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 Time Domain01:21

Linear Approximation in Time Domain

460
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,...
460
State Space Representation01:27

State Space Representation

785
The frequency-domain technique, commonly used in analyzing and designing feedback control systems, is effective for linear, time-invariant systems. However, it falls short when dealing with nonlinear, time-varying, and multiple-input multiple-output systems. The time-domain or state-space approach addresses these limitations by utilizing state variables to construct simultaneous, first-order differential equations, known as state equations, for an nth-order system.
Consider an RLC circuit, a...
785
Multicompartment Models: Overview01:14

Multicompartment Models: Overview

712
Multicompartment models are mathematical constructs that depict how drugs are distributed and eliminated within the body. They segment the body into several compartments, symbolizing various physiological or anatomical areas connected through drug transfer processes such as absorption, metabolism, distribution, and elimination.
These models offer a more comprehensive representation of drug behavior in the body than one-compartment models. They accommodate the complexity of drug distribution,...
712
Linear Approximation in Frequency Domain01:26

Linear Approximation in Frequency Domain

502
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....
502
Multimachine Stability01:25

Multimachine Stability

698
Multimachine stability analysis is crucial for understanding the dynamics and stability of power systems with multiple synchronous machines. The objective is to solve the swing equations for a network of M machines connected to an N-bus power system.
In analyzing the system, the nodal equations represent the relationship between bus voltages, machine voltages, and machine currents. The nodal equation is given by:
698
State Function, Exact and Inexact Differentials01:27

State Function, Exact and Inexact Differentials

173
A state function is a thermodynamic property that depends solely on the current state of a system, irrespective of its history or how it arrived at that state. These functions are represented by capital letters, such as U, H, and S, which stand for internal energy, enthalpy, and entropy, respectively.For instance, the value of internal energy depends on the system's state variables and remains unaffected by the process path. This means that whether the system underwent a linear process or a...
173

You might also read

Related Articles

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

Sort by
Same author

Data-driven, ML-assisted approaches to problem well-posedness.

PNAS nexus·2026
Same author

Probabilistic Cardiac Digital Twins for Robust Patient-Specific Modeling.

bioRxiv : the preprint server for biology·2026
Same author

Biochemical implementation of acceleration sensing and PIDA control.

NPJ systems biology and applications·2025
Same author

Visual Measurements of Breathing Parameters in Children With a Particular Focus on Phase Angle: A Pilot Study.

Cureus·2025
Same author

From disorganized data to emergent dynamic models: Questionnaires to partial differential equations.

PNAS nexus·2025
Same author

VTA projections to M1 are essential for reorganization of layer 2-3 network dynamics underlying motor learning.

Nature communications·2025

Related Experiment Video

Updated: May 5, 2026

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids
11:03

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids

Published on: December 4, 2017

7.6K

Nonlinear intrinsic variables and state reconstruction in multiscale simulations.

Carmeline J Dsilva1, Ronen Talmon, Neta Rabin

  • 1Department of Chemical and Biological Engineering, Princeton University, Princeton, New Jersey 08544, USA.

The Journal of Chemical Physics
|December 11, 2013
PubMed
Summary

This study introduces nonlinear intrinsic variables (NIV) to simplify complex simulation data. NIV helps merge diverse datasets and uncover hidden variables, aiding in understanding physical processes.

More Related Videos

Single-Molecule Tracking Microscopy - A Tool for Determining the Diffusive States of Cytosolic Molecules
10:20

Single-Molecule Tracking Microscopy - A Tool for Determining the Diffusive States of Cytosolic Molecules

Published on: September 5, 2019

7.9K
Quantification of Strain in a Porcine Model of Skin Expansion Using Multi-View Stereo and Isogeometric Kinematics
14:14

Quantification of Strain in a Porcine Model of Skin Expansion Using Multi-View Stereo and Isogeometric Kinematics

Published on: April 16, 2017

10.7K

Related Experiment Videos

Last Updated: May 5, 2026

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids
11:03

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids

Published on: December 4, 2017

7.6K
Single-Molecule Tracking Microscopy - A Tool for Determining the Diffusive States of Cytosolic Molecules
10:20

Single-Molecule Tracking Microscopy - A Tool for Determining the Diffusive States of Cytosolic Molecules

Published on: September 5, 2019

7.9K
Quantification of Strain in a Porcine Model of Skin Expansion Using Multi-View Stereo and Isogeometric Kinematics
14:14

Quantification of Strain in a Porcine Model of Skin Expansion Using Multi-View Stereo and Isogeometric Kinematics

Published on: April 16, 2017

10.7K

Area of Science:

  • Computational Physics
  • Data Science
  • Chemical Kinetics

Background:

  • High-dimensional simulation data from molecular dynamics and kinetic Monte Carlo methods are crucial for understanding physical phenomena.
  • Extracting meaningful low-dimensional descriptions from this data is essential for both scientific insight and simulation acceleration.

Purpose of the Study:

  • To introduce and illustrate the application of nonlinear intrinsic variables (NIV) for mining high-dimensional multiscale simulation data.
  • To demonstrate how NIV can functionally merge different simulation ensembles and partial observations.
  • To show NIV's capability in inferring variables not explicitly measured.

Main Methods:

  • The approach utilizes inherent process variability to filter measurement noise.
  • A unique reference coordinate frame is systematically recovered.
  • Nonlinear intrinsic variables (NIV) are applied to analyze simulation data.

Main Results:

  • NIV successfully merges distinct simulation ensembles and partial observations.
  • The method effectively infers unmeasured variables from simulation data.
  • Noise is filtered, and a consistent coordinate frame is established.

Conclusions:

  • Nonlinear intrinsic variables (NIV) provide an effective framework for analyzing and simplifying high-dimensional simulation data.
  • This approach enhances the understanding of physical phenomena by revealing underlying structures.
  • NIV has broad applicability, demonstrated in enzyme reaction networks and molecular dynamics simulations.