Jove
Visualize
Contact Us
JoVE
x logofacebook logolinkedin logoyoutube logo
ABOUT JoVE
OverviewLeadershipBlogJoVE Help Center
AUTHORS
Publishing ProcessEditorial BoardScope & PoliciesPeer ReviewFAQSubmit
LIBRARIANS
TestimonialsSubscriptionsAccessResourcesLibrary Advisory BoardFAQ
RESEARCH
JoVE JournalMethods CollectionsJoVE Encyclopedia of ExperimentsArchive
EDUCATION
JoVE CoreJoVE BusinessJoVE Science EducationJoVE Lab ManualFaculty Resource CenterFaculty Site
Terms & Conditions of Use
Privacy Policy
Policies

Related Concept Videos

Surface Integrals01:28

Surface Integrals

A curved roof has a surface area that is generally larger than its flat projection. To estimate the cost of painting it, the curved surface area must first be calculated. If the roof is represented parametrically by a vector-valued function r(u,v), then each point in a parameter domain D corresponds to a point on the surface S. This connection allows the curved surface to be studied through a two-dimensional parameter region.The parameter domain D is divided into many small rectangles. A...
Quadric Surfaces01:28

Quadric Surfaces

Quadric surfaces are three-dimensional surfaces characterized by second-degree equations in the variables x, y, and z. These surfaces are smooth and continuous, and specific combinations of squared and linear terms define their shapes. The main types of quadric surfaces include ellipsoids, cones, paraboloids, and hyperboloids. Each type exhibits distinct geometric features depending on how the variables are arranged and related within the equation.Ellipsoids are closed surfaces formed when all...
Surface Area Calculations01:22

Surface Area Calculations

Surface area calculations for a graph z = f(x, y) are fundamental in engineering applications involving curved structures such as satellite dishes. A parabolic dish reflects communication signals efficiently, but engineers must determine its exact curved surface area to estimate coating materials, fabrication costs, and structural requirements. Since the rim of the dish forms a circular boundary, the surface area is calculated over a circular domain in the xy-plane.Parametric Representation of...
Partial Differential Equations01:21

Partial Differential Equations

A stone dropped into a still pond generates waves that propagate outward in circular patterns, creating a dynamic surface whose elevation depends on both position and time. At any given location, the water level oscillates as the wave passes, while at any fixed moment, the surface exhibits smooth, curved structures extending across space. This dual dependence requires a mathematical description that accounts for variation in multiple variables simultaneously.At a fixed point on the water...

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by
Same author

The IMMUNO-BIOMAP trial in NSCLC: An adaptive multimodal framework for biomarker-guided care.

Cell reports. Medicine·2026
Same author

How I Do It: "And That's a BINGO!" Using a Self-Directed, Gamified Instrument to Structure Learning on the Obstetrics Clerkship.

Journal of surgical education·2026
Same author

[<sup>68</sup>Ga]Ga-DOTA-5G PET/CT Detects Brain and Bone Metastases in a Patient with Metastatic Pancreatic Cancer.

Journal of nuclear medicine : official publication, Society of Nuclear Medicine·2026
Same author

Consortium on Bridging Radiation Segmentectomy (COBRAS): A Multicenter Study of Complete Pathologic Necrosis in Hepatocellular Carcinoma.

Radiology·2026
Same author

Continuous blood pressure monitoring via hemodynamic parameter and pulse transit time derived from capacitive sensing pads.

Physiological measurement·2026
Same author

Neoadjuvant radiotherapy for primary retroperitoneal well-differentiated liposarcoma: a Transatlantic Australasian Retroperitoneal Sarcoma Working Group (TARPSWG) propensity score matched analysis.

EClinicalMedicine·2026
Same journal

Application of ephrin-B2 loaded glycol chitosan-silk fibroin hydrogel in the treatment of diabetic refractory wounds.

Scientific reports·2026
Same journal

International expert Delphi consensus on thromboprophylaxis in metabolic and bariatric surgery.

Scientific reports·2026
Same journal

Assessing the cross-region knowledge transfer capability of selected deep learning building vectorization methods in the context of available training datasets.

