Some current and some older projects



Here are some brief descriptions, links, and accompanying images for a number of my research projects.

A Guide to First-Passage Processes

The above link includes list of errata, exercises, and 3 book reviews (last updated Jan. 25, 2003).

My book, "A Guide to First-Passage Processes" was published by Cambridge University Press in August 2001. The cover illustration is given below. It is meant to illustrate first-passage in a finite interval where death awaits at one boundary and a restaurant date awaits at the other. Click on the title to get more information, including book reviews, list of errata, and exercises. Click here to view the table of contents.






Spatial pattern formation in A+B--->0

Spatial distribution of A (red) and B (blue) particles. Domain density profile for isotropic diffusion. Domain density profile for driven diffusion. Cartoon of A+B--->0 dissolution process with driven diffusion


Coarsening in Ising ferromagnets

Long-lived diagonal stripe configuration with periodic boundary conditions. Probability that configurations are still evolving versus time. A typical metastable state of the 3-d Ising model.
Metastable state of the Ising model on the Cayley tree.


Cooling of inelastic gases

Space-time snapshot of the particles.

Anomalous decay in asynchronous ballistic annihilation

Space-time diagram of A+A--->0 in one dimension when each particle equiprobably has a velocity +V or -V, as well as a superimposed diffusion with diffusion coefficient D.

Space-time snapshot of the particles.


"Golden" random walk

This is a symmetric random walk in one dimension in which the length of the nth step equal to g-n, where g=(1+sqrt(5))/2 is the golden ratio. The probability distribution of this process is shown below.

Probability distribution at resolution 64 bins. Probability distribution at resolution 256 bins. Probability distribution at resolution 1024 bins.



Ballistic Deposition at Glancing Angles

Snapshots of the evolution of a growing surface when particles are ballistically incident at angles of +7.125 or -7.125 degrees (arctan(1/8)) from the horizontal and stick irreversibly to the deposit upon first contact.

Snapshot after 2 million particles. Snapshot after 10 million particles. Snapshot after 50 million particles.



Distribution of Citations


Distribution of City Populations

Baseball Data


Sidney Redner <redner@bu.edu>
Last modified: Thu Nov 6 12:08:14 EST 2003