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

Hyperbolic and Inverse Hyperbolic Functions: Problem Solving01:30

Hyperbolic and Inverse Hyperbolic Functions: Problem Solving

218
An arched gate can be effectively modeled using a hyperbolic cosine profile because this type of function is smooth and symmetric about the vertical axis. When the arch is centered at the origin, its maximum height occurs at the center point. This symmetry ensures that any height below the crown of the arch is reached at two horizontal positions that are equal in distance from the centerline but lie on opposite sides.To determine where the gate reaches a height of five meters, the height of the...
218
Geometry of Hyperbolas01:30

Geometry of Hyperbolas

671
A hyperbola consists of all points where the absolute difference of distances to two fixed points, called foci, remains constant. The standard equation isEach branch extends infinitely and approaches two asymptotes, which guide the curve’s behavior. The parameters a and b define key features: a measures the distance from the center to each vertex along the transverse axis, while b influences the slopes of the asymptotes. The asymptotes have equationsA rectangle centered at the origin with...
671
Hyperbolas01:30

Hyperbolas

605
A hyperbola is a conic section produced when a double-napped cone is intersected by a plane at an angle steeper than the slope of the cone, such that it cuts through both nappes. This intersection yields two separate, mirror-image curves known as branches, which open away from each other along the transverse axis. The nearest points on each branch to the hyperbola’s center are termed vertices, and the distance from the center to a vertex is denoted by a. Perpendicular to the transverse...
605
Separable Differential Equations01:20

Separable Differential Equations

318
A separable differential equation is a type of first-order differential equation where the derivative dy/dx can be expressed as a product of two functions: one that depends only on x and another that depends only on y. This allows for the rearrangement of the equation so that all terms involving y are on one side, and all terms involving x are on the other. This process, known as the separation of variables, simplifies the process of solving the equation by enabling the integration of both...
318
Transmission-Line Differential Equations01:26

Transmission-Line Differential Equations

1.1K
Transmission lines are essential components of electrical power systems. They are characterized by the distributed nature of resistance (R), inductance (L), and capacitance (C) per unit length. To analyze these lines, differential equations are employed to model the variations in voltage and current along the line.
Line Section Model
A circuit representing a line section of length Δx helps in understanding the transmission line parameters. The voltage V(x) and current i(x) are measured...
1.1K
Electrostatic Boundary Conditions01:16

Electrostatic Boundary Conditions

1.2K
Consider an external electric field propagating through a homogeneous medium. When the electric field crosses the surface boundary of the medium, it undergoes a discontinuity. The electric field can be resolved into normal and tangential components. The amount by which the field changes at any boundary is given by the difference between the field components above and below the surface boundary.
The surface integral of an electric field is given by Gauss's law in integral form and is related to...
1.2K

You might also read

Related Articles

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

Sort by
Same author

The properties of chondrocyte membrane reservoirs and their role in impact-induced cell death.

Biophysical journal·2013
Same author

Vibrations of Euler's disk.

Physical review. E, Statistical, nonlinear, and soft matter physics·2005
Same author

Should tendon and aponeurosis be considered in series?

Journal of biomechanics·2005
Same author

An articular cartilage contact model based on real surface geometry.

Journal of biomechanics·2004
Same author

Aspects of skeletal muscle modelling.

Philosophical transactions of the Royal Society of London. Series B, Biological sciences·2003

Related Experiment Video

Updated: Apr 17, 2026

Author Spotlight: Computing the Effects of a Local Radiofrequency Hyperthermia Intervention on Tumor Biomechanics
10:23

Author Spotlight: Computing the Effects of a Local Radiofrequency Hyperthermia Intervention on Tumor Biomechanics

Published on: December 1, 2023

1.2K

Boundary conditions for hyperbolic systems of partial differentials equations.

Amr G Guaily1, Marcelo Epstein2

  • 1Engineering Mathematics and Physics Department, Faculty of Engineering, Cairo University, Giza 12613, Egypt.

Journal of Advanced Research
|February 17, 2015
PubMed
Summary

A new algorithm simplifies setting boundary conditions for hyperbolic partial differential equations. This method, using incoming/outgoing characteristics, works for gas dynamics and viscoelastic fluid flow problems.

Keywords:
Boundary conditionsCharacteristicsEuler equationsHyperbolic systemsViscoelastic liquids

More Related Videos

Investigating the Three-dimensional Flow Separation Induced by a Model Vocal Fold Polyp
09:58

Investigating the Three-dimensional Flow Separation Induced by a Model Vocal Fold Polyp

Published on: February 3, 2014

8.9K
Uncoupling Coriolis Force and Rotating Buoyancy Effects on Full-Field Heat Transfer Properties of a Rotating Channel
10:03

Uncoupling Coriolis Force and Rotating Buoyancy Effects on Full-Field Heat Transfer Properties of a Rotating Channel

Published on: October 5, 2018

8.7K

Related Experiment Videos

Last Updated: Apr 17, 2026

Author Spotlight: Computing the Effects of a Local Radiofrequency Hyperthermia Intervention on Tumor Biomechanics
10:23

Author Spotlight: Computing the Effects of a Local Radiofrequency Hyperthermia Intervention on Tumor Biomechanics

Published on: December 1, 2023

1.2K
Investigating the Three-dimensional Flow Separation Induced by a Model Vocal Fold Polyp
09:58

Investigating the Three-dimensional Flow Separation Induced by a Model Vocal Fold Polyp

Published on: February 3, 2014

8.9K
Uncoupling Coriolis Force and Rotating Buoyancy Effects on Full-Field Heat Transfer Properties of a Rotating Channel
10:03

Uncoupling Coriolis Force and Rotating Buoyancy Effects on Full-Field Heat Transfer Properties of a Rotating Channel

Published on: October 5, 2018

8.7K

Area of Science:

  • Computational fluid dynamics
  • Applied mathematics
  • Numerical analysis

Background:

  • Hyperbolic systems of partial differential equations require accurate boundary conditions for numerical solutions.
  • Determining appropriate boundary conditions can be complex and problem-specific.
  • Existing methods may lack generality or ease of application.

Purpose of the Study:

  • To present a straightforward algorithm for determining boundary conditions for hyperbolic partial differential equations.
  • To validate the proposed algorithm using established and novel fluid dynamics problems.

Main Methods:

  • The algorithm utilizes the concept of incoming and outgoing characteristics.
  • It is applied to the Euler system of equations in gas dynamics.
  • The method is also tested on the equations for viscoelastic liquid flow.

Main Results:

  • The algorithm successfully identified boundary condition sets for the Euler equations, consistent with existing literature.
  • Validation on viscoelastic fluid flow demonstrated the algorithm's applicability to complex non-Newtonian fluid dynamics.
  • The proposed method proved to be easy to apply.

Conclusions:

  • The developed algorithm offers an effective and accessible approach for setting boundary conditions in hyperbolic systems.
  • This method enhances the numerical simulation of various fluid dynamics phenomena, including gas dynamics and viscoelastic flows.
  • The incoming/outgoing characteristics approach provides a robust framework for boundary condition determination.