Search research articles

ABOUT JoVE

Overview Leadership Blog JoVE Help Center

AUTHORS

Publishing Process Editorial Board Scope & Policies Peer Review FAQ Submit

LIBRARIANS

Testimonials Subscriptions Access Resources Library Advisory Board FAQ

RESEARCH

JoVE Journal Methods Collections JoVE Encyclopedia of Experiments Archive

EDUCATION

JoVE Core JoVE Business JoVE Science Education JoVE Lab Manual Faculty Resource Center Faculty Site

Terms & Conditions of Use

Related Concept Videos

Mechanistic Models: Compartment Models in Individual and Population Analysis

Mechanistic Models: Compartment Models in Individual and Population Analysis

Mechanistic models are utilized in individual analysis using single-source data, but imperfections arise due to data collection errors, preventing perfect prediction of observed data. The mathematical equation involves known values (Xi), observed concentrations (Ci), measurement errors (εi), model parameters (ϕj), and the related function (ƒi) for i number of values. Different least-squares metrics quantify differences between predicted and observed values. The ordinary least squares (OLS)...

Modeling with Differential Equations

Modeling with Differential Equations

Population dynamics can be described mathematically by considering the population size P(t) as a function of time. The rate of change of the population is then represented by the derivative of P(t). A simple assumption is that the rate of growth is proportional to the size of the population itself. This leads to an exponential growth model, where the population increases rapidly without bound. While this is a useful first approximation, it does not reflect realistic long-term...

Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving

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...

Imperfections in Crystal Structure: Stoichiometric Point Defects

Imperfections in Crystal Structure: Stoichiometric Point Defects

Schottky defects arise when some lattice points in a crystal, such as those in NaCl, remain unoccupied, creating lattice vacancies without disturbing the overall electrical neutrality of the crystal. This defect is common in ionic crystals where the positive and negative ions are similar in size, as seen in sodium chloride and cesium chloride. The presence of Schottky defects enables the crystal to conduct electricity to a small extent through an ionic mechanism. Electric fields cause nearby...

Protein Diffusion in the Membrane

Protein Diffusion in the Membrane

Proteins show rotational as well as lateral diffusion across the membrane. The lateral diffusion of proteins was confirmed through the cell fusion experiment where mouse and human cells were fused, resulting in hybrid cells. When the human and mouse cells fused, the specific membrane proteins on human and mouse cells were marked with the red and green-fluorescent markers, respectively. Initially, the red and green fluorescence was located on the respective hemisphere of the cell. As time...

X-ray Crystallography

X-ray Crystallography

The size of the unit cell and the arrangement of atoms in a crystal may be determined from measurements of the diffraction of X-rays by the crystal, termed X-ray crystallography.
Diffraction
Diffraction is the change in the direction of travel experienced by an electromagnetic wave when it encounters a physical barrier whose dimensions are comparable to those of the wavelength of the light. X-rays are electromagnetic radiation with wavelengths about as long as the distance between neighboring...

You might also read

Related Articles

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

Sort by

Same author

Numerical study of long-time dynamics and ergodic-nonergodic transitions in dense simple fluids.

Physical review. E, Statistical, nonlinear, and soft matter physics·2015

Same author

Universal long-time dynamics in dense simple fluids.

Physical review. E, Statistical, nonlinear, and soft matter physics·2014

Same author

Kinetic equations governing Smoluchowski dynamics in equilibrium.

Physical review. E, Statistical, nonlinear, and soft matter physics·2012

Same author

Smoluchowski dynamics and the ergodic-nonergodic transition.

Physical review. E, Statistical, nonlinear, and soft matter physics·2011

Same author

Fundamental theory of statistical particle dynamics.

Physical review. E, Statistical, nonlinear, and soft matter physics·2010

Same author

Fluctuating nonlinear hydrodynamics does not support an ergodic-nonergodic transition.

Physical review. E, Statistical, nonlinear, and soft matter physics·2009

Same journal

Tension on dsDNA bound to ssDNA-RecA filaments may play an important role in driving efficient and accurate homology recognition and strand exchange.

Physical review. E, Statistical, nonlinear, and soft matter physics·2016

Same journal

Publisher's Note: Amplitude-phase coupling drives chimera states in globally coupled laser networks [Phys. Rev. E 91, 040901(R) (2015)].

Physical review. E, Statistical, nonlinear, and soft matter physics·2016

Same journal

Erratum: Shapes of sedimenting soft elastic capsules in a viscous fluid [Phys. Rev. E 92, 033003 (2015)].

Physical review. E, Statistical, nonlinear, and soft matter physics·2016

Same journal

Erratum: Attenuation of excitation decay rate due to collective effect [Phys. Rev. E 90, 022142 (2014)].

Physical review. E, Statistical, nonlinear, and soft matter physics·2016

Same journal

Publisher's Note: Role of connectivity and fluctuations in the nucleation of calcium waves in cardiac cells [Phys. Rev. E 92, 052715 (2015)].

Physical review. E, Statistical, nonlinear, and soft matter physics·2016

Same journal

Publisher's Note: Lattice Boltzmann approach for complex nonequilibrium flows [Phys. Rev. E 92, 043308 (2015)].

Physical review. E, Statistical, nonlinear, and soft matter physics·2016

See all related articles

Search research articles

Related Experiment Video

Updated: Jun 8, 2026

Synthesis of Cyclic Polymers and Characterization of Their Diffusive Motion in the Melt State at the Single Molecule Level

Synthesis of Cyclic Polymers and Characterization of Their Diffusive Motion in the Melt State at the Single Molecule Level

Published on: September 26, 2016

Random diffusion model with structure corrections.

David D McCowan¹, Gene F Mazenko

¹The James Franck Institute and Department of Physics, The University of Chicago, Chicago, Illinois 60637, USA.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics

|September 28, 2010

Summary

This summary is machine-generated.

This study explores a generalized random diffusion model with density-dependent diffusion. It investigates the persistence of system slowing down and dynamic structure factor prepeak features in this refined model.

More Related Videos

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

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

Published on: September 5, 2019

Related Experiment Videos

Last Updated: Jun 8, 2026

Synthesis of Cyclic Polymers and Characterization of Their Diffusive Motion in the Melt State at the Single Molecule Level

Synthesis of Cyclic Polymers and Characterization of Their Diffusive Motion in the Melt State at the Single Molecule Level

Published on: September 26, 2016

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

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

Published on: September 5, 2019

Area of Science:

Physics
Statistical Mechanics
Continuum Models

Background:

The random diffusion model describes conserved scalar fields with density-dependent diffusion.
Previous models featured sharp wave-number cutoffs, limiting natural large-scale behavior.

Purpose of the Study:

To generalize the random diffusion model with a more natural large wave-number cutoff.
To investigate the survival of key dynamic features like system slowing and prepeak development.

Main Methods:

Generalization of the random diffusion model.
Analysis of dynamic structure factor and wave-number cutoffs.
Development of a method for experimental data analysis.

Main Results:

The generalized model retains features such as system slowing.
The prepeak in the dynamic structure factor persists under the new cutoff conditions.
A novel method is presented for identifying hidden prepeaks in experimental data.

Conclusions:

The generalized random diffusion model provides a more robust framework for studying conserved scalar fields.
Key dynamic phenomena are preserved, enhancing the model's applicability.
The new analysis method aids in interpreting experimental observations of complex diffusion dynamics.