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Office:
Stratton Hall, 108
Phone: +1-508-831-5241
Fax: +1-508-831-5824
vernescu@wpi.edu

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Bogdan M. Vernescu

Combining theory with practice in educating students is at the core of WPI's philosophy. I find great pleasure in working with undergraduates and graduate students at the interface between mathematical theory and its applications.

My research has been mainly focused on using mathematical techniques for modeling multiscale phenomena, with an emphasis on the multiscale mechanics of heterogeneous materials. Whether natural (e.g., rocks, bones, tissues, muscles), or man-made (e.g., composite materials, ceramics, emulsions, electrorheological or magnetorheological materials), heterogeneous materials exhibit several scales in space and/or in time, caused by the inhomogeneities, or by the complexity of the mechanical processes. A major question is the derivation of the macroscale (effective) properties of the heterogeneous material as a function of the properties of the constituents and of the local geometry; an "averaging" over the microscales yields the macroscopic constitutive behavior. The associated partial differential equations, have highly oscillating coefficients, and this averaging translates into the convergence of the solutions.

Research Interests

  • Partial Differential Equations
  • Homogenization
  • Calculus of Variations
  • Fluid/Solid Mechanics

Education

  • BS/MS, University of Bucharest, Romania, 1982
  • PhD, Institute of Mathematics, Romania, 1989

Featured Publications

  • C. C. Mei and B. Vernescu, Homogenization Methods for Multiscale Mechanics, World Scientific Publishing Co., 2010.
  • B. S. Tilley, B. Vernescu and J. Plummer, Geometry-Driven Charge Accumulation in Electrokinetic Flows between Thin, Closely Spaced Laminates, SIAM J. Appl. Math. 72, 1 (2012) pp. 39-60.
  • F. Maris, B. Vernescu, Effective leak conditions across a membrane, Complex Variables and Elliptic Equations, 57, 2-4 (2012) pp. 437-453.
  • D. Onofrei and B. Vernescu, Error Estimates for Periodic Homogenization with Non-smooth Coefficients, Asymptotic Analysis, 54, (2007) 103-123.
  • B. Vernescu, Multiple-scale Analysis of Electrorheological Fluids, International Journal of Modern Physics B, 16, 17-18, (2002), 2643-2648.

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Professional Highlights

  • President, National Professional Science Master's Association, 2007-2008, 2012
  • Honorary Member, Institute of Mathematics, Romanian Academy, 2005
  • Visiting Professor, Universities of Rouen, Nancy, Chambery, and Metz, France
  • Visiting Associate Professor, MIT, 1998
 
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