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Related Concept Videos

Magnetostatic Boundary Conditions01:28

Magnetostatic Boundary Conditions

An electric field suffers a discontinuity at a surface charge. Similarly, a magnetic field is discontinuous at a surface current. The perpendicular component of a magnetic field is continuous across the interface of two magnetic mediums. In contrast, its parallel component, perpendicular to the current, is discontinuous by the amount equal to the product of the vacuum permeability and the surface current. Like the scalar potential in electrostatics, the vector potential is also continuous...
Laminar and Turbulent Flow01:07

Laminar and Turbulent Flow

Fluid dynamics is the study of fluids in motion. Velocity vectors are often used to illustrate fluid motion in applications like meteorology. For example, wind—the fluid motion of air in the atmosphere—can be represented by vectors indicating the speed and direction of the wind at any given point on a map. Another method for representing fluid motion is a streamline. A streamline represents the path of a small volume of fluid as it flows. When the flow pattern changes with time, the streamlines...
Mesh Analysis01:20

Mesh Analysis

Mesh analysis is a valuable method for simplifying circuit analysis using mesh currents as key circuit variables. Unlike nodal analysis, which focuses on determining unknown voltages, mesh analysis applies Kirchhoff's voltage law (KVL) to find unknown currents within a circuit. This method is particularly convenient in reducing the number of simultaneous equations that need to be solved.
A fundamental concept in mesh analysis is the definition of meshes and mesh currents. A mesh is a closed...
Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving01:29

Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving

Mechanistic models play a crucial role in algorithms for numerical problem-solving, particularly in nonlinear mixed effects modeling (NMEM). These models aim to minimize specific objective functions by evaluating various parameter estimates, leading to the development of systematic algorithms. In some cases, linearization techniques approximate the model using linear equations.
In individual population analyses, different algorithms are employed, such as Cauchy's method, which uses a...
Mesh Analysis for AC Circuits01:12

Mesh Analysis for AC Circuits

In the domain of radio communication, the significance of impedance matching must be considered. It is crucial to ensure the efficient transmission of signals between radio transmitters and receivers. Achieving this balance involves using impedance-matching circuits, with one fundamental configuration comprising a resistor, capacitor, and inductor.
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Turbulent Flow: Problem Solving01:09

Turbulent Flow: Problem Solving

Carbonation is a process used to dissolve carbon dioxide gas in a liquid, commonly used in the production of carbonated beverages. Achieving efficient carbonation requires careful control of temperature, pressure, and flow conditions. By adjusting these parameters, carbonation efficiency can be maximized, producing a higher concentration of CO2 in the liquid.
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Related Experiment Video

Updated: Jun 19, 2026

Fast Grid Preparation for Time-Resolved Cryo-Electron Microscopy
10:05

Fast Grid Preparation for Time-Resolved Cryo-Electron Microscopy

Published on: November 6, 2021

Block-structured adaptive meshes and reduced grids for atmospheric general circulation models.

Christiane Jablonowski1, Robert C Oehmke, Quentin F Stout

  • 1Department of Atmospheric, Oceanic, and Space Sciences, University of Michigan, Ann Arbor, MI 48109, USA. cjablono@umich.edu

Philosophical Transactions. Series A, Mathematical, Physical, and Engineering Sciences
|October 21, 2009
PubMed
Summary

Adaptive mesh refinement in climate models offers flexibility. Reduced grids are useful for advection but require caution in nonlinear simulations, while static adaptations effectively capture baroclinic waves.

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Scalable Nanohelices for Predictive Studies and Enhanced 3D Visualization
08:03

Scalable Nanohelices for Predictive Studies and Enhanced 3D Visualization

Published on: November 12, 2014

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Last Updated: Jun 19, 2026

Fast Grid Preparation for Time-Resolved Cryo-Electron Microscopy
10:05

Fast Grid Preparation for Time-Resolved Cryo-Electron Microscopy

Published on: November 6, 2021

Scalable Nanohelices for Predictive Studies and Enhanced 3D Visualization
08:03

Scalable Nanohelices for Predictive Studies and Enhanced 3D Visualization

Published on: November 12, 2014

Area of Science:

  • Atmospheric Science
  • Computational Fluid Dynamics
  • Climate Modeling

Background:

  • Adaptive mesh refinement (AMR) provides flexible resolution for climate and weather models.
  • AMR can coarsen grids in polar regions, creating reduced grid setups.
  • Existing dynamical cores can be enhanced with adaptive grid techniques.

Purpose of the Study:

  • To apply a spherical, block-structured AMR technique to the Lin-Rood finite-volume dynamical core.
  • To investigate the performance of static mesh adaptations and reduced grids.
  • To evaluate the suitability of these techniques for weather and climate research.

Main Methods:

  • Implementation of a hydrostatic dynamics package using conservative and monotonic finite-volume discretization.
  • Development of an adaptive dynamical core on a flexible latitude-longitude grid.
  • Testing in two- and three-dimensional model configurations using shallow water test cases.

Main Results:

  • Reduced grid configurations show viability for pure advection but need moderate use in nonlinear simulations.
  • Static grid adaptations successfully resolve three-dimensional baroclinic waves in storm-track regions.
  • Testing included advection of a cosine bell, moving vortices, steady-state flow, Rossby-Haurwitz wave, and cross-polar flows.

Conclusions:

  • Adaptive mesh refinement offers a flexible framework for variable-resolution climate and weather models.
  • Reduced grids are suitable for specific applications like advection, but nonlinear dynamics require careful consideration.
  • Static grid adaptations are effective for resolving key atmospheric phenomena like baroclinic waves.