Related Experiment Video
Updated: Mar 28, 2026
08:01
The Diffusion of Passive Tracers in Laminar Shear Flow
Published on: May 1, 2018
9.1K
First-Passage Times in d-Dimensional Heterogeneous Media
G Vaccario1, C Antoine1, J Talbot1
1Laboratoire de Physique Théorique de la Matiére Condensée, UPMC, CNRS UMR 7600, Sorbonne Universités, 4, Place Jussieu, 75252 Paris, Cedex 05, France.
Physical Review Letters
|December 27, 2015
Summary
This study reveals that the interpretation convention for diffusion models significantly impacts mean first-passage time (MFPT) calculations in heterogeneous environments. Different conventions yield distinct residence times, crucial for understanding diffusion in biological systems.
Area of Science:
- Statistical Physics
- Chemical Physics
- Biophysics
Background:
- Theoretical studies of mean first-passage time (MFPT) often overlook diffusive heterogeneity.
- Real-world systems exhibit complex diffusion patterns not captured by simplified models.
Purpose of the Study:
- To derive exact analytical expressions for MFPT and residence times in heterogeneous diffusion systems.
- To investigate the impact of different interpretational conventions (Itō, Stratonovich, isothermal) on diffusion dynamics.
Main Methods:
- Developed exact analytical expressions for MFPT and residence times.
- Modeled a spherically symmetric d-dimensional heterogeneous system with two concentric media.
- Incorporated different diffusion coefficients, an absorbing inner boundary, and a reflecting outer boundary.
Main Results:
- The choice of convention for the overdamped Langevin equation with multiplicative noise affects predictions for residence times and MFPT.
- Residence time in the outer region and MFPT are convention-dependent.
- Residence time in the inner region remains independent of the chosen convention.
Conclusions:
- The convention dependence of residence times and MFPT offers new insights into heterogeneous diffusion processes.
- Findings are relevant for understanding diffusion in biological contexts like cells, tumors, and animal foraging ranges.
Related Concept Videos
01:05Collisions in Multiple Dimensions: Introduction
7.3K
It is far more common for collisions to occur in two dimensions; that is, the initial velocity vectors are neither parallel nor antiparallel to each other. Let's see what complications arise from this. The first idea is that momentum is a vector. Like all vectors, it can be expressed as a sum of perpendicular components (usually, though not always, an x-component and a y-component, and a z-component if necessary). Thus, when the statement of conservation of momentum is written for a...
7.3K
01:18Uniform Depth Channel Flow: Problem Solving
610
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...
610
01:11Relative Velocity in Two Dimensions
9.3K
Relative velocity is the velocity of an object as observed from a particular reference frame, or the velocity of one reference frame with respect to another reference frame. The concept of relative velocity can be used to describe motion in two dimensions. Consider a particle P and two reference frames S and S′. The position of the origin of S′ as measured in S is , the position of P as measured in S′ is , and the position of P as measured in S is , which can be evaluated by utilizing...
9.3K
01:10First Law: Particles in One-dimensional Equilibrium
8.5K
Newton's first law of motion states that a body at rest remains at rest, or if in motion, remains in motion at constant velocity, unless acted on by a net external force. It also states that there must be a cause for any change in velocity (a change in either magnitude or direction) to occur. This cause is a net external force. For example, consider what happens to an object sliding along a rough horizontal surface. The object quickly grinds to a halt, due to the net force of friction. If...
8.5K
01:10Relative Velocity in One Dimension
11.2K
The understanding of the concept of reference frames is essential to discuss relative motion in one or more dimensions. When we say that an object has a certain velocity, we must state the velocity with respect to a given reference frame. In most examples, this reference frame has been Earth. For instance, if a statement reads that a person is sitting in a train moving at 10 m/s east, then it implies that the person on the train is moving relative to the surface of Earth at this velocity,...
11.2K
01:18First Law: Particles in Two-dimensional Equilibrium
16.9K
Recall that a particle in equilibrium is one for which the external forces are balanced. Static equilibrium involves objects at rest, and dynamic equilibrium involves objects in motion without acceleration; but it is important to remember that these conditions are relative. For instance, an object may be at rest when viewed from one frame of reference, but that same object would appear to be in motion when viewed by someone moving at a constant velocity.
Newton's first law tells us about...
Newton's first law tells us about...
16.9K