Mark H. Holmes

Books

Project Web-Sites

Course Materials

A Few Awards

Larger Grants (as Project Director)

Hobbies, etc

Addresses, etc

Ranking of Mathematicians (New)

Professor
Ph.D. University of California, Los Angeles
Mathematical Biology, Perturbation Methods, Scientific Computing

Currently, I'm interested in the development and analysis of mathematical models for physiological systems. One topic of study is mechanoperception, that is, the study of how a living organism senses and then recognizes mechanical stimuli. The mechanoreceptors that I'm presently working on are from the auditory system, cells in connective tissue, and tactile receptors.

The mechanisms through which skin transduces tactile stimuli from a mechanical to neural signal are not understood. Therefore, the goal of my research is to construct a mathematical model that describes this process. This project involves the study of the non-linear deformation of skin, the dynamics of the receptor system, and the nonlinear diffusion associated with the electro-chemical processes in the nerve. In this project I work very closely with neurophysiologists at the University of Syracuse.

Another of my research areas concerns modeling the biological tissues found in joints (such as the knee). The models are based on multiphasic continuum theories that realistically account for the multiple constituents found in tissue.

Books

Introduction to Numerical Methods for Differential Equations, Springer-Verlag, 2006. Web page
Introduction to Perturbation Methods, Springer-Verlag, New York, 1995.: Table of Contents; Answers to Selected Exercises; Errata List: 2nd Printing, 1st Printing
Mixture Theories for the Mechanics of Biological Tissues, RPI Web Book, 1995. Info Page

Project Web-Sites

Project CSUMS

RTG coming soon (grant starts about Aug 15, 2007)

Project Links

A Few Awards

Guggenheim Fellow

Y.C. Fung Young Investigator Award (ASME)

2000 Premier Award for Excellence in Engineering Education Courseware

2001 ASME Curriculum Innovation Award

2002 Award for Innovative Excellence in Teaching, Learning and Technology

2002 Best Paper Award, 13th International Conference on College Teaching and Learning

2007 ICTCM Award for Excellence and Innovation with the Use of Technology in Collegiate Mathematics

2007 Rensselaer Trustee's Outstanding Teacher Award

Larger Grants (as Project Director)

"RTG: Research Training Group in Large-Scale Nonlinear Systems," with G. Kovacic, P. Kramer, Y. Lvov, and V. Roytburd, $1,272,000, National Science Foundation. Summary for first three years of grant.

"CSUMS: Computational Science Training in the Mathematical Sciences at Rensselaer," with I. Herron, G. Kovacic, P. Kramer, and V. Roytburd, $1,251,000, National Science Foundation. Summary for first three years of grant.

"Initiative for Vertical Integration of Research and Education in Applied Mathematics," with J. Flaherty, G. Kovacic, J. McLaughlin, and D. Schwendeman, $3,830,000, National Science Foundation. Summary for last two years of grant.

"Mathematics and its Applications in Engineering and Science: Building the Links," with W. Boyce, R. Spilker, K. Conner, and J. Wilson, $4,016,000, National Science Foundation.