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

Region of Convergence of Laplace Tarnsform01:20

Region of Convergence of Laplace Tarnsform

749
The Region of Convergence (ROC) is a fundamental concept in signal processing and system analysis, particularly associated with the Laplace transform. The ROC represents an area in the complex plane where the Laplace transform of a given signal converges, determining the transform's applicability and utility.
Consider a decaying exponential signal that begins at a specific time. When deriving its Laplace transform, the time-domain variable is replaced with a complex variable. This...
749
Divergence and Curl of Magnetic Field01:26

Divergence and Curl of Magnetic Field

3.3K
The magnetic field due to a volume current distribution given by the Biot–Savart Law can be expressed as follows:
3.3K
Divergence and Curl of Electric Field01:25

Divergence and Curl of Electric Field

6.3K
The divergence of a vector is a measure of how much the vector spreads out (diverges) from a point. For example, an electric field vector diverges from the positive charge and converges at the negative charge. The divergence of an electric field is derived using Gauss's law and is equal to the charge density divided by the permittivity of space. Mathematically, it is expressed as
6.3K
Reynolds Transport Theorem01:24

Reynolds Transport Theorem

1.4K
The Reynolds transport theorem provides a framework to relate the time rate of change of an extensive property within a system to that in a control volume, which is crucial for analyzing fluid dynamics. Extensive properties, such as mass, velocity, acceleration, temperature, and momentum, can be expressed in terms of the mass of a fluid portion. These properties are called extensive because they depend on the system's size, while intensive properties are their corresponding values per unit...
1.4K
Divergence and Curl01:15

Divergence and Curl

2.2K
The divergence of a vector field at a point is the net outward flow of the flux out of a small volume through a closed surface enclosing the volume, as the volume tends to zero. More practically, divergence measures how much a vector field spreads out or diverges from a given point. For an outgoing flux, conventionally, the divergence is positive. The diverging point is often called the "source" of the field. Meanwhile, the negative divergence of a vector field at a point means that the...
2.2K
Vector Algebra: Graphical Method01:10

Vector Algebra: Graphical Method

14.9K
Vectors can be multiplied by scalars, added to other vectors, or subtracted from other vectors. The vector sum of two (or more) vectors is called the resultant vector or, for short, the resultant.
We use the laws of geometry to construct resultant vectors, followed by trigonometry to find vector magnitudes and directions. For a geometric construction of the sum of two vectors in a plane, we follow the parallelogram rule. Suppose two vectors are at arbitrary positions. Translate either one of...
14.9K

You might also read

Related Articles

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

Sort by
Same author

Tensor-network study of Ising model on infinite hyperbolic dodecahedral lattice.

Physical review. E·2026
Same author

Vertex representation of hyperbolic tensor networks.

Physical review. E·2025
Same author

Local and global magnetization on the Sierpiński carpet.

Physical review. E·2023
Same author

Calculation of critical exponents on fractal lattice Ising model by higher-order tensor renormalization group method.

Physical review. E·2023
Same author

Ising ferromagnets and antiferromagnets in an imaginary magnetic field.

Physical review. E·2022
Same author

Entanglement Renyi Negativity across a Finite Temperature Transition: A Monte Carlo Study.

Physical review letters·2020
Same journal

Erratum: Low-dimensional model for adaptive networks of spiking neurons [Phys. Rev. E 111, 014422 (2025)].

Physical review. E·2026
Same journal

Disentangling the effects of many-body forces on depletion interactions.

Physical review. E·2026
Same journal

Charge transport and mode transition in dual-energy electron beam diodes.

Physical review. E·2026
Same journal

Optimization of multisite reactions in complex compartmentalized media.

Physical review. E·2026
Same journal

Origin of geometric cohesion in nonconvex granular materials: Interplay between interdigitation and rotational constraints enhancing frictional stability.

Physical review. E·2026
Same journal

Interaction of walkers with a standing Faraday wave.

