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College of Liberal Arts and Sciences | Mathematics

February 25, 2019 | 2:45 p.m. - 4:00 p.m.
Category: Lecture
Location: Faculty/Administration #1140 | Map
656 W. Kirby
Detroit, MI 48202
Cost: Free

Speaker: Chun Liu, Illinois Institute of Technology

Title: Thermal Effects in General Diffusion


(joint work with Francesco De Anna , Pei Liu and Hao Wu)

Almost all biological activities involve transport and distribution of ions and charged particles in complicated biological environments. The complicated coupling and competition between different ionic solutions in various biological environments give the intricate specificity and selectivity in these systems. These systems are often associated with complicated, but specific biological relevant special biological and chemical conditions, such as the high concentration of specific species in solutions, which make most of the “ideal” assumptions in classical and conventional approaches irrelevant or unsuitable in the studies of biological problems.

In the talk, I will explore the underlying mechanism governing various diffusion processes [4]. We will employ a general framework of energetic variational approaches, consisting of in particular, Onsager’s Maximum Dissipation Principles [1, 2, 3], and their specific applications in biology and physiology [5]. I will discuss several extended general diffusion systems motivated by the study of ion channels and ionic solutions in biological cells. In particular, I will focus on our recent results in studying the interactions between different species, the boundary effects [8] and in some cases, the thermal effects [6, 7].


[1] Rayleigh, L., previously John Strutt. Some General Theorems Relating to Vibrations. Pro- ceedings of the London Mathematical Society IV (1873) 357-368.

[2] Onsager, L. Reciprocal Relations in Irreversible Processes. II. Physical Review 38 (1931) 2265-2279.

[3] 458 Onsager, L. Reciprocal Relations in Irreversible Processes. I. Physical Review 37 (1931) 405-109.

[4] (with Arkadz Kirshtein and Mi-Ho Giga) Variational Modeling And Complex Fluids, Hand- book of Mathematical Analysis in Mechanics of Viscous Fluids, edited by Anton Novotny and Yoshikazu Giga, Springer (2018).

[5] (with Shixin Xu and Ping Sheng) An Energetic Variational Approach for Ion Transport. Communications on Mathematical Sciences, textbf12,(4) (2014) 779-789.

[6] (with Pei Liu and Simo Wu) Non-Isothermal Electrokinetics: Energetic Variational Approach, Communication in Mathematical Sciences, 16(5) (2018)1451-1463 .

[7] (with Francesco De Anna) Non-isothermal general Ericksen-Leslie system: derivation, analysis and thermodynamics consistency, Archive of Rational Mechanics and Analysis, 231(2) (2018) 637-717.

[8] (with Hao Wu) An Energetic Variational Approach for the Cahn-Hilliard Equation with Dynamic Boundary Conditions: Derivation and Analysis to appear in Archive of Rational Mechanics and Analysis (2018).

For more information about this event, please contact Department of Mathematics at 3135772479 or