Ron Buckmire

Personal

First Name: Ron
Last Name: Buckmire

Education

Degree: Ph.D.
Graduation Year: 1994

Degree: B.S.
Graduation Year: 1989

Degree: M.S.
Graduation Year: 1992

Summary

Associate Professor of Mathematics Occidental College

Biography

Birth place: Grenville, Grenada

Field: Computational aerodynamics, scientific computation

In three years Ron Buckmire earned a B.S. in mathematics degree from Rensselaer Polytechnic Institute (1989). He also holds both an M.S. (1992) and a Ph.D. (1994) from Rensselaer Polytechnic Institute in Applied Mathematics. He was Minority Scholar-In-Residence Postdoctoral Fellowship, Occidental College, 1994 to 1996.

When 18, Buckmire won the British Chess Championship. According to Bibuld's Blacklist, Ron Buckmire had a USCF chess rating higher than 2440. Though currently lower, he is a U.S. National Master, U.S. Senior Master and FIDE Master.

Dr. Buckmire is also famous for the creation of the Queer Resources Directory, which is the oldest and largest Internet online resource of information about gay/lesbian/bisexual/transgendered people, as well as AIDS and HIV.

From Ron Buckmire's web page:

RESEARCH INTERESTS

I am primarily interested in numerical analysis and applied mathematics. The title of the volume my first published paper appears in says it best: Math Is For Solving Problems(Editors Cook and Roytburd, SIAM, 1996).

My thesis work (under Julian D. Cole and Don W. Schwendeman) was in theoretical aerodynamics/ scientific computing. There I showed that it was possible to compute solutions of the Transonic Small Disturbance equations that in the case of flow around a slender body of revolution without fore-aft symmetry possessed vanishingly small shocks. This was a very tricky calculation because it involves trying to obtain the solution accurately as near as one can get to a rather nasty singularity. In 1998, I was invited to present these results at the 2nd Theoretical Fluid Mechanics meeting at the annual American Institute of Aeronautics and Astronautics conference. Along the way we stumbled upon an interesting way to discretize the radial derivatives in our partial differential equation. I later discovered that Professor Ron Mickens of Clark Atlanta University had been writing about these same kinds of "nonstandard finite difference" schemes for years.

I have always been interested in applying mathematics to unusual phenomena so when I had a sabbatical coming up in Spring 2000 I suggested to my colleague David Edwards that we come up with a new mathematical model for "how movies make money."

My latest work has been a return to nonstandard finite difference schemes, particularly Mickens discretizations of the radial operators in the cylindrical and spherical Laplacian operators.
A famous old problem, called the Bratu problem, is a nonlinear version of Helmholtz equation where the right hand side of
Laplacian u = - f is exponential. In cylindrical and planar coordinates there are known exact solutions to the Bratu problem, making it ideal for numerical benchmarking of a finite difference scheme.

Papers reviewed in MATH REVIEWS

  1. Buckmire, Ron Application of a Mickens finite-difference scheme to the cylindrical Bratu-Gelfand problemNumer. Methods Partial Differential Equations 20 (2004), no. 3, 327--337.
  2. Buckmire, Ron Investigations of nonstandard, Mickens-type, finite-difference schemes for singular boundary value problems in cylindrical or spherical coordinatesNumer. Methods Partial Differential Equations 19(2003), no. 3, 380--398.

NONSTANDARD FINITE DIFFERENCES

* Summer 2003 "Plasma Problem" (joint with R.E. Mickens)
* June 2003 Contributed Presentation, "Application of Mickens finite differences to single-variable Bratu problems," SIAM Annual Meeting, Montreal, Quebec, Canada
* June 2003 "On exact and numerical solutions to the one-dimensional planar Bratu problem"
* May  2003 "Application of a Mickens finite difference to the cylindrical Bratu-Gelfand problem"
* September 2002 "Investigations of Nonstandard, Mickens-type, Finite-Difference Schemes for Singular Boundary Value Problems in Cylindrical or Spherical Coordinates"
* July 1995 "A New Finite-Difference Scheme for Singular Differential Equations in Cylindrical or Spherical Coordinates"

MATHEMATICAL MODELLING

* October 2000 "A Differential Equation Model of North American Cinematic Box-Office Dynamics" (with David Edwards)
* Summer 2003 "A Revised Mathematical Model for Cinematic Box-Office Prediction"

COMPUTATIONAL AERODYNAMICS

* July 1994 The Design of Shock-Free Transonic Slender Bodies  (Ph.D. Thesis)
* July 1998  "On The Design of Shock-Free, Transonic Slender Bodies of Revolution" (AIAA Paper 98-2686)

GENDER, SEXUALITY and THE LAW

* May1997 "You Can't Get There From Here: The Impact of California's Proposition 209 on Same-Sex Marriage"

Lifetime

Year Born: 1968