Multiple solutions and numerical analysis to the dynamic and stationary models coupling a delayed energy balance model involving latent heat and discontinuous albedo with a deep ocean

We study a climatologically important interaction of two of the main components of the geophysical system by adding an energy balance model for the averaged atmospheric temperature as dynamic boundary condition to a diagnostic ocean model having an additional spatial dimension. In this work, we give deeper insight than previous papers in the literature, mainly with respect to the 1990 pioneering model by Watts and Morantine. We are taking into consideration the latent heat for the two phase ocean as well as a possible delayed term. Non-uniqueness for the initial boundary value problem, uniqueness under a non-degeneracy condition and the existence of multiple stationary solutions are proved here. These multiplicity results suggest that an S-shaped bifurcation diagram should be expected to occur in this class of models generalizing previous energy balance models. The numerical method applied to the model is based on a finite volume scheme with nonlinear weighted essentially non-oscillatory reconstruction and Runge–Kutta total variation diminishing for time integration.

Generic bifurcation of refracted systems

In this article we discuss some qualitative and geometric aspects of non-smooth dynamical systems theory. Our goal is to study the diagram bifurcation of typical singularities that occur generically in one parameter families of certain piecewise smooth vector fields named Refracted Systems. Such systems has a codimension-one submanifold as its discontinuity set. © 2012 Elsevier Ltd.

Information provision and network performance represented by Macroscopic Fundamental Diagram

The existence of the Macroscopic Fundamental Diagram (MFD), which relates network space-mean density and flow, has been shown in urban networks under homogeneous traffic conditions. Since the MFD represents the area-wide network traffic performances, studies on perimeter control strategies and an area traffic state estimation utilizing the MFD concept has been reported. The key requirements for the well-defined MFD is the homogeneity of the area wide traffic condition, which is not universally expected in real world. For the practical application of the MFD concept, several researchers have identified the influencing factors for network homogeneity. However, they did not explicitly take drivers’ behaviour under real time information provision into account, which has a significant impact on the shape of the MFD. This research aims to demonstrate the impact of drivers’ route choice behaviour on network performance by employing the MFD as a measurement. A microscopic simulation is chosen as an experimental platform. By changing the ratio of en-route informed drivers and pre-trip informed drivers as well as by taking different route choice parameters, various scenarios are simulated in order to investigate how drivers’ adaptation to the traffic congestion influences the network performance and the MFD shape. This study confirmed and addressed the impact of information provision on the MFD shape and highlighted the significance of the route choice parameter setting as an influencing factor in the MFD analysis.

Real time information provision benefit measured by macroscopic fundamental diagram

The existence of Macroscopic Fundamental Diagram (MFD), which relates space-mean density and flow, has been shown in urban networks under homogeneous traffic conditions. Since MFD represents the area-wide network traffic performances, studies on perimeter control strategies and an area traffic state estimation utilizing the MFD concept has been reported. One of the key requirements for well-defined MFD is the homogeneity of the area-wide traffic condition with links of similar properties, which is not universally expected in real world. For the practical application of the MFD concept, several researchers have identified the influencing factors for network homogeneity. However, they did not explicitly take the impact of drivers’ behaviour and information provision into account, which has a significant impact on simulation outputs. This research aims to demonstrate the effect of dynamic information provision on network performance by employing the MFD as a measurement. A microscopic simulation, AIMSUN, is chosen as an experiment platform. By changing the ratio of en-route informed drivers and pre-trip informed drivers different scenarios are simulated in order to investigate how drivers’ adaptation to the traffic congestion influences the network performance with respect to the MFD shape as well as other indicators, such as total travel time. This study confirmed the impact of information provision on the MFD shape, and addressed the usefulness of the MFD for measuring the dynamic information provision benefit.

