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Geothermal Energy
Published in Robert Ehrlich, Harold A. Geller, John R. Cressman, Renewable Energy, 2023
Robert Ehrlich, Harold A. Geller, John R. Cressman
The thermal gradient is the rate of change of temperature with depth. The Earth has a radius of 6,400 km, and at its center, the temperature is believed to be 7,000 K, giving the convenient value of about 1 K/km or 1°C/km for the average gradient. The gradient, however, does vary enormously both as a function of depth and as a function of the particular location on Earth. Figure 6.2 illustrates the former variation, which is strongly correlated with the composition of each interior region. The largest gradient (the topmost section of the graph) is on the Earth’s crust, where the gradient averages 25–30 K/km. Since the crust is solid and heat cannot be transferred by convection, we may apply the heat conduction equation for the flow across a layer (slab) of thickness Δz to find the thermal gradient. The heat flow per unit area across the slab is given by q˙=kΔT/Δz, where k is the thermal conductivity and ΔT is the temperature difference across the slab. Hence,
Subsurface Processes
Published in Stephen M. Testa, Geological Aspects of Hazardous Waste Management, 2020
Mathematical relationships are quite useful in understanding nonintuitive processes, notably transport; thus, some basic mathematics is required. A key mathematical concept, the gradient, is defined in regards to groundwater flow in Chapter 4, and is briefly reiterated here because it is one of the most important concepts for all aspects of subsurface science as well as any study of the earth. A gradient is a change in the value of one variable with respect to another variable, like a slope. Most of our discussion will include gradients of some property with respect to distance or time, e.g., a pressure gradient across the boundary between two soils, a concentration gradient across a membrane, or a thermal gradient across a surface. Gradients are the real driving forces for change in earth systems and in the environment. Obviously, large or steep gradients can result in rapid and dramatic changes. Often, our ability to restore a contaminated site or successfully dispose of hazardous waste depends upon our ability to minimize particular gradients within the system.
Remedial Investigations and Remedial Design
Published in Benjamin Alter, Environmental Consulting Fundamentals, 2019
Contamination can be delineated if a concentration gradient can be identified. A concentration gradient is a predictable change in concentration over a given horizontal or vertical distance. If successive soil samples exhibit a decreasing concentration trend for a particular contaminant, and this trend is consistent with the conceptual site model, then the horizontal and vertical location at which the soils will comply with remediation standards, known as the compliance point, can be estimated. Figure 8.2 shows the delineation of soil contamination using a concentration gradient to calculate the compliance points, both horizontally and vertically. The concentration gradient can be used to predict the compliance point, which then can be verified by additional soil sampling.
Traffic sign extraction using deep hierarchical feature learning and mobile light detection and ranging (LiDAR) data on rural highways
Published in Journal of Intelligent Transportation Systems, 2023
Maged Gouda, Alexander Epp, Rowan Tilroe, Karim El-Basyouny
To develop a training dataset, several filters are usually applied to the original point cloud to extract sign data using several point features, such as roughness and z-gradient. It is worth noting that applying intensity filters for data labeling is not recommended since lower intensity signs and points within individual signs are usually lost, which negatively impacts the performance of the neural network. In the proposed method, several variables are used in a trial-and-error process until all sign points are extracted. The method is designed to minimize false negatives, without undue regard for the large number of false positives it produces (as these may be easily removed manually). Below is a definition of the most used variables in the filtering process (CC, 2019): Roughness: is equal to the distance between a point and the best fitting plane to its neighbors.Gradient: gradient is the rate of change in any feature value at a point (e.g., elevation) compared to its neighbors.z-gradient: is the gradient of the elevation of a point relative to its neighbors.Number of neighbor density (N): counts the number of neighbor points to each point in the point cloud within a sphere of radius R.
Structural topology optimization through implicit boundary evolution based on the Allen–Cahn equation
Published in Engineering Optimization, 2021
Jiawen Gao, Baowei Song, Zhaoyong Mao
Gradient-based algorithms are used to solve the optimization problem. Using the Lagrange multiplier method, the above constrained optimization problem is transformed into an unconstrained optimization problem, which is easy to solve: where λ is the Lagrange multiplier. The updating strategy for λ is: where is a penalization factor and is the minimum penalty factor. is a constant and is set to 0.9 in this work.