Scientific reports·2026
Same journal

Feasibility and preliminary effects of outdoor versus indoor cognitive-motor therapy in women with Alzheimer's disease: A randomized single-blind pilot study.

Scientific reports·2026
Same journal

Hallmarks of social action in the vocal turn-taking of wild common marmosets (Callithrix jacchus).

Scientific reports·2026
Same journal

Role and mechanism of AOPPs-induced NOX4-mediated ferroptosis in intervertebral disc degeneration.

Scientific reports·2026
See all related articles

Related Experiment Video

Updated: Jun 23, 2026

Probing C84-embedded Si Substrate Using Scanning Probe Microscopy and Molecular Dynamics
13:58

Probing C84-embedded Si Substrate Using Scanning Probe Microscopy and Molecular Dynamics

Published on: September 28, 2016

Fast large scale full-wave multiple-scattering computation for three-dimensional random rough surfaces.

Firoz Kanti Borah1, Leung Tsang2, Edward Kim3

  • 1Department of Electrical and Computer Engineering, University of Michigan, Ann Arbor, MI, USA. firozb@umich.edu.

Scientific Reports
|June 21, 2026
PubMed
Summary
This summary is machine-generated.

A new computational method, fast multilevel sparse-matrix canonical-grid (FML-SMCG), accurately models wave scattering from complex rough surfaces. This breakthrough enables detailed simulations previously impossible, advancing fields from optics to geoscience.

More Related Videos

Scattering And Absorption of Light in Planetary Regoliths
11:34

Scattering And Absorption of Light in Planetary Regoliths

Published on: July 1, 2019

Measurements of Long-range Electronic Correlations During Femtosecond Diffraction Experiments Performed on Nanocrystals of Buckminsterfullerene
08:44

Measurements of Long-range Electronic Correlations During Femtosecond Diffraction Experiments Performed on Nanocrystals of Buckminsterfullerene

Published on: August 22, 2017

Related Experiment Videos

Last Updated: Jun 23, 2026

Probing C84-embedded Si Substrate Using Scanning Probe Microscopy and Molecular Dynamics
13:58

Probing C84-embedded Si Substrate Using Scanning Probe Microscopy and Molecular Dynamics

Published on: September 28, 2016

Scattering And Absorption of Light in Planetary Regoliths
11:34

Scattering And Absorption of Light in Planetary Regoliths

Published on: July 1, 2019

Measurements of Long-range Electronic Correlations During Femtosecond Diffraction Experiments Performed on Nanocrystals of Buckminsterfullerene
08:44

Measurements of Long-range Electronic Correlations During Femtosecond Diffraction Experiments Performed on Nanocrystals of Buckminsterfullerene

Published on: August 22, 2017

Area of Science:

  • Physics
  • Computational Electromagnetics
  • Materials Science

Background:

  • Wave scattering from rough surfaces is crucial in diverse scientific fields.
  • Modeling complex roughness (large heights, slopes, multiscale features) exceeds classical theories and numerical limits.

Purpose of the Study:

  • Introduce a novel computational method for full-wave scattering simulations.
  • Enable accurate modeling of wave interactions with highly complex rough surfaces.

Main Methods:

  • Developed a fast multilevel sparse-matrix canonical-grid (FML-SMCG) method.
  • Performed full-wave simulations of 3D rough dielectric surfaces using FML-SMCG.
  • Simulated surfaces with large roughness (rms heights up to 3 wavelengths) and areas (up to 256x256 wavelengths).

Main Results:

  • Achieved tenfold increases in roughness and sixteen-by-sixteen increases in simulated area compared to prior studies.
  • Demonstrated FML-SMCG's capability through five diverse scattering examples.
  • Successfully modeled optical and microwave scattering phenomena, including fractal surfaces, ocean surfaces, and soil surfaces under snow.

Conclusions:

  • The FML-SMCG method offers a general and powerful computational framework for wave scattering problems.
  • This approach significantly advances the ability to study wave interactions with rough surfaces across various physical regimes.