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I present a fast algorithm for modeling invasion percolation (IP) with trapping (TIP). IP is a numerical algorithm that models quasi-static (i.e. slow) fluid invasion in porous media. Trapping occurs when the invading fluid (that is injected) forms continuous surfaces surrounding patches of the displaced fluid (that is assumed incompressible and originally saturates the invaded medium). In TIP, the invading fluid is not allowed to enter the trapped patches. I demonstrate that TIP can be modeled in two steps: (1) Run an IP simulation without trapping (NTIP). (2) Identify the sites that invaded trapped regions and remove them from the chronological list of sites invaded in NTIP. Fast algorithms exist for solving NTIP. The focus of this paper is to propose an efficient solution for step (2). I show that it can be solved using a disjoint set data structure and going backward in time, i.e. by un-invading all sites invaded in NTIP in reverse order. Time reversal of the invasion greatly reduces the computational complexity for the identification of trapped sites as one only needs to investigate sites neighbor to the latest invaded/un-invaded site. This differs from traditional approaches where trapping is performed in real time, i.e. as the IP simulation is running, and where it is sometimes necessary to investigate the whole lattice to identify newly trapped regions. With the proposed algorithm, the total computational time for the identification and the removal of trapped sites goes as O ( N ), where N is the total number of sites in the lattice. [ABSTRACT FROM AUTHOR]

Abstract: The ability to guide relief vehicles to safety and quickly pass through environments affected by fires is critical in fighting forest fires. In this paper, we focus on route determination in the case of forest fires, and propose a data model that supports finding paths among moving obstacles. This data model captures both static information, such as the type of the response team, the topology of the road network, and dynamic information, such as sensor information, changing availabilities of roads during disasters, and the position of the vehicle. We use a fire simulation model to calculate the fire evolution. The spread of the fire is represented as movements of obstacles that block the responders׳ path in the road network. To calculate safe and optimal routes avoiding obstacles, the A⁎ algorithm is extended to consider the predicted availabilities of roads. We prove the optimality of the path calculated by our algorithm and then evaluate it in simulated scenarios. The results show that our model and algorithm are effective in planning routes that avoid one or more fire-affected areas and that the outlook for further investigation is promising. [Copyright &y& Elsevier]

Abstract: Measurements of structure orientations are afflicted with uncertainties which arise from many sources. Commonly, such uncertainties involve instrument imprecision, external disturbances and human factors. The aggregated uncertainty depends on the uncertainty of each of the sources. The orientation of an object measured in a borehole (e.g. a fracture) is calculated using four parameters: the bearing and inclination of the borehole and two relative angles of the measured object to the borehole. Each parameter may be a result of one or several measurements. The aim of this paper is to develop a method to both calculate and visualize the aggregated uncertainty resulting from the uncertainty in each of the four geometrical constituents. Numerical methods were used to develop a VBA-application in Microsoft Excel to calculate the aggregated uncertainty. The code calculates two different representations of the aggregated uncertainty: a 1-parameter uncertainty, the ‘minimum dihedral angle’, denoted by Ω; and, a non-parametric visual representation of the uncertainty, denoted by χ. The simple 1-parameter uncertainty algorithm calculates the minimum dihedral angle accurately, but overestimates the probability space that plots as an ellipsoid on a lower hemisphere stereonet. The non-parametric representation plots the uncertainty probability space accurately, usually as a sector of an annulus for steeply inclined boreholes, but is difficult to express numerically. The 1-parameter uncertainty can be used for evaluating statistics of large datasets whilst the non-parametric representation is useful when scrutinizing single or a few objects. [Copyright &y& Elsevier]

Theoretical geochemical models for electrolyte solutions based on classical thermodynamic principles rely largely upon molal concentrations as input because molality (wt/wt) is independent of temperature and pressure. On the other hand, there are countless studies in the literature where concentrations are expressed as molarity (wt/vol) because these units are more easily measured. To convert from molarity to molality requires an estimate of solution density. Unfortunately, in many, if not most, cases where molarity is the concentration of choice, solution densities are not measured. For concentrated brines such as seawater or even more dense brines, the difference between molarity and molality is significant. Without knowledge of density, these brinish, molar-based studies are closed to theoretical electrolyte solution models. The objective of this paper is to present an algorithm that can accurately calculate the density of molar-based solutions, and, as a consequence, molality. The algorithm consist of molar inputs into a molal-based model that can calculate density (FREZCHEM). The algorithm uses an iterative process for calculating absolute salinity , density , and the conversion factor for molarity to molality. Three cases were examined ranging in density from 1.023 to 1.203 kg(soln.)/l. In all three cases, the , , and values converged to within 1ppm by nine iterations. In all three cases, the calculated densities agreed with experimental measurements to within . This algorithm opens a large literature based on molar concentrations to exploration with theoretical models based on molal concentrations and classical thermodynamic principles. [Copyright &y& Elsevier]

Abstract: For many scientists working with digital topographic data, extracting lineaments or linear features is an important step in structuring and analyzing raw data. A ridge axis, which represents the top a mountain ridge, is one of the most important topographic features used in a wide variety of applications. Algorithms and software for automating the extraction of ridges or ridge axes from DEMs are, however, still not easily available or not widely acceptable. In this paper, we present a user-friendly Visual Basic program that automates the extraction of the ridge axis system from DEM data, based on the profile-recognition and polygon-breaking algorithm (PPA). An important feature of PPA is that it takes a global approach, as opposed to the local neighborhood operators used in many other algorithms. Each segment detected by PPA considers not only relations with contiguous neighboring grid points, but also strives to preserve the continuity of the global trend. This is an attempt to simulate human operators, who always factor in the overall trend of the lineament before delineating its local parts. PPA starts by connecting all points in a neighborhood that can possibly lie on the ridge axis, thus forming a belt of polygons in the first step. Next, a polygon breaking process eliminates unwanted segments according to the assumption that a ridge segment cannot be the side of any closed polygon, and that the result should be a purely dendritic line pattern. Finally, a branch-reduction process is executed to eliminate all parallel false ridges that remained due to the conservative approach taken in the first step. Results indicate that PPA is reasonably successful in picking out ridges that would have been identified manually by experts. In addition to providing a detailed user interface for executing PPA, several modifications were made to significantly improve the computational efficiency of PPA, as compared to the original version published in 1998. The source codes are provided for free download on the website listed above. [Copyright &y& Elsevier]