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

Dimensionless Groups in Fluid Mechanics01:15

Dimensionless Groups in Fluid Mechanics

Dimensionless groups in fluid mechanics provide simplified ratios that help analyze fluid behavior without relying on specific units. The Reynolds number (Re), which represents the ratio of inertial to viscous forces, distinguishes between laminar and turbulent flows, making it essential in the design of pipelines and aerodynamic surfaces. The Froude number (Fr), the ratio of inertial to gravitational forces, is particularly useful in predicting wave formation and hydraulic jumps in...
Divergence Theorem in 3D Space01:20

Divergence Theorem in 3D Space

In vector calculus, flux measures the total flow of a vector field through a surface. For a closed surface in three-dimensional space, this means measuring how much of the field passes outward through every point on the boundary. Directly calculating this flux can be difficult when the surface has a complicated or irregular shape. The Divergence Theorem provides a powerful alternative by relating surface flux to behavior inside the enclosed region.The Divergence Theorem states that the outward...
Cylinders in Three-Dimensional Space01:28

Cylinders in Three-Dimensional Space

A cylindrical surface is generated when a two-dimensional profile curve is translated along a straight line in three-dimensional space. The translated copies of the curve form a surface composed of parallel rulings, each oriented in the same fixed direction. This construction allows many three-dimensional forms to be described using relatively simple planar equations.In Cartesian coordinates, a cylindrical surface is often recognized by an equation that omits one of the three variables. For...
Quadric Surfaces01:28

Quadric Surfaces

Quadric surfaces are three-dimensional surfaces characterized by second-degree equations in the variables x, y, and z. These surfaces are smooth and continuous, and specific combinations of squared and linear terms define their shapes. The main types of quadric surfaces include ellipsoids, cones, paraboloids, and hyperboloids. Each type exhibits distinct geometric features depending on how the variables are arranged and related within the equation.Ellipsoids are closed surfaces formed when all...
Collisions in Multiple Dimensions: Introduction01:05

Collisions in Multiple Dimensions: Introduction

It is far more common for collisions to occur in two dimensions; that is, the initial velocity vectors are neither parallel nor antiparallel to each other. Let's see what complications arise from this. The first idea is that momentum is a vector. Like all vectors, it can be expressed as a sum of perpendicular components (usually, though not always, an x-component and a y-component, and a z-component if necessary). Thus, when the statement of conservation of momentum is written for a problem,...
Reynolds Transport Theorem01:24

Reynolds Transport Theorem

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 mass.

You might also read

Related Articles

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

Sort by
Same author

Overlap locking and nonperturbative effects in spin glasses.

Proceedings of the National Academy of Sciences of the United States of America·2026
Same author

Predictability of complex networks.

Proceedings of the National Academy of Sciences of the United States of America·2026
Same author

Rare trajectories in a prototypical mean-field disordered model: Insights into landscape and instantons.

Physical review. E·2026
Same author

Solution of the critical dynamics of the mean-field Kob-Andersen model.

Physical review. E·2025
Same author

Critical exponents of the spin-glass transition in a field at zero temperature.

Proceedings of the National Academy of Sciences of the United States of America·2025
Same author

Mandibular reconstruction with anterolateral thigh free flap and bridging plate: a retrospective study of 34 oncological cases.

Frontiers in surgery·2025
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 29, 2026

Reservoir Condition Pore-scale Imaging of Multiple Fluid Phases Using X-ray Microtomography
08:02

Reservoir Condition Pore-scale Imaging of Multiple Fluid Phases Using X-ray Microtomography

Published on: February 25, 2015

k-core percolation in four dimensions.

Giorgio Parisi1, Tommaso Rizzo

  • 1Dipartimento di Fisica, Università di Roma La Sapienza, P. le Aldo Moro 2, 00185 Roma, Italy.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|October 15, 2008
PubMed
Summary
This summary is machine-generated.

We studied k-core percolation on a four-dimensional lattice, a model for jamming transitions. For k=4, we found a strictly first-order transition, while for k=3, the transition is continuous.

More Related Videos

Three-dimensional Particle Tracking Velocimetry for Turbulence Applications: Case of a Jet Flow
13:02

Three-dimensional Particle Tracking Velocimetry for Turbulence Applications: Case of a Jet Flow

Published on: February 27, 2016

Dynamic Pore-scale Reservoir-condition Imaging of Reaction in Carbonates Using Synchrotron Fast Tomography
10:18

Dynamic Pore-scale Reservoir-condition Imaging of Reaction in Carbonates Using Synchrotron Fast Tomography

Published on: February 21, 2017

Related Experiment Videos

Last Updated: Jun 29, 2026

Reservoir Condition Pore-scale Imaging of Multiple Fluid Phases Using X-ray Microtomography
08:02

Reservoir Condition Pore-scale Imaging of Multiple Fluid Phases Using X-ray Microtomography

Published on: February 25, 2015

Three-dimensional Particle Tracking Velocimetry for Turbulence Applications: Case of a Jet Flow
13:02

Three-dimensional Particle Tracking Velocimetry for Turbulence Applications: Case of a Jet Flow

Published on: February 27, 2016

Dynamic Pore-scale Reservoir-condition Imaging of Reaction in Carbonates Using Synchrotron Fast Tomography
10:18

Dynamic Pore-scale Reservoir-condition Imaging of Reaction in Carbonates Using Synchrotron Fast Tomography

Published on: February 21, 2017

Area of Science:

  • Statistical Physics
  • Complex Networks
  • Percolation Theory

Background:

  • The k-core percolation model on the Bethe lattice is a simplified approach to understanding jamming transitions.
  • This model exhibits a hybrid nature, combining first-order and second-order transition characteristics.

Purpose of the Study:

  • To numerically investigate k-core percolation on a four-dimensional regular lattice.
  • To characterize the nature of the transition for different k values, specifically k=4 and k=3.

Main Methods:

  • Numerical simulations were employed to study k-core percolation.
  • The investigation focused on a four-dimensional regular lattice structure.

Main Results:

  • For k=4, a discontinuous, strictly first-order transition was confirmed. The k-core density showed no pre-transition singularities, and the correlation length remained finite.
  • For k=3, the transition was found to be continuous.

Conclusions:

  • The study clarifies the distinct transition behaviors of k-core percolation in higher dimensions.
  • Results indicate that the dimensionality and the parameter k significantly influence the nature of the jamming transition.