Physical review. E·2026
See all related articles

Related Experiment Video

Updated: Sep 30, 2025

Multifractal Spectrum Analysis for Assessing Pulmonary Nodule Malignancy
05:24

Multifractal Spectrum Analysis for Assessing Pulmonary Nodule Malignancy

Published on: January 10, 2025

524

J_{1}-J_{2} fractal studied by multirecursion tensor-network method.

Jozef Genzor1, Andrej Gendiar2, Ying-Jer Kao1

  • 1Department of Physics, National Taiwan University, Taipei 10607, Taiwan.

Physical Review. E
|March 16, 2022
PubMed
Summary
This summary is machine-generated.

Researchers developed a new tensor-network algorithm to analyze thermodynamic properties of fractal spin lattices. This method enhances the higher-order tensor renormalization group (HOTRG) for complex, non-uniform systems.

More Related Videos

VDJ-Seq: Deep Sequencing Analysis of Rearranged Immunoglobulin Heavy Chain Gene to Reveal Clonal Evolution Patterns of B Cell Lymphoma
15:07

VDJ-Seq: Deep Sequencing Analysis of Rearranged Immunoglobulin Heavy Chain Gene to Reveal Clonal Evolution Patterns of B Cell Lymphoma

Published on: December 28, 2015

26.9K
Quantifying Microglia Morphology from Photomicrographs of Immunohistochemistry Prepared Tissue Using ImageJ
08:44

Quantifying Microglia Morphology from Photomicrographs of Immunohistochemistry Prepared Tissue Using ImageJ

Published on: June 5, 2018

69.7K

Related Experiment Videos

Last Updated: Sep 30, 2025

Multifractal Spectrum Analysis for Assessing Pulmonary Nodule Malignancy
05:24

Multifractal Spectrum Analysis for Assessing Pulmonary Nodule Malignancy

Published on: January 10, 2025

524
VDJ-Seq: Deep Sequencing Analysis of Rearranged Immunoglobulin Heavy Chain Gene to Reveal Clonal Evolution Patterns of B Cell Lymphoma
15:07

VDJ-Seq: Deep Sequencing Analysis of Rearranged Immunoglobulin Heavy Chain Gene to Reveal Clonal Evolution Patterns of B Cell Lymphoma

Published on: December 28, 2015

26.9K
Quantifying Microglia Morphology from Photomicrographs of Immunohistochemistry Prepared Tissue Using ImageJ
08:44

Quantifying Microglia Morphology from Photomicrographs of Immunohistochemistry Prepared Tissue Using ImageJ

Published on: June 5, 2018

69.7K

Area of Science:

  • Condensed Matter Physics
  • Statistical Mechanics
  • Computational Physics

Background:

  • Tensor-network algorithms are crucial for studying quantum many-body systems.
  • The higher-order tensor renormalization group (HOTRG) is effective for uniform lattices.
  • Analyzing fractal lattices presents unique computational challenges due to their complex geometry and lack of translational invariance.

Purpose of the Study:

  • To generalize existing tensor-network algorithms for studying thermodynamic properties of fractal spin lattices.
  • To adapt the higher-order tensor renormalization group (HOTRG) for systems with complex, self-similar structures.
  • To enable the analysis of spin models on lattices without translational invariance.

Main Methods:

  • Generalization of a tensor-network algorithm.
  • Modification of the higher-order tensor renormalization group (HOTRG) algorithm.
  • Introduction of 10 independent local tensors and 15 recursion relations for impurity tensor measurements.
  • Application to the Ising model on a J1-J2 planar fractal lattice.

Main Results:

  • The generalized tensor-network algorithm successfully studied thermodynamic properties of fractal spin lattices.
  • The modified HOTRG algorithm accommodates complex lattice structures and non-uniform couplings (J1 and J2).
  • The study analyzed the Ising model on a fractal with a Hausdorff dimension of approximately 1.792.

Conclusions:

  • The developed generalized tensor-network algorithm is versatile and applicable to various fractal patterns.
  • This approach is suitable for studying models lacking translational invariance, expanding the scope of tensor-network methods.
  • The research provides a new computational tool for investigating complex physical systems with fractal geometries.