Empirical evaluation of brisbane macroscopic fundamental diagram

The Macroscopic Fundamental Diagram (MFD) relates space-mean density and flow, and the existence with dynamic features was confirmed in congested urban network with real data set from loop detectors and taxi probes. Since the MFD represents the area-wide network traffic performances, it gives foundations for perimeter control strategies and an area traffic state estimation enabling area-based network control. However, limited works have been reported on real world example from signalised arterial network. This paper fuses data from multiple sources (Bluetooth, Loops and Signals) and develops a framework for the development of the MFD for Brisbane. Existence of the MFD in Brisbane network is confirmed. Different MFDs (from whole network and several sub regions) are evaluated to discover the spatial partitioning in network performance representation.

The impact of incidents on macroscopic fundamental diagram

Macroscopic Fundamental Diagram (MFD) has been proved to exist in large urban road and freeway networks by theoretic method and real data in cities. However hysteresis and scatters have also been found existed both on motorway network and urban road. This paper investigates how the incident variables affect the scatter and shape of the MFD using both the simulated data and the real data collected from the Pacific Motorway M3 in Brisbane, Australia. Three key components of incident are investigated based on the simulated data: incident location, incident duration time and traffic demand. Results based on the simulated data indicate that MFD shape is a property not only of the network itself but also of the incident characteristics variables. MFDs for three types of real incidents (crash, hazard and breakdown) are explored separately. The results based on the empirical data are consistent with the simulated results. The hysteresis phenomenon occurs on both the upstream and the downstream of the incident location, but for opposite hysteresis loops. Gradient of the MFD for the upstream is more than that for the downstream on the incident site, when traffic demand is off peak.

Brisbane Macroscopic Fundamental Diagram : empirical findings on network partitioning and incident detection

The Macroscopic Fundamental Diagram (MFD) relates space-mean density and flow, and the existence with dynamic features was confirmed in congested urban network in downtown Yokohama with real data set. Since the MFD represents the area-wide network traffic performances, studies on perimeter control strategies and an area traffic state estimation utilizing the MFD concept has been reported. However, limited works have been reported on real world example from signalised arterial network. This paper fuses data from multiple sources (Bluetooth, Loops and Signals) and develops a framework for the development of the MFD for Brisbane, Australia. Existence of the MFD in Brisbane arterial network is confirmed. Different MFDs (from whole network and several sub regions) are evaluated to discover the spatial partitioning in network performance representation. The findings confirmed the usefulness of appropriate network partitioning for traffic monitoring and incident detections. The discussion addressed future research directions

Macroscopic fundamental diagram for Brisbane, Australia: empirical findings on network partitioning and incident detection

The Macroscopic Fundamental Diagram (MFD) relates space-mean density and flow, and the existence with dynamic features was confirmed in congested urban network in downtown Yokohama with real data set. Since the MFD represents the area-wide network traffic performances, studies on perimeter control strategies and an area traffic state estimation utilizing the MFD concept has been reported. However, limited works have been reported on real world example from signalised arterial network. This paper fuses data from multiple sources (Bluetooth, Loops and Signals) and presents a framework for the development of the MFD for Brisbane, Australia. Existence of the MFD in Brisbane arterial network is confirmed. Different MFDs (from whole network and several sub regions) are evaluated to discover the spatial partitioning for network performance representation. The findings confirmed the usefulness of appropriate network partitioning for traffic monitoring and incident detections. The discussion addressed future research directions.

A comparison of stability and bifurcation criteria for inflated spherical elastic shells

The nonlinear stability analysis introduced by Chen and Haughton [1] is employed to study the full nonlinear stability of the non-homogeneous spherically symmetric deformation of an elastic thick-walled sphere. The shell is composed of an arbitrary homogeneous, incompressible elastic material. The stability criterion ultimately requires the solution of a third-order nonlinear ordinary differential equation. Numerical calculations performed for a wide variety of well-known incompressible materials are then compared with existing bifurcation results and are found to be identical. Further analysis and comparison between stability and bifurcation are conducted for the case of thin shells and we prove by direct calculation that the two criteria are identical for all modes and all materials.

Exploring the properties of macroscopic fundamental diagram : analysing Brisbane urban network

This thesis explored traffic characteristics at the aggregate level for area-wide traffic monitoring of large urban area. It focused on three aspects: understanding a macroscopic network performance under real-time traffic information provision, measuring traffic performance of a signalised arterial network using available data sets, and discussing network zoning for monitoring purposes in the case of Brisbane, Australia. This work presented the use of probe vehicle data for estimating traffic state variables, and illustrated dynamic features of regional traffic performance of Brisbane. The results confirmed the viability and effectiveness of area-wide traffic monitoring.

Flow pattern analysis in a highly stenotic patient-specific carotid bifurcation model using a turbulence model

The aim of this study is to investigate the blood flow pattern in carotid bifurcation with a high degree of luminal stenosis, combining in vivo magnetic resonance imaging (MRI) and computational fluid dynamics (CFD). A newly developed two-equation transitional model was employed to evaluate wall shear stress (WSS) distribution and pressure drop across the stenosis, which are closely related to plaque vulnerability. A patient with an 80% left carotid stenosis was imaged using high resolution MRI, from which a patient-specific geometry was reconstructed and flow boundary conditions were acquired for CFD simulation. A transitional model was implemented to investigate the flow velocity and WSS distribution in the patient-specific model. The peak time-averaged WSS value of approximately 73Pa was predicted by the transitional flow model, and the regions of high WSS occurred at the throat of the stenosis. High oscillatory shear index values up to 0.50 were present in a helical flow pattern from the outer wall of the internal carotid artery immediately after the throat. This study shows the potential suitability of a transitional turbulent flow model in capturing the flow phenomena in severely stenosed carotid arteries using patient-specific MRI data and provides the basis for further investigation of the links between haemodynamic variables and plaque vulnerability. It may be useful in the future for risk assessment of patients with carotid disease.

A follow up MRI-based geometry and computational fluid dynamics study of carotid bifurcation

Cardiovascular disease is the leading causes of death in the developed world. Wall shear stress (WSS) is associated with the initiation and progression of atherogenesis. This study combined the recent advances in MR imaging and computational fluid dynamics (CFD) and evaluated the patient-specific carotid bifurcation. The patient was followed up for 3 years. The geometry changes (tortuosity, curvature, ICA/CCA area ratios, central to the cross-sectional curvature, maximum stenosis) and the CFD factors (Velocity distribute, Wall Shear Stress (WSS) and Oscillatory Shear Index (OSI)) were compared at different time points.The carotid stenosis was a slight increase in the central to the cross-sectional curvature, and it was minor and variable curvature changes for carotid centerline. The OSI distribution presents ahigh-values in the same region where carotid stenosis and normal border, indicating complex flow and recirculation.The significant geometric changes observed during the follow-up may also cause significant changes in bifurcation hemodynamics.

Spool valve mechanism used in a 20 K Gifford-McMahon cycle cryorefrigerator and its effect on the P-V diagram

The design and fabrication of a spool valve for a two-stage Gifford-McMahon cycle cryorefrigerator is described. The effect of this valve on the P-V diagram and practical methods of reducing the P-V degradation are also discussed.

The averaging principle and the diagram technique

Rae and Davidson have found a striking connection between the averaging method generalised by Kruskal and the diagram technique used by the Brussels school in statistical mechanics. They have considered conservative systems whose evolution is governed by the Liouville equation. In this paper we have considered a class of dissipative systems whose evolution is governed not by the Liouville equation but by the last-multiplier equation of Jacobi whose Fourier transform has been shown to be the Hopf equation. The application of the diagram technique to the interaction representation of the Jacobi equation reveals the presence of two kinds of interactions, namely the transition from one mode to another and the persistence of a mode. The first kind occurs in the treatment of conservative systems while the latter type is unique to dissipative fields and is precisely the one that determines the asymptotic Jacobi equation. The dynamical equations of motion equivalent to this limiting Jacobi equation have been shown to be the same as averaged equations.