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

BIBO stability of continuous and discrete -time systems01:24

BIBO stability of continuous and discrete -time systems

System stability is a fundamental concept in signal processing, often assessed using convolution. For a system to be considered bounded-input bounded-output (BIBO) stable, any bounded input signal must produce a bounded output signal. A bounded input signal is one where the modulus does not exceed a certain constant at any point in time.
To determine the BIBO stability, the convolution integral is utilized when a bounded continuous-time input is applied to a Linear Time-Invariant (LTI) system.
The Entropy as a State Function01:14

The Entropy as a State Function

Consider an arbitrary process that moves between two specific states (A and B) in a cyclic manner. This process is reversible and broken down into smaller parts that each follow a Carnot cycle. A Carnot cycle has two isothermal (constant temperature) processes. During these processes, the ratio of the amount of heat transferred to their respective temperature remains constant. The other two processes in the Carnot cycle are also reversible but adiabatic, which means they occur without any heat...
Transmission-Line Differential Equations01:26

Transmission-Line Differential Equations

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 from the...
Separable Differential Equations01:20

Separable Differential Equations

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...
Entropy Change in Reversible Processes01:10

Entropy Change in Reversible Processes

In the Carnot engine, which achieves the maximum efficiency between two reservoirs of fixed temperatures, the total change in entropy is zero. The observation can be generalized by considering any reversible cyclic process consisting of many Carnot cycles. Thus, it can be stated that the total entropy change of any ideal reversible cycle is zero.
The statement can be further generalized to prove that entropy is a state function. Take a cyclic process between any two points on a p-V diagram.
Reversible and Irreversible Processes01:14

Reversible and Irreversible Processes

The thermodynamic processes can be classified into reversible and irreversible processes. The processes that can be restored to their initial state are called reversible processes. It is only possible if the process is in quasi-static equilibrium, i.e., it takes place in infinitesimally small steps, and the system remains at equilibrium However, these are ideal processes and do not occur naturally. An ideal system undergoing a reversible process is always in thermodynamic equilibrium within...

You might also read

Related Articles

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

Sort by
Same author

Complete genome sequence of <i>Clostridium botulinum</i> TMIPH-CB191 (GTC 18335) isolated from a human in Japan.

Microbiology resource announcements·2026
Same author

Complete genome sequence of <i>Elizabethkingia</i> sp<i>.</i> GTC18459 isolated from a snake skin in Japan.

Microbiology resource announcements·2026
Same author

Complete genome sequence of <i>Francisella salimarina</i> GTC 22824 isolated from coastal seawater in Osaka, Japan.

Microbiology resource announcements·2026
Same author

High prevalence of atypical enteropathogenic Escherichia coli contaminating retail chicken meat in Vietnam: virulence gene profiles, sequence types, and antimicrobial resistance.

Journal of infection and chemotherapy : official journal of the Japan Society of Chemotherapy·2026
Same author

Complete genome sequences of <i>Lichenicola</i> spp. GTC18330 and 18331 isolated from bee products in Gifu, Japan.

Microbiology resource announcements·2026
Same author

<i>Prevotella mikamonis</i> sp. nov., isolated from equine clinical specimens.

International journal of systematic and evolutionary microbiology·2026

Related Experiment Video

Updated: Jul 4, 2026

Experimental Investigation of Secondary Flow Structures Downstream of a Model Type IV Stent Failure in a 180&#176; Curved Artery Test Section
11:00

Experimental Investigation of Secondary Flow Structures Downstream of a Model Type IV Stent Failure in a 180° Curved Artery Test Section

Published on: July 19, 2016

Transcritical bifurcations in nonintegrable Hamiltonian systems.

Matthias Brack1, Kaori Tanaka

  • 1Institute for Theoretical Physics, University of Regensburg, D-93040 Regensburg, Germany.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|June 4, 2008
PubMed
Summary

Transcritical bifurcations in Hamiltonian systems are common, especially for systems with librating orbits. This study details their properties and semiclassical approximations for quantum systems.

More Related Videos

Scalable Quantum Integrated Circuits on Superconducting Two-Dimensional Electron Gas Platform
05:39

Scalable Quantum Integrated Circuits on Superconducting Two-Dimensional Electron Gas Platform

Published on: August 2, 2019

4D Printed Bifurcated Stents with Kirigami-Inspired Structures
06:52

4D Printed Bifurcated Stents with Kirigami-Inspired Structures

Published on: July 25, 2019

Related Experiment Videos

Last Updated: Jul 4, 2026

Experimental Investigation of Secondary Flow Structures Downstream of a Model Type IV Stent Failure in a 180&#176; Curved Artery Test Section
11:00

Experimental Investigation of Secondary Flow Structures Downstream of a Model Type IV Stent Failure in a 180° Curved Artery Test Section

Published on: July 19, 2016

Scalable Quantum Integrated Circuits on Superconducting Two-Dimensional Electron Gas Platform
05:39

Scalable Quantum Integrated Circuits on Superconducting Two-Dimensional Electron Gas Platform

Published on: August 2, 2019

4D Printed Bifurcated Stents with Kirigami-Inspired Structures
06:52

4D Printed Bifurcated Stents with Kirigami-Inspired Structures

Published on: July 25, 2019

Area of Science:

  • Mathematical Physics
  • Dynamical Systems Theory
  • Quantum Chaos

Background:

  • Nonintegrable Hamiltonian systems exhibit complex dynamics, including bifurcations of periodic orbits.
  • Understanding these bifurcations is crucial for characterizing system stability and behavior.

Purpose of the Study:

  • To investigate transcritical bifurcations of periodic orbits in 2D nonintegrable Hamiltonian systems.
  • To establish existence criteria and analyze properties of these bifurcations using symplectic maps.
  • To explore their occurrence in generalized Hénon-Heiles Hamiltonians and their semiclassical implications.

Main Methods:

  • Utilizing a mathematical description of transcritical bifurcations in families of symplectic maps.
  • Performing numerical simulations on generalized Hénon-Heiles Hamiltonians.
  • Deriving normal forms for transcritical and isochronous pitchfork bifurcations.
  • Developing uniform approximations for semiclassical trace formulas.

Main Results:

  • Transcritical bifurcations are typical for Hamiltonians with straight-line librating orbits, even without discrete symmetries.
  • Isochronous pitchfork bifurcations are identified as exceptional cases.
  • Excellent agreement was found between semiclassical and quantum mechanical computations of the density of states.

Conclusions:

  • Transcritical bifurcations play a significant role in the dynamics of nonintegrable Hamiltonian systems.
  • The derived semiclassical approximations accurately predict quantum mechanical properties like the density of states.
  • This work provides a framework for analyzing complex dynamics in quantum chaos.