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

Linear Approximation in Frequency Domain01:26

Linear Approximation in Frequency Domain

423
Linear systems are characterized by two main properties: superposition and homogeneity. Superposition allows the response to multiple inputs to be the sum of the responses to each individual input. Homogeneity ensures that scaling an input by a scalar results in the response being scaled by the same scalar.
In contrast, nonlinear systems do not inherently possess these properties. However, for small deviations around an operating point, a nonlinear system can often be approximated as linear....
423
Nonlinear Pharmacokinetics: Overview01:19

Nonlinear Pharmacokinetics: Overview

1.4K
Nonlinear or dose-dependent pharmacokinetics is a phenomenon that occurs when the pharmacokinetic parameters of certain drugs deviate from linear pharmacokinetics at higher doses. These drugs do not follow the expected first-order kinetics, where the rate of drug elimination is directly proportional to the drug concentration. Instead, they exhibit a nonlinear relationship, which can be attributed to several factors.
Nonlinearity can arise due to the saturation of plasma protein-binding or...
1.4K
Calculations of Electric Potential I01:15

Calculations of Electric Potential I

2.7K
Consider a ring of radius R with a uniform charge density λ. What will the electric potential be at point M, which is located on the axis of the ring at a distance x from the center of the ring?
The ring is divided into infinitesimal small arcs such that point M is equidistant from all the arcs. Here, the cylindrical coordinate system is used to calculate the electric potential at point M. A general element of the arc between angles θ and θ + dθ is of the length Rdθ and has a charge of...
2.7K
Calculations of Electric Potential II01:27

Calculations of Electric Potential II

2.5K
An electric dipole is a system of two equal but opposite charges, separated by a fixed distance. This system is used to model many real-world systems, including atomic and molecular interactions. One of these systems is the water molecule, but only under certain circumstances. These circumstances are met inside a microwave oven, where electric fields with alternating directions make the water molecules change orientation. This vibration is equivalent to heat at the molecular level.
Consider a...
2.5K
Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving01:29

Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving

393
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...
393
Linear Approximation in Time Domain01:21

Linear Approximation in Time Domain

394
Nonlinear systems often require sophisticated approaches for accurate modeling and analysis, with state-space representation being particularly effective. This method is especially useful for systems where variables and parameters vary with time or operating conditions, such as in a simple pendulum or a translational mechanical system with nonlinear springs.
For a simple pendulum with a mass evenly distributed along its length and the center of mass located at half the pendulum's length,...
394

You might also read

Related Articles

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

Sort by
Same author

Quantitative Homogenization for the Obstacle Problem and Its Free Boundary.

Archive for rational mechanics and analysis·2024
Same author

Higher-Order Linearization and Regularity in Nonlinear Homogenization.

Archive for rational mechanics and analysis·2020
Same author

Brain metabolic alterations in adolescents and young adults with fetal alcohol spectrum disorders.

Alcoholism, clinical and experimental research·2006
Same author

Preliminary findings of proton magnetic resonance spectroscopy in occipital cortex during sleep deprivation.

Psychiatry research·2006

Related Experiment Video

Updated: Mar 22, 2026

Experimental and Data Analysis Workflow for Soft Matter Nanoindentation
13:04

Experimental and Data Analysis Workflow for Soft Matter Nanoindentation

Published on: January 18, 2022

5.0K

Guide to nonlinear potential estimates.

Tuomo Kuusi1, Giuseppe Mingione2

  • 1Aalto University Institute of Mathematics, P.O. Box 11100, 00076  Aalto, Finland.

Bulletin of Mathematical Sciences
|April 13, 2016
PubMed
Summary
This summary is machine-generated.

Nonlinear potential theory now has linear pointwise estimates, analogous to fundamental solutions in nonlinear equations. New potential estimates and fine properties for measure data problems are described.

More Related Videos

Assessing Cerebral Autoregulation via Oscillatory Lower Body Negative Pressure and Projection Pursuit Regression
11:26

Assessing Cerebral Autoregulation via Oscillatory Lower Body Negative Pressure and Projection Pursuit Regression

Published on: December 10, 2014

12.9K
Computational Modeling of Retinal Neurons for Visual Prosthesis Research - Fundamental Approaches
10:50

Computational Modeling of Retinal Neurons for Visual Prosthesis Research - Fundamental Approaches

Published on: June 21, 2022

2.2K

Related Experiment Videos

Last Updated: Mar 22, 2026

Experimental and Data Analysis Workflow for Soft Matter Nanoindentation
13:04

Experimental and Data Analysis Workflow for Soft Matter Nanoindentation

Published on: January 18, 2022

5.0K
Assessing Cerebral Autoregulation via Oscillatory Lower Body Negative Pressure and Projection Pursuit Regression
11:26

Assessing Cerebral Autoregulation via Oscillatory Lower Body Negative Pressure and Projection Pursuit Regression

Published on: December 10, 2014

12.9K
Computational Modeling of Retinal Neurons for Visual Prosthesis Research - Fundamental Approaches
10:50

Computational Modeling of Retinal Neurons for Visual Prosthesis Research - Fundamental Approaches

Published on: June 21, 2022

2.2K

Area of Science:

  • Mathematics
  • Nonlinear Analysis
  • Potential Theory

Background:

  • Linear pointwise estimates using fundamental solutions are a cornerstone of potential theory.
  • Extending these estimates to nonlinear equations presents significant challenges.
  • Existing methods for nonlinear problems often lack generality.

Purpose of the Study:

  • To establish a comprehensive account of the analogy between linear and nonlinear pointwise estimates.
  • To introduce novel, unifying families of potential estimates for nonlinear equations.
  • To explore and describe new fine properties of solutions in measure data problems.

Main Methods:

  • Development of generalized integral operators.
  • Application of sophisticated harmonic analysis techniques.
  • Construction of novel comparison principles for nonlinear potentials.

Main Results:

  • Demonstration of precise analogs for linear pointwise estimates in the nonlinear context.
  • Introduction of new, versatile families of potential estimates applicable to a broad range of nonlinear equations.
  • Characterization of fine properties of solutions, particularly concerning their behavior with respect to measure data.

Conclusions:

  • The findings bridge a gap between linear and nonlinear potential theory, offering powerful new tools.
  • The introduced estimates provide a unified framework for analyzing nonlinear equations.
  • The study advances the understanding of solutions to measure data problems in nonlinear analysis.