Related Experiment Video
Updated: Sep 22, 2025
11:03
An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids
Published on: December 4, 2017
8.6K
Stochastic telegrapher's approach for solving the random Boltzmann-Lorentz gas.
Manuel O Cáceres1,2, Marco Nizama3
1Comision Nacional de Energia Atomica, Centro Atomico Bariloche and Instituto Balseiro, Universidad Nacional de Cuyo, Av. E. Bustillo 9500, CP8400, Bariloche, Argentina.
Physical Review. E
|May 20, 2022
Summary
The Boltzmann-Lorentz gas with disordered scattering centers is analyzed using stochastic telegrapher's equations. Time-fluctuations can delay diffusion, extending ballistic dynamics and offering insights into biophysical models.
Area of Science:
- Statistical Mechanics
- Nonlinear Dynamics
- Mathematical Physics
Background:
- The Boltzmann-Lorentz equation models gases with disordered scattering.
- Stochastic hyperbolic equations offer alternative analytical frameworks.
- Disordered systems present challenges in predicting transport phenomena.
Purpose of the Study:
- To analyze the 1D random Boltzmann-Lorentz equation using stochastic telegrapher's equations.
- To derive exact analytical results for transport properties under global binary disorder.
- To investigate the impact of time-fluctuations on diffusive behavior and characterize statistical properties.
Main Methods:
- Transformation of the Boltzmann-Lorentz gas model into stochastic telegrapher's equations.
- Exact analytical derivation of the second moment, velocity autocorrelation function, and self-diffusion coefficient.
- Analysis of time-fluctuations in energy loss and space probability distribution.
Main Results:
- Exact analytical results obtained for transport properties under Markovian and non-Markovian disorder.
- Demonstration that time-fluctuations delay the diffusive regime via a timescale t_c, prolonging ballistic dynamics.
- Identification of the mean value of a stochastic telegrapher's Fourier mode as a key statistical descriptor.
Conclusions:
- The study successfully links the Boltzmann-Lorentz gas to stochastic telegrapher's equations, providing analytical solutions.
- Time-fluctuations significantly influence transport dynamics, delaying diffusion and extending ballistic transport.
- The findings have potential applications in biophysics, particularly for run-and-tumble models with fluctuating parameters.
Related Concept Videos
01:20Maxwell-Boltzmann Distribution: Problem Solving
1.8K
Individual molecules in a gas move in random directions, but a gas containing numerous molecules has a predictable distribution of molecular speeds, which is known as the Maxwell-Boltzmann distribution, f(v).
This distribution function f(v) is defined by saying that the expected number N (v1,v2) of particles with speeds between v1 and v2 is given by
This distribution function f(v) is defined by saying that the expected number N (v1,v2) of particles with speeds between v1 and v2 is given by
1.8K
01:27Distribution of Molecular Speeds
4.2K
The motion of molecules in a gas is random in magnitude and direction for individual molecules, but a gas of many molecules has a predictable distribution of molecular speeds. This predictable distribution of molecular speeds is known as the Maxwell-Boltzmann distribution. The distribution of molecular speeds in liquids is comparable to that of gases but not identical and can help to understand the phenomenon of the boiling and vapor pressure of a liquid. Consider that a molecule requires a...
4.2K
01:22Mean free path and Mean free time
4.1K
Consider the gas molecules in a cylinder. They move in a random motion as they collide with each other and change speed and direction. The average of all the path lengths between collisions is known as the "mean free path."
4.1K
02:39Entropy
31.5K
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...
31.5K
03:07Kinetic Molecular Theory: Molecular Velocities, Temperature, and Kinetic Energy
28.2K
The kinetic molecular theory qualitatively explains the behaviors described by the various gas laws. The postulates of this theory may be applied in a more quantitative fashion to derive these individual laws.
28.2K
01:10Van der Waals Equation
4.6K
The ideal gas law is an approximation that works well at high temperatures and low pressures. The van der Waals equation of state (named after the Dutch physicist Johannes van der Waals, 1837−1923) improves it by considering two factors.
First, the attractive forces between molecules, which are stronger at higher densities and reduce the pressure, are considered by adding to the pressure a term equal to the square of the molar density multiplied by a positive coefficient a. Second, the volume...
First, the attractive forces between molecules, which are stronger at higher densities and reduce the pressure, are considered by adding to the pressure a term equal to the square of the molar density multiplied by a positive coefficient a. Second, the volume...
4.6K