. Moreover, periodic data and sporadic data are two types of real-time data traffic with different priorities in an NCS. Due to the lack of support for prioritized transmission service, the real-time performance for periodic and sporadic data in an NCS network is often degraded significantly, particularly under congested network conditions. To address these problems, a new transport layer protocol called Reliable Real-Time Transport Protocol (RRTTP) is proposed in this thesis. As a UDP-based protocol, RRTTP inherits UDP’s simplicity and fast transmission features. To improve the reliability, a retransmission and an acknowledgement mechanism are designed in RRTTP to compensate for packet losses. They are able to avoid unnecessary retransmission of the out-of-date packets in NCSs, and collisions are unlikely to happen, and small transmission delay can be achieved. Moreover, a prioritized transmission mechanism is also designed in RRTTP to improve the real-time performance of NCS networks under congested traffic conditions. Furthermore, the proposed RRTTP is implemented in the Network Simulator 2 for comprehensive simulations. The simulation results demonstrate that RRTTP outperforms TCP and UDP in terms of real-time transmissions in an NCS over wireless networks.

Cross-layer design and optimization for wireless networked control systems

Wireless networked control systems (WNCSs) have been widely used in the areas of manufacturing and industrial processing over the last few years. They provide real-time control with a unique characteristic: periodic traffic. These systems have a time-critical requirement. Due to current wireless mechanisms, the WNCS performance suffers from long time-varying delays, packet dropout, and inefficient channel utilization. Current wirelessly networked applications like WNCSs are designed upon the layered architecture basis. The features of this layered architecture constrain the performance of these demanding applications. Numerous efforts have attempted to use cross-layer design (CLD) approaches to improve the performance of various networked applications. However, the existing research rarely considers large-scale networks and congestion network conditions in WNCSs. In addition, there is a lack of discussions on how to apply CLD approaches in WNCSs. This thesis proposes a cross-layer design methodology to address the issues of periodic traffic timeliness, as well as to promote the efficiency of channel utilization in WNCSs. The design of the proposed CLD is highlighted by the measurement of the underlying network condition, the classification of the network state, and the adjustment of sampling period between sensors and controllers. This period adjustment is able to maintain the minimally allowable sampling period, and also maximize the control performance. Extensive simulations are conducted using the network simulator NS-2 to evaluate the performance of the proposed CLD. The comparative studies involve two aspects of communications, with and without using the proposed CLD, respectively. The results show that the proposed CLD is capable of fulfilling the timeliness requirement under congested network conditions, and is also able to improve the channel utilization efficiency and the proportion of effective data in WNCSs.

Cross-layer design for traffic management in wireless networked control systems

Wireless networked control systems (WNCSs) have been increasingly deployed in industrial applications. As they require timely data packet transmissions, it is difficult to make efficient use of the limited channel resources, particularly in contention based wireless networks in the layered network architecture. Aiming to maintain the WNCSs under critical real-time traffic condition at which the WNCSs marginally meet the real-time requirements, a cross-layer design (CLD) approach is presented in this paper to adaptively adjust the control period to achieve improved channel utilization while still maintaining effective and timely packet transmissions. The effectiveness of the proposed approach is demonstrated through simulation studies.