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

Scaling01:26

Scaling

676
In designing and analyzing filters, resonant circuits, or circuit analysis at large, working with standard element values like 1 ohm, 1 henry, or 1 farad can be convenient before scaling these values to more realistic figures. This approach is widely utilized by not employing realistic element values in numerous examples and problems; it simplifies mastering circuit analysis through convenient component values. The complexity of calculations is thereby reduced, with the understanding that...
676
Scale-Up Processes01:14

Scale-Up Processes

92
The scale-up of microbial fermentation processes is essential in industrial biotechnology, allowing the transition from laboratory-scale experiments to commercial-scale production while aiming to maintain product yield and quality. This process requires meticulous adjustment of equipment design, process parameters, and contamination control strategies to accommodate increasing culture volumes.At the laboratory scale, cultures are typically maintained in 1 to 10-liter glass or autoclavable...
92
Dimensional Analysis02:19

Dimensional Analysis

26.8K
The concept of dimension is important because every mathematical equation linking physical quantities must be dimensionally consistent, implying that mathematical equations must meet the following two rules. The first rule is that, in an equation, the expressions on each side of the equal sign must have the same dimensions. This is fairly intuitive since we can only add or subtract quantities of the same type (dimension). The second rule states that, in an equation, the arguments of any of the...
26.8K
Dimensional Analysis01:23

Dimensional Analysis

2.5K
Dimensional analysis is a powerful tool that is used in physics and engineering to understand and predict the behavior of physical systems. The basic idea behind dimensional analysis is to express physical quantities in terms of fundamental dimensions such as the mass, length, and time. Derived dimensions like the velocity, acceleration, and force are derived from the combinations of these fundamental dimensions.
Dimensional analysis allows us to analyze and compare physical quantities on a...
2.5K
Dimensional Analysis03:40

Dimensional Analysis

68.5K
Dimensional analysis, also known as the factor label method, is a versatile approach for mathematical operations. The main principle behind this approach is: the units of quantities must be subjected to the same mathematical operations as their associated numbers. This method can be applied to computations ranging from simple unit conversions to more complex and multi-step calculations involving several different quantities and their units.
Conversion Factors and Dimensional Analysis
The unit...
68.5K
Dimensional Analysis01:27

Dimensional Analysis

852
Dimensional analysis is a valuable technique in fluid mechanics for simplifying complex problems by reducing them into dimensionless groups. These groups capture the essential relationships between the variables involved, allowing researchers and engineers to analyze fluid flow without dealing with each variable individually. This approach reduces the number of independent variables, allowing for easier analysis and better understanding of physical phenomena.
In fluid mechanics, dimensional...
852

You might also read

Related Articles

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

Sort by
Same author

Modeling future cliff-front waves during sea level rise and implications for coastal cliff retreat rates.

Scientific reports·2024
Same author

Sea-level rise may not uniformly accelerate cliff erosion rates.

Nature communications·2023
Same author

Open science discovery of potent noncovalent SARS-CoV-2 main protease inhibitors.

Science (New York, N.Y.)·2023
Same author

Metastate analysis of the ground states of two-dimensional Ising spin glasses.

Physical review. E·2023
Same author

Local Resampling Trick for Focused Molecular Dynamics.

Journal of chemical theory and computation·2023
Same author

Nontrivial maturation metastate-average state in a one-dimensional long-range Ising spin glass: Above and below the upper critical range.

Physical review. E·2021

Related Experiment Video

Updated: Apr 18, 2026

Scalable Nanohelices for Predictive Studies and Enhanced 3D Visualization
08:03

Scalable Nanohelices for Predictive Studies and Enhanced 3D Visualization

Published on: November 12, 2014

11.0K

Finite-size scaling above the upper critical dimension.

Matthew Wittmann1, A P Young2

  • 1Department of Physics, University of California, Santa Cruz, California 95064, USA.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|January 24, 2015
PubMed
Summary

Finite-size scaling (FSS) analysis reveals distinct behaviors for different fluctuation types above the upper critical dimension. The exponent η is confirmed as 0, with data collapsing using a modified scaling variable.

More Related Videos

Experimental Manipulation of Body Size to Estimate Morphological Scaling Relationships in Drosophila
06:00

Experimental Manipulation of Body Size to Estimate Morphological Scaling Relationships in Drosophila

Published on: October 1, 2011

14.5K
High-resolution Volume Imaging of Neurons by the Use of Fluorescence eXclusion Method and Dedicated Microfluidic Devices
09:11

High-resolution Volume Imaging of Neurons by the Use of Fluorescence eXclusion Method and Dedicated Microfluidic Devices

Published on: March 26, 2018

7.5K

Related Experiment Videos

Last Updated: Apr 18, 2026

Scalable Nanohelices for Predictive Studies and Enhanced 3D Visualization
08:03

Scalable Nanohelices for Predictive Studies and Enhanced 3D Visualization

Published on: November 12, 2014

11.0K
Experimental Manipulation of Body Size to Estimate Morphological Scaling Relationships in Drosophila
06:00

Experimental Manipulation of Body Size to Estimate Morphological Scaling Relationships in Drosophila

Published on: October 1, 2011

14.5K
High-resolution Volume Imaging of Neurons by the Use of Fluorescence eXclusion Method and Dedicated Microfluidic Devices
09:11

High-resolution Volume Imaging of Neurons by the Use of Fluorescence eXclusion Method and Dedicated Microfluidic Devices

Published on: March 26, 2018

7.5K

Area of Science:

  • Statistical Mechanics
  • Condensed Matter Physics
  • Critical Phenomena

Background:

  • Finite-size scaling (FSS) theory describes how system properties change near critical points in finite systems.
  • Understanding FSS is crucial for interpreting experimental and simulation data, especially concerning boundary conditions.
  • Previous FSS models faced challenges in reconciling different fluctuation behaviors and hyperscaling violations.

Purpose of the Study:

  • To unify the understanding of finite-size scaling (FSS) for both free and periodic boundary conditions above the upper critical dimension.
  • To clarify the applicability of modified and standard FSS theories based on fluctuation types (k=0 vs. k≠0).
  • To determine the precise value of the critical exponent η and validate FSS predictions with simulations.

Main Methods:

  • Developing a unified theoretical framework for FSS applicable above the upper critical dimension.
  • Distinguishing between k=0 and k≠0 fluctuations and their impact on FSS.
  • Utilizing large-scale numerical simulations of the five-dimensional Ising model.
  • Analyzing the scaling behavior of susceptibility and employing a modified scaling variable T-T(L).

Main Results:

  • Modified FSS applies only to k=0 fluctuations, while standard FSS applies to k≠0 fluctuations.
  • The exponent η, describing correlation decay, is unambiguously determined to be η=0.
  • Finite-size rounding and shift effects were analyzed for free boundary conditions.
  • Data collapse was achieved using the finite-size pseudocritical temperature T(L) as the scaling variable, encompassing behaviors at both T(L) and the bulk critical temperature T(c).
  • Simulation results for the 5D Ising model support the theoretical predictions.

Conclusions:

  • A unified view of FSS is established for dimensions above the upper critical dimension.
  • The exponent η=0 is confirmed, resolving ambiguities in previous analyses.
  • The study provides a robust framework for understanding critical phenomena in finite systems, validated by strong numerical evidence.