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Related Concept Videos

Areas Within Irregular Boundaries01:26

Areas Within Irregular Boundaries

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Calculating areas within irregular boundaries, such as along rivers or curved roads, is crucial in various fields, including surveying, engineering, and environmental management. Surveyors often begin by creating a traverse, a connected series of straight lines approximating the area's boundary. The coordinates of each traverse point are essential for calculating the enclosed area. The double meridian distance formula is a widely used technique for this purpose. This method utilizes the...
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Curvilinear Motion: Rectangular Components01:23

Curvilinear Motion: Rectangular Components

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Curvilinear motion characterizes the movement of a particle or object along a curved path, notably evident when envisioning a car navigating a winding road. If the car starts at point A, its position vector is established within a fixed frame of reference, where the ratio of the position vector to its magnitude signifies the unit vector pointing in the position vector's direction.
As the car advances, its position evolves over time. Quantifying the car's velocity involves computing the...
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Rectangular and Triangular Pulse Function01:19

Rectangular and Triangular Pulse Function

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The unit rectangular pulse function is mathematically represented by a rectangular function centered at the origin with a height of one unit. This function is defined by two parameters: T, which specifies the center location of the pulse along the time axis, and τ, which determines the pulse duration.
For example, consider a rectangular pulse with a 5V amplitude, a 3-second duration, and centered at t=2 seconds. This pulse can be expressed using the rectangular function, written as,
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Area Computation by the Alternative Coordinate Method01:24

Area Computation by the Alternative Coordinate Method

821
The alternative coordinate method, also known as the Shoelace Formula, is a technique for determining the area of a traverse using Cartesian coordinates. This method relies on the sequential arrangement of x and y coordinates for each point of the shape, ensuring accuracy and ease of application.In this approach, each corner's x and y coordinates are listed as fractions, with the x-coordinate as the numerator and the y-coordinate as the denominator. These coordinates are arranged sequentially...
821
Relation between Poisson's ratio, Modulus of Elasticity and Modulus of Rigidity01:15

Relation between Poisson's ratio, Modulus of Elasticity and Modulus of Rigidity

776
Deformation occurs in axial and transverse directions when an axial load is applied to a slender bar. This deformation impacts the cubic element within the bar, transforming it into either a rectangular parallelepiped or a rhombus, contingent on its orientation. This transformation process induces shearing strain. Axial loading elicits both shearing and normal strains. Applying an axial load instigates equal normal and shearing stresses on elements oriented at a 45° angle to the load axis.
776
Parallel-Axis Theorem for an Area01:12

Parallel-Axis Theorem for an Area

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The moment of inertia is a fundamental concept in mechanical engineering that plays a significant role in designing rotationally symmetric objects such as flywheels, gears, and other mechanical systems. In this context, we will discuss the moment of inertia of a flywheel rotating about its centroidal axis and how it relates to the moment of inertia about an axis parallel to it.
For a flywheel approximated as a solid disc, consider an infinitesimal differential element with an arbitrary distance...
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Related Experiment Video

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Stretching Micropatterned Cells on a PDMS Membrane
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Extending the MODPATH Algorithm to Rectangular Unstructured Grids.

David W Pollock1

  • 1U.S. Geological Survey, 411 National Center, Reston, VA 20192. dwpolloc@usgs.gov.

Ground Water
|March 11, 2015
PubMed
Summary

A modified particle-tracking algorithm for MODPATH now supports MODFLOW-USG's unstructured grids. This enhancement enables accurate particle movement simulations in complex hydrogeological models.

Area of Science:

  • Hydrogeology
  • Computational Hydrology
  • Numerical Modeling

Background:

  • MODFLOW-USG introduces unstructured grids, posing challenges for existing particle-tracking methods.
  • Traditional particle-tracking algorithms in MODPATH require adaptations for these new grid types.

Purpose of the Study:

  • To modify the MODPATH particle-tracking algorithm for compatibility with MODFLOW-USG unstructured grids.
  • To ensure accurate simulation of groundwater flow paths in complex geological formations.

Main Methods:

  • The semi-analytical particle-tracking algorithm in MODPATH was adapted.
  • Grid cells with multi-cell face connections were divided into sub-cells to handle unstructured grids.

Main Results:

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  • The modified algorithm successfully extends particle tracking to rectangular-based unstructured grids.
  • This addresses limitations of previous versions when used with MODFLOW-USG.

    • Conclusions:

    • The developed method enhances the capability of MODPATH for simulating groundwater flow in complex, unstructured grid systems.
    • This advancement will be integrated into the upcoming version of MODPATH, improving its utility for hydrogeological studies.