Search research articles

ABOUT JoVE

Overview Leadership Blog JoVE Help Center

AUTHORS

Publishing Process Editorial Board Scope & Policies Peer Review FAQ Submit

LIBRARIANS

Testimonials Subscriptions Access Resources Library Advisory Board FAQ

RESEARCH

JoVE Journal Methods Collections JoVE Encyclopedia of Experiments Archive

EDUCATION

JoVE Core JoVE Business JoVE Science Education JoVE Lab Manual Faculty Resource Center Faculty Site

Terms & Conditions of Use

Related Concept Videos

Mechanical Systems

Mechanical Systems

Mechanical systems are analogous to to electrical networks where springs and masses play similar roles to inductors and capacitors, respectively. A viscous damper in mechanical systems functions similarly to a resistor in electrical networks, dissipating energy. The forces acting on a mass in such systems include an applied force in the direction of motion, counteracted by forces from the spring, a viscous damper, and the mass's acceleration. This interplay of forces is mathematically described...

Linear Approximation in Frequency Domain

Linear Approximation in Frequency Domain

Linear systems are characterized by two main properties: superposition and homogeneity. Superposition allows the response to multiple inputs to be the sum of the responses to each individual input. Homogeneity ensures that scaling an input by a scalar results in the response being scaled by the same scalar.
In contrast, nonlinear systems do not inherently possess these properties. However, for small deviations around an operating point, a nonlinear system can often be approximated as linear.

State Space Representation

State Space Representation

The frequency-domain technique, commonly used in analyzing and designing feedback control systems, is effective for linear, time-invariant systems. However, it falls short when dealing with nonlinear, time-varying, and multiple-input multiple-output systems. The time-domain or state-space approach addresses these limitations by utilizing state variables to construct simultaneous, first-order differential equations, known as state equations, for an nth-order system.
Consider an RLC circuit, a...

Linear Approximation in Time Domain

Linear Approximation in Time Domain

Nonlinear systems often require sophisticated approaches for accurate modeling and analysis, with state-space representation being particularly effective. This method is especially useful for systems where variables and parameters vary with time or operating conditions, such as in a simple pendulum or a translational mechanical system with nonlinear springs.
For a simple pendulum with a mass evenly distributed along its length and the center of mass located at half the pendulum's length, the...

Relation between Mathematical Equations and Block Diagrams

Relation between Mathematical Equations and Block Diagrams

In a spring-mass-damper system, the second-order differential equation describes the dynamic behavior of the system. When transformed into the Laplace domain under zero initial conditions, this equation can be effectively analyzed and manipulated. The transformation into the Laplace domain converts differential equations into algebraic equations, simplifying the process of isolating the output.

Second Order systems II

Second Order systems II

In an underdamped second-order system, where the damping ratio ζ is between 0 and 1, a unit-step input results in a transfer function that, when transformed using the inverse Laplace method, reveals the output response. The output exhibits a damped sinusoidal oscillation, and the difference between the input and output is termed the error signal. This error signal also demonstrates damped oscillatory behavior. Eventually, as the system reaches a steady state, the error diminishes to zero.
If ζ...

You might also read

Related Articles

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

Sort by

Same author

Detection of a novel bunyavirus associated with fever, thrombocytopenia and leukopenia syndrome in Henan Province, China, using real-time reverse transcription PCR.

Journal of medical microbiology·2013

Same author

Anorectal dysfunction following low anterior resection for rectal carcinoma: a comparison between handsewn and stapled anastomosis.

Colorectal disease : the official journal of the Association of Coloproctology of Great Britain and Ireland·2013

Same author

Construction and expression of antibody targeted plasminogen activator*

Enzyme and microbial technology·2000

Same author

Numerical studies on the dynamics of the globally coupled maps with sequential updating

Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics·2000

Same author

Coherent resonance in a one-way coupled system

Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics·2000

Same author

Titanium(IV) chloride and the amine-promoted baylis-hillman reaction

Organic letters·2000

Search research articles

Related Experiment Video

Updated: Jul 11, 2026

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids

Published on: December 4, 2017

Analytical systematic approximate method of a two-state dissipative system

Wang¹, Jiang, Wan

¹Department of Astronomy and Applied Physics, University of Science and Technology of China, Hefei, China.

Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

|October 14, 2000

Summary

This study investigates environmental changes and occupation probability in a dissipative two-state system. A novel approximate method offers microscopic insights into quantum tunneling dynamics.

More Related Videos

Single-Molecule Tracking Microscopy - A Tool for Determining the Diffusive States of Cytosolic Molecules

Single-Molecule Tracking Microscopy - A Tool for Determining the Diffusive States of Cytosolic Molecules

Published on: September 5, 2019

An Introduction to Processing, Fitting, and Interpreting Transient Absorption Data

An Introduction to Processing, Fitting, and Interpreting Transient Absorption Data

Published on: February 16, 2024

Related Experiment Videos

Last Updated: Jul 11, 2026

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids

Published on: December 4, 2017

Single-Molecule Tracking Microscopy - A Tool for Determining the Diffusive States of Cytosolic Molecules

Single-Molecule Tracking Microscopy - A Tool for Determining the Diffusive States of Cytosolic Molecules

Published on: September 5, 2019

An Introduction to Processing, Fitting, and Interpreting Transient Absorption Data

An Introduction to Processing, Fitting, and Interpreting Transient Absorption Data

Published on: February 16, 2024

Area of Science:

Quantum Mechanics
Statistical Physics
Condensed Matter Physics

Background:

Dissipative two-state systems are fundamental in quantum mechanics.
Understanding environmental interactions is crucial for predicting system behavior.
Tunneling dynamics govern transitions in quantum systems.

Purpose of the Study:

To investigate occupation probability in a dissipative two-state system.
To analyze environmental changes affecting the system.
To provide microscopic insights into system dynamics.

Main Methods:

A systematic approximate method was employed.
The study utilized a system state vector with clear physical interpretations.
This approach facilitates exploration of tunneling dynamics.

Main Results:

The research elucidates changes in occupation probability.
Environmental influences on the two-state system were quantified.
The method provides a detailed microscopic view of dynamical behaviors.

Conclusions:

The approximate method offers a powerful tool for analyzing dissipative quantum systems.
Microscopic insights into tunneling and environmental effects were achieved.
This work advances the understanding of quantum system dynamics.