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

Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving01:29

Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving

397
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...
397
Mechanistic Models: Compartment Models in Individual and Population Analysis01:23

Mechanistic Models: Compartment Models in Individual and Population Analysis

321
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...
321
Model Approaches for Pharmacokinetic Data: Distributed Parameter Models01:06

Model Approaches for Pharmacokinetic Data: Distributed Parameter Models

310
Pharmacokinetic models are mathematical constructs that represent and predict the time course of drug concentrations in the body, providing meaningful pharmacokinetic parameters. These models are categorized into compartment, physiological, and distributed parameter models.
The distributed parameter models are specifically designed to account for variations and differences in some drug classes. This model is particularly useful for assessing regional concentrations of anticancer or...
310
Linear Approximation in Time Domain01:21

Linear Approximation in Time Domain

406
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,...
406
¹H NMR: Long-Range Coupling01:27

¹H NMR: Long-Range Coupling

2.9K
The coupling interactions of nuclei across four or more bonds are usually weak, with J values less than 1 Hz. While these are usually not observed in spectra, the presence of multiple bonds along the coupling pathway can result in observable long-range coupling.
In alkenes, spin information is communicated via σ–π overlap, as seen in allylic (four-bond) and homoallylic (five-bond) couplings. These coupling interactions are stronger when the σ bond is parallel to the alkene...
2.9K
Quadratic Models01:23

Quadratic Models

302
Quadratic models are mathematical representations used to describe relationships in which the rate of change changes at a constant rate. These models appear in a wide variety of natural and engineered systems, especially those involving motion, forces, and optimization. One common application is analyzing the vertical motion of objects influenced by gravity, such as a ball thrown into the air.In such scenarios, the object's height changes over time in a curved pattern, rising to a maximum point...
302

You might also read

Related Articles

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

Sort by
Same author

Spectral Signatures of Prime Factorization.

Entropy (Basel, Switzerland)·2026
Same author

Neighbourhood topology unveils pathological hubs in the brain networks of epilepsy-surgery patients.

Brain communications·2025
Same author

Mean Field Approaches to Lattice Gauge Theories: A Review.

Entropy (Basel, Switzerland)·2025
Same author

Energy exchange statistics and fluctuation theorem for nonthermal asymptotic states.

Physical review. E·2025
Same author

Universal Work Statistics in Long-Range Interacting Quantum Systems.

Physical review letters·2025
Same author

Universality in long-range interacting systems: The effective dimension approach.

Physical review. E·2024

Related Experiment Video

Updated: Mar 29, 2026

Excitonic Hamiltonians for Calculating Optical Absorption Spectra and Optoelectronic Properties of Molecular Aggregates and Solids
08:04

Excitonic Hamiltonians for Calculating Optical Absorption Spectra and Optoelectronic Properties of Molecular Aggregates and Solids

Published on: May 27, 2020

9.1K

Fixed-point structure and effective fractional dimensionality for O(N) models with long-range interactions.

Nicoló Defenu1,2, Andrea Trombettoni1,2,3, Alessandro Codello4

  • 1SISSA, Via Bonomea 265, I-34136 Trieste, Italy.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|December 15, 2015
PubMed
Summary

We investigate O(N) models with power-law decaying interactions using renormalization group methods. An effective fractional dimension is derived, providing insights into critical exponents and universality classes for these complex systems.

More Related Videos

Structure-Based Simulation and Sampling of Transcription Factor Protein Movements along DNA from Atomic-Scale Stepping to Coarse-Grained Diffusion
09:17

Structure-Based Simulation and Sampling of Transcription Factor Protein Movements along DNA from Atomic-Scale Stepping to Coarse-Grained Diffusion

Published on: March 1, 2022

3.6K
Author Spotlight: Evaluation of Protein-Condensate Dynamics in Live Human Cells
06:48

Author Spotlight: Evaluation of Protein-Condensate Dynamics in Live Human Cells

Published on: January 5, 2024

5.8K

Related Experiment Videos

Last Updated: Mar 29, 2026

Excitonic Hamiltonians for Calculating Optical Absorption Spectra and Optoelectronic Properties of Molecular Aggregates and Solids
08:04

Excitonic Hamiltonians for Calculating Optical Absorption Spectra and Optoelectronic Properties of Molecular Aggregates and Solids

Published on: May 27, 2020

9.1K
Structure-Based Simulation and Sampling of Transcription Factor Protein Movements along DNA from Atomic-Scale Stepping to Coarse-Grained Diffusion
09:17

Structure-Based Simulation and Sampling of Transcription Factor Protein Movements along DNA from Atomic-Scale Stepping to Coarse-Grained Diffusion

Published on: March 1, 2022

3.6K
Author Spotlight: Evaluation of Protein-Condensate Dynamics in Live Human Cells
06:48

Author Spotlight: Evaluation of Protein-Condensate Dynamics in Live Human Cells

Published on: January 5, 2024

5.8K

Area of Science:

  • Statistical Mechanics
  • Condensed Matter Physics
  • Quantum Field Theory

Background:

  • O(N) models are fundamental in statistical mechanics and quantum field theory.
  • Interactions decaying as power laws introduce long-range correlations.
  • Renormalization group methods are crucial for understanding critical phenomena.

Purpose of the Study:

  • To analyze O(N) models with power-law decaying interactions using renormalization group methods.
  • To compute critical exponents by introducing an effective fractional dimension.
  • To explore the full theory space including both short- and long-range propagator terms.

Main Methods:

  • Renormalization group (RG) analysis.
  • Calculation of critical exponents.
  • Investigation of effective fractional dimensions.
  • Analysis of propagator terms and wave function renormalization.

Main Results:

  • An effective fractional dimension D(eff) is derived for O(N) models with power-law interactions.
  • The effective dimension is D(eff)=2d/σ neglecting wave function renormalization, exact in the spherical model limit.
  • Including wave function renormalization yields D(eff)=(2-η(SR))d/σ, matching standard scaling arguments.
  • Explicit results for the exponent ν in two and three dimensions are provided.
  • A comprehensive analysis of the fixed-point structure and multicritical long-range universality classes is presented.

Conclusions:

  • The effective dimension is an approximation, and its error is estimated.
  • The proposed method offers a complete description of the theory space for these models.
  • This work advances the understanding of critical phenomena in systems with long-range interactions.