Constitutive relations in Fractional Mechanics

Abstract

For simple material media, which are linear, homogeneous, time

invariant, and isotropic, constitutive laws involve macroscopic

parameters that are constant. Examples are Hooke’s law in linear

elasticity or Ohm’s law in electrostatics. In this talk, we are

interested in media such as human tissue and fractured porous media,

where the propagation phenomena are more complex.  These media can be lossy or fractal, and we shall make a case for using constitutive

relations involving fractional derivatives as a better model and fit

for data.

Bio:

I obtained my PhD in Mathematics from the University of Minnesota in

1995. I have been a researcher at CIMAT since 1996 and a member of the National System of Researchers in Physics, Mathematics, and Earth

Sciences. I do research in Differential Equations, Functional Analysis,

Numerical Methods, and Fractional Mechanics. I have been a visiting professor at the international and national level:

CIMNE Barcelona Spain;

GM-LMI INSA Rouen France;

Chemical and Petroleum Engineering Department, University of Calgary Canada;

CICESE;

University of Guadalajara.

I have been the PI in charge of several multidisciplinary projects and

mathematical modeling on behalf of CIMAT, highlighting the following: Partial Differential Equations Related to Waves and Inverse Problems:

applications to physics, biology, and clean energy.  ECOS 2015

Air injection to the reservoir as an enhanced recovery system.

CONACYT-SENER-HIDROCARBUROS 2009-01.

I have developed specialized consulting projects for companies such as

Condumex, Pemex Exploration and Production, Corporación Industrial

Uruapan. I have directed several undergraduate and graduate theses in

Mathematics, Computer Science, and Engineering. I regularly teach courses in Differential Equations, Mathematical Analysis, and Numerical Methods. In outreach, I have organized national and international workshops and conferences in Differential Equations and Numerical Methods. Special mention, the School of Modeling and Numerical Methods, organized at CIMAT since 2006.