This volume is a result of a special session at the AMS Fall Southeastern Sec-
tional Meeting, which was held at Tulane University in New Orleans, LA, October,
2012. That special session was focused on simulating the motion of an incompress-
ible fluid driven by flexible immersed structures. Active biological tissue is typically
constructed of fibers that are surrounded by fluid; the fibers not only hold the tissue
together but also transmit forces that ultimately result in fluid motion. In other
cases, the fluid may flow through flexible conduits such as blood vessels or airways
that both react to and affect the fluid dynamics. Additional examples arise in the
context of external fluid flows in biological and engineering applications, such as the
dynamics of insect wings, flagellated or ciliated organisms, suspensions