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

Logarithmic Differentiation01:28

Logarithmic Differentiation

When a car’s weight and driving forces act on a tire, they impose an external load on the rubber material. This load is resisted internally by forces distributed throughout the tire structure, which are defined as stress. The resulting deformation of the rubber due to this stress is quantified as strain. The relationship between stress and strain governs how the tire deforms under load and is central to understanding its mechanical response during operation.Rubber exhibits a nonlinear...
Applications of Logarithms01:28

Applications of Logarithms

Logarithmic functions are powerful tools for simplifying the mathematical representation of phenomena involving exponential changes. Their ability to convert multiplicative relationships into additive ones is especially valuable in various scientific and engineering contexts. One notable application of logarithms is measuring sound intensity, specifically through the decibel (dB) scale used in acoustics.Sound intensity levels vary over an extensive range, from the faintest audible whisper to...
Poisson's And Laplace's Equation01:25

Poisson's And Laplace's Equation

The electric potential of the system can be calculated by relating it to the electric charge densities that give rise to the electric potential. The differential form of Gauss's law expresses the electric field's divergence in terms of the electric charge density.
Pharmacodynamic Models: Logarithmic Concentration–Effect Model01:15

Pharmacodynamic Models: Logarithmic Concentration–Effect Model

The log-linear model is a pharmacological framework used to describe the relationship between drug concentration and its effect. This model is particularly relevant when the observed effects range between 20% and 80% of the drug’s maximum effect (Emax), where a near-linear relationship is observed between the log of drug concentration and the measured effect. However, the log-linear model does not predict the maximum possible effect (Emax) or the effect at zero drug concentration, limiting its...
Derivatives of Logarithmic Functions01:22

Derivatives of Logarithmic Functions

Logarithmic and Exponential RelationshipA logarithmic function is the inverse of an exponential function. If y = logb x then, it can be rewritten as by = x. This relationship allows for implicit differentiation, making logarithmic functions useful in calculus. Logarithmic scales are widely used to represent data that span multiple orders of magnitude, such as earthquake magnitudes (Richter scale) and sound intensity (decibels).Differentiation of Logarithmic FunctionsTo differentiate y = logb x,...
Laws of Logarithms I01:30

Laws of Logarithms I

Logarithms are fundamental mathematical operations that serve as the inverse of exponentiation. They provide a means to express how many times a base must be raised to yield a given number. For base 10, often referred to as the common logarithm, the notation is written simply as log. Thus, if 10n = x, then log⁡(x) = n. This relationship makes logarithms especially valuable in simplifying complex calculations involving multiplication, division, and exponentiation.Logarithmic expressions are...

You might also read

Related Articles

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

Sort by
Same author

Aftermath epidemics: Percolation on the sites visited by generalized random walks.

Physical review. E·2023
Same author

Many universality classes in an interface model restricted to non-negative heights.

Physical review. E·2023
Same author

On Generalized Schürmann Entropy Estimators.

Entropy (Basel, Switzerland)·2022
Same author

Universality of Critically Pinned Interfaces in Two-Dimensional Isotropic Random Media.

Physical review letters·2018
Same author

How fast does a random walk cover a torus?

Physical review. E·2018
Same author

Self-Trapping Self-Repelling Random Walks.

Physical review letters·2017
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

Related Experiment Video

Updated: Jun 22, 2026

Controlled Synthesis and Fluorescence Tracking of Highly Uniform Poly(N-isopropylacrylamide) Microgels
11:34

Controlled Synthesis and Fluorescence Tracking of Highly Uniform Poly(N-isopropylacrylamide) Microgels

Published on: September 8, 2016

Logarithmic corrections in (4+1) -dimensional directed percolation.

Peter Grassberger1

  • 1John-von-Neumann Institute for Computing, Forschungszentrum Jülich, D-52425 Jülich, Germany.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|June 13, 2009
PubMed
Summary
This summary is machine-generated.

We simulated directed site percolation in four spatial dimensions, achieving precise critical probability estimates. Our findings reveal logarithmic corrections are crucial for accurate modeling, outperforming simpler approximations.

More Related Videos

A Psychophysics Paradigm for the Collection and Analysis of Similarity Judgments
08:12

A Psychophysics Paradigm for the Collection and Analysis of Similarity Judgments

Published on: March 1, 2022

Related Experiment Videos

Last Updated: Jun 22, 2026

Controlled Synthesis and Fluorescence Tracking of Highly Uniform Poly(N-isopropylacrylamide) Microgels
11:34

Controlled Synthesis and Fluorescence Tracking of Highly Uniform Poly(N-isopropylacrylamide) Microgels

Published on: September 8, 2016

A Psychophysics Paradigm for the Collection and Analysis of Similarity Judgments
08:12

A Psychophysics Paradigm for the Collection and Analysis of Similarity Judgments

Published on: March 1, 2022

Area of Science:

  • Statistical Physics
  • Complex Systems
  • Computational Physics

Background:

  • Percolation theory models the connectivity of random networks.
  • Understanding critical phenomena in higher dimensions is computationally challenging.
  • Logarithmic corrections significantly impact critical behavior analysis.

Purpose of the Study:

  • To provide precise estimates for the critical probability (p_c) in directed site percolation on 4D lattices.
  • To compare simulation results with theoretical calculations of logarithmic corrections.
  • To investigate the role of leading and next-to-leading logarithmic terms in fitting simulation data.

Main Methods:

  • Directed site percolation simulations on simple and body-centered hypercubic lattices in 4+1 dimensions.
  • Utilized efficient simulation techniques: hashing, histogram reweighing, and improved estimators.
  • Analyzed simulation data by fitting to theoretical models including logarithmic corrections.

Main Results:

  • Obtained highly precise estimates for the critical probability (p_c) on the studied lattices.
  • Demonstrated that leading logarithmic terms alone yield inaccurate power estimates (off by ~50%).
  • Including next-to-leading terms improved fits but lacked mutual consistency; a consistent set of parameters offered significant improvement over leading log approximations.

Conclusions:

  • Logarithmic corrections are essential for accurate analysis of directed percolation in 4D.
  • A specific combination of observables was identified as being free of logarithmic terms, offering a robust measurement.
  • The study provides a benchmark for theoretical models of critical phenomena in higher dimensions.