Related Experiment Video
Updated: May 30, 2026
10:32
Image-based Lagrangian Particle Tracking in Bed-load Experiments
Published on: July 20, 2017
Smoothly varying hopping rates in driven flow with exclusion
R B Stinchcombe1, S L A de Queiroz
1Rudolf Peierls Centre for Theoretical Physics, University of Oxford, Oxford, United Kingdom. r.stinchcombe1@physics.ox.ac.uk
Summary
This study analyzes the one-dimensional totally asymmetric simple exclusion process (TASEP) with varying hopping rates. Theoretical predictions for density profiles and currents were confirmed by numerical simulations.
Area of Science:
- Statistical Mechanics
- Condensed Matter Physics
- Non-equilibrium Systems
Background:
- The totally asymmetric simple exclusion process (TASEP) is a fundamental model in statistical mechanics.
- Understanding TASEP with position-dependent rates is crucial for modeling complex systems.
- Previous studies often focused on uniform rates, limiting applicability.
Purpose of the Study:
- To theoretically solve the one-dimensional TASEP with position-dependent hopping rates.
- To investigate the impact of smooth spatial rate variations on system dynamics.
- To validate theoretical predictions through numerical simulations.
Main Methods:
- Mean-field adiabatic approximation for theoretical analysis.
- Numerical simulations for systems with linear hopping rate gradients.
- Analysis of both periodic and open-boundary conditions.
Main Results:
- The study provides an analytical solution for TASEP with general smooth spatial rate variations.
- Numerical simulations confirm theoretical predictions for steady-state average density profiles and currents.
- Accurate prediction of open-system phase boundaries was achieved.
Conclusions:
- The mean-field adiabatic approximation is effective for TASEP with position-dependent rates.
- Spatial variation in hopping rates significantly influences TASEP dynamics.
- The model accurately describes phenomena like density profiles and phase transitions.
Related Concept Videos
01:29Gradually Varying Flow
Gradually varying flow (GVF) in open channels describes situations where water depth changes slowly along the channel due to factors like non-uniform bed slope, channel shape variations, or obstructions. This flow type occurs when the depth adjusts gradually to balance gravitational forces, shear forces, and energy requirements, resulting in a low rate of depth change.Characteristics of Gradually Varying FlowGVF is commonly observed in natural streams, rivers, and canals, where flow depth...
01:24Rapidly Varying Flow
Rapidly varying flow (RVF) in open channels is characterized by abrupt changes in flow depth over a short distance, with the rate of depth change relative to distance often approaching unity. These flows are inherently complex due to their transient and multi-dimensional nature, making exact analysis difficult. However, approximate solutions using simplified models provide valuable insights into their behavior.Key Features of Rapidly Varying FlowRVF is commonly observed in scenarios involving...
01:27Steady Flow of a Fluid Stream
Consider a control volume, such as a pipe with solid boundaries, through which fluid flows and changes direction due to the impulse exerted by the resulting force from the pipe walls. In steady flow, the mass of fluid entering the control volume at a given time, t, with velocity v1, is equal to the mass leaving after infinitesimal time dt, with velocity v2.
During this process, the momentum of the fluid within the control volume remains constant over the time interval dt. By applying the...
During this process, the momentum of the fluid within the control volume remains constant over the time interval dt. By applying the...
01:18Uniform Depth Channel Flow: Problem Solving
To calculate the flow rate for a trapezoidal channel, first, identify the bottom width, side slope, and flow depth of the channel. The cross-sectional area (A) corresponding to the depth of flow (y), channel bottom width (B), and side slope (θ) is determined by:Next, calculate the wetted perimeter, which includes the bottom width and the sloped side lengths in contact with the water. Using the values of the cross-sectional area and the wetted perimeter, determine the hydraulic radius by...
01:30Bernoulli's Equation for Flow Along a Streamline
Bernoulli's equation relates the energy conservation in a fluid moving along a streamline. The equation applies to incompressible and inviscid fluids under steady flow. For such a flow, Newton's second law is applied to a small fluid element, which experiences forces due to pressure differences, gravity, and velocity variations. The force balance leads to the following form of Bernoulli's equation:
01:17Steady, Laminar Flow Between Parallel Plates
Understanding steady, laminar flow between parallel plates is essential for analyzing and designing flow in narrow rectangular channels, commonly found in various water conveyance and drainage systems. The Navier-Stokes equations govern fluid motion and are generally challenging to solve due to their nonlinearity. However, simplifications are possible in certain cases, like the steady laminar flow between parallel plates. For this scenario, we assume steady, incompressible, laminar flow.