The formation of the coronal flow/ADAF

We develop a new method to describe the accretion flow in the corona above a thin disk around a black hole in vertical and radial extent. The model is based on the same physics as the earlier one-zone model, but now modified including inflow and outflow of mass, energy and angular momentum from and towards neighboring zones. We determine the radially extended coronal flow for different mass flow rates in the cool disk resulting in the truncation of the thin disk at different distance from the black hole. Our computations show how the accretion flow gradually changes to a pure vertically extended coronal or advection-dominated accretion flow (ADAF). Different regimes of solutions are discussed. For some cases wind loss causes an essential reduction of the mass flow.Comment: 8 pages, 4 figures, accepted for publication in A&

A semi-analytical model of disk evaporation by thermal conduction

The conditions for disk evaporation by electron thermal conduction are examined, using a simplified semi--analytical 1-D model. The model is based on the mechanism proposed by Meyer & Meyer-Hofmeister (1994) in which an advection dominated accretion flow evaporates the top layers from the underlying disk by thermal conduction. The evaporation rate is calculated as a function of the density of the advective flow, and an analysis is made of the time scales and length scales of the dynamics of the advective flow. It is shown that evaporation can only completely destroy the disk if the conductive length scale is of the order of the radius. This implies that radial conduction is an essential factor in the evaporation process. The heat required for evaporation is in fact produced at small radii and transported radially towards the evaporation region.Comment: 9 pages, 4 postscript figures, accepted for publication in A&

Modelling Replacement Demand: A Random Coefficient Approach

Replacement demand due to regular and early retirement, disablement, temporary withdrawals of women owing to birth and child raising, et cetera, constitutes an important element of the future demand for newcomers on the labour market. It is, however, often neglected in manpower forecasting studies. In this paper, we develop a flow model with which we can forecast the replacement demand at a detailed level of types of education. The essential element of the model is the determination of the yearly outflow coefficients for each type of education, distinguished by age category and gender. Instead of applying a fixed coefficient approach (Willems and De Grip (1993), we will introduce the random coefficient estimation technique in the model. This technique takes the reliability of the flow coefficients explicitly into account. If a specific flow coefficient is unreliable, the random coefficient estimate will tend towards the mean value for that age category over the types of education. This means that ad hoc corrections based on judgmental forecasting can be considerably reduced. Moreover, it will be shown that the random coefficient estimates of labour market outflow are more reliable than the estimates of the Willems/De Grip model.labour market entry;

Developments in modelling of backward erosion piping

One of the failure mechanisms that can affect the safety of a dyke or another water-retaining structure is backward erosion piping, a phenomenon that results in the formation of shallow pipes at the interface of a sandyor silty foundation and a cohesive cover layer. Themodels available for predicting the critical head at which the pipe progresses to the upstreamside have been validated and adapted on the basis of experiments with two-dimensional (2D) configurations. However, the experimental base for backward erosion in three-dimensional (3D) configurations in which the flow concentrates towards one point, a situation that is commonly encountered in the field, is limited. This paper presents additional 3D configuration experiments at two scales with a range of sand types. The critical gradients, the formed pipes and the erosion mechanism were analysed for the available experiments, indicating that the erosion mechanism is more complex than previously assumed, as both erosion at the tip of the pipe (primary erosion) and in the pipe (secondary erosion) are relevant. In addition, a 3D configuration was found to result in significantly lower critical gradients than those predicted by an accepted calculation model calibrated on the basis of 2D experiments, a finding that is essential for the application of the model in the field

Modelling shared space users via rule-based social force model

The promotion of space sharing in order to raise the quality of community living and safety of street surroundings is increasingly accepted feature of modern urban design. In this context, the development of a shared space simulation tool is essential in helping determine whether particular shared space schemes are suitable alternatives to traditional street layouts. A simulation tool that enables urban designers to visualise pedestrians and cars trajectories, extract flow and density relation in a new shared space design and achieve solutions for optimal design features before implementation. This paper presents a three-layered microscopic mathematical model which is capable of representing the behaviour of pedestrians and vehicles in shared space layouts and it is implemented in a traffic simulation tool. The top layer calculates route maps based on static obstacles in the environment. It plans the shortest path towards agents' respective destinations by generating one or more intermediate targets. In the second layer, the Social Force Model (SFM) is modified and extended for mixed traffic to produce feasible trajectories. Since vehicle movements are not as flexible as pedestrian movements, velocity angle constraints are included for vehicles. The conflicts described in the third layer are resolved by rule-based constraints for shared space users. An optimisation algorithm is applied to determine the interaction parameters of the force-based model for shared space users using empirical data. This new three-layer microscopic model can be used to simulate shared space environments and assess, for example, new street designs

An optimization model for the US Air-Traffic System

A systematic approach for monitoring U.S. air traffic was developed in the context of system-wide planning and control. Towards this end, a network optimization model with nonlinear objectives was chosen as the central element in the planning/control system. The network representation was selected because: (1) it provides a comprehensive structure for depicting essential aspects of the air traffic system, (2) it can be solved efficiently for large scale problems, and (3) the design can be easily communicated to non-technical users through computer graphics. Briefly, the network planning models consider the flow of traffic through a graph as the basic structure. Nodes depict locations and time periods for either individual planes or for aggregated groups of airplanes. Arcs define variables as actual airplanes flying through space or as delays across time periods. As such, a special case of the network can be used to model the so called flow control problem. Due to the large number of interacting variables and the difficulty in subdividing the problem into relatively independent subproblems, an integrated model was designed which will depict the entire high level (above 29000 feet) jet route system for the 48 contiguous states in the U.S. As a first step in demonstrating the concept's feasibility a nonlinear risk/cost model was developed for the Indianapolis Airspace. The nonlinear network program --NLPNETG-- was employed in solving the resulting test cases. This optimization program uses the Truncated-Newton method (quadratic approximation) for determining the search direction at each iteration in the nonlinear algorithm. It was shown that aircraft could be re-routed in an optimal fashion whenever traffic congestion increased beyond an acceptable level, as measured by the nonlinear risk function