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

Classification of Systems-I

Classification of Systems-I

Linearity is a system property characterized by a direct input-output relationship, combining homogeneity and additivity.
Homogeneity dictates that if an input x(t) is multiplied by a constant c, the output y(t) is multiplied by the same constant. Mathematically, this is expressed as:

Entropy

Entropy

Salt particles that have dissolved in water never spontaneously come back together in solution to reform solid particles. Moreover, a gas that has expanded in a vacuum remains dispersed and never spontaneously reassembles. The unidirectional nature of these phenomena is the result of a thermodynamic state function called entropy (S). Entropy is the measure of the extent to which the energy is dispersed throughout a system, or in other words, it is proportional to the degree of disorder of a...

Entropy

Entropy

The first law of thermodynamics is quantitatively formulated via an equation relating the internal energy of a system, the heat exchanged by it, and the work done on it. A quantitative formulation of the second law of thermodynamics leads to defining a state function, the entropy.
When an ideal gas expands isothermally, the disorder in the gas increases. From the molecular perspective, the gas molecules have more volume to move around in.
Consider an infinitesimal step in the expansion, which...

Second Law of Thermodynamics

Second Law of Thermodynamics

In the quest to identify a property that may reliably predict the spontaneity of a process, a promising candidate has been identified: entropy. Processes that involve an increase in entropy of the system (ΔS > 0) are very often spontaneous; however, examples to the contrary are plentiful. By expanding consideration of entropy changes to include the surroundings, a significant conclusion regarding the relation between this property and spontaneity may be reached. In thermodynamic models, the...

Second Law of Thermodynamics

Second Law of Thermodynamics

The Second Law of Thermodynamics states that entropy, or the amount of disorder in a system, increases each time energy is transferred or transformed. Each energy transfer results in a certain amount of energy that is lost—usually in the form of heat—that increases the disorder of the surroundings. This can also be demonstrated in a classic food web. Herbivores harvest chemical energy from plants and release heat and carbon dioxide into the environment. Carnivores harvest the...

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....

You might also read

Related Articles

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

Sort by

Same author

Three Cases of Gun-Shot Wound of Bladder.

Buffalo medical and surgical journal·2023

Same author

Seven Cases of Aphonia.

Buffalo medical and surgical journal·2023

Same author

Cases Occurring at Union Chapel Hospital, Washington, D. C., 1862.

Buffalo medical and surgical journal·2023

Same author

Cases Occurring at Union Chapel Hospital 1862.

Buffalo medical and surgical journal·2023

Same author

Spontaneous Perforation of the Stomach.

Buffalo medical and surgical journal·2023

Same author

Correspondence.

Buffalo medical and surgical journal·2023

Search research articles

Related Experiment Video

Updated: Dec 18, 2025

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

Local Theory of Disordered Systems.

W H Butler¹, W Kohn¹

¹Department of Physics, University of California, San Diego, La Jolla, California.

Journal of Research of the National Bureau of Standards. Section A, Physics and Chemistry

|June 12, 2020

Summary

This summary is machine-generated.

This study introduces a new method for analyzing disordered systems by averaging microscopic properties. This approach offers exponentially small errors, making it practical for studying highly disordered materials.

Keywords:

Binary alloys density of states disordered systems periodically continued neighborhood

More Related Videos

Excitonic Hamiltonians for Calculating Optical Absorption Spectra and Optoelectronic Properties of Molecular Aggregates and Solids

Excitonic Hamiltonians for Calculating Optical Absorption Spectra and Optoelectronic Properties of Molecular Aggregates and Solids

Published on: May 27, 2020

Fabrication and Characterization of Disordered Polymer Optical Fibers for Transverse Anderson Localization of Light

Fabrication and Characterization of Disordered Polymer Optical Fibers for Transverse Anderson Localization of Light

Published on: July 29, 2013

Related Experiment Videos

Last Updated: Dec 18, 2025

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

Excitonic Hamiltonians for Calculating Optical Absorption Spectra and Optoelectronic Properties of Molecular Aggregates and Solids

Excitonic Hamiltonians for Calculating Optical Absorption Spectra and Optoelectronic Properties of Molecular Aggregates and Solids

Published on: May 27, 2020

Fabrication and Characterization of Disordered Polymer Optical Fibers for Transverse Anderson Localization of Light

Fabrication and Characterization of Disordered Polymer Optical Fibers for Transverse Anderson Localization of Light

Published on: July 29, 2013

Area of Science:

Condensed Matter Physics
Materials Science
Computational Physics

Background:

Crystalline solids exhibit periodicity, naturally described in momentum space.
Disordered systems lack periodicity, making momentum space descriptions less intuitive.
Physical properties in disordered systems become localized, suggesting neighborhood-based analysis.

Purpose of the Study:

To develop a theoretical framework for analyzing macroscopic disordered systems using microscopic averages.
To investigate the electronic density of states in noninteracting electrons scattered by disordered centers.
To address and overcome inherent errors in neighborhood averaging methods.

Main Methods:

Averaging properties over small microscopic neighborhoods in coordinate space.
Focusing on noninteracting electrons in a field of disordered scattering centers.
Employing statistical mechanics for scatterers and periodic repetition of neighborhoods to control errors.

Main Results:

Identified two classes of errors (d/L and 1/N) that are too large for practical use.
Developed a method to avoid these errors through advanced statistical mechanics and periodic repetition.
Achieved exponentially small remaining errors, dependent on the ratio of neighborhood size to characteristic lengths (e.g., mean free path).

Conclusions:

The small neighborhood averaging theory provides a practical and accurate method for studying disordered systems.
The exponential convergence makes this approach particularly useful for highly disordered materials.
Numerical examples demonstrate the validity and applicability of the developed method.