# Correlation function induced by a generalized diffusion equation with the presence of a harmonic potential

## Abstract

An integro-differential diffusion equation with linear force, based on the continuous time random walk model, is considered. The equation generalizes the ordinary and fractional diffusion equations, which includes short, intermediate and long-time memory effects described by the waiting time probability density function. Analytical expression for the correlation function is obtained and analyzed, which can be used to describe, for instance, internal motions of proteins. The result shows that the generalized diffusion equation has a broad application and it may be used to describe different kinds of systems. - Highlights: • Calculation of the correlation function. • The correlation function is connected to the survival probability. • The model can be applied to the internal dynamics of proteins.

- Authors:

- Publication Date:

- OSTI Identifier:
- 22447591

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Annals of Physics; Journal Volume: 353; Other Information: Copyright (c) 2014 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; CORRELATION FUNCTIONS; DIFFUSION; DIFFUSION EQUATIONS; GRAPH THEORY; HARMONIC POTENTIAL; PROBABILITY; PROBABILITY DENSITY FUNCTIONS; PROTEINS; RANDOMNESS

### Citation Formats

```
Fa, Kwok Sau, E-mail: kwok@dfi.uem.br.
```*Correlation function induced by a generalized diffusion equation with the presence of a harmonic potential*. United States: N. p., 2015.
Web. doi:10.1016/J.AOP.2014.11.013.

```
Fa, Kwok Sau, E-mail: kwok@dfi.uem.br.
```*Correlation function induced by a generalized diffusion equation with the presence of a harmonic potential*. United States. doi:10.1016/J.AOP.2014.11.013.

```
Fa, Kwok Sau, E-mail: kwok@dfi.uem.br. Sun .
"Correlation function induced by a generalized diffusion equation with the presence of a harmonic potential". United States.
doi:10.1016/J.AOP.2014.11.013.
```

```
@article{osti_22447591,
```

title = {Correlation function induced by a generalized diffusion equation with the presence of a harmonic potential},

author = {Fa, Kwok Sau, E-mail: kwok@dfi.uem.br},

abstractNote = {An integro-differential diffusion equation with linear force, based on the continuous time random walk model, is considered. The equation generalizes the ordinary and fractional diffusion equations, which includes short, intermediate and long-time memory effects described by the waiting time probability density function. Analytical expression for the correlation function is obtained and analyzed, which can be used to describe, for instance, internal motions of proteins. The result shows that the generalized diffusion equation has a broad application and it may be used to describe different kinds of systems. - Highlights: • Calculation of the correlation function. • The correlation function is connected to the survival probability. • The model can be applied to the internal dynamics of proteins.},

doi = {10.1016/J.AOP.2014.11.013},

journal = {Annals of Physics},

number = ,

volume = 353,

place = {United States},

year = {Sun Feb 15 00:00:00 EST 2015},

month = {Sun Feb 15 00:00:00 EST 2015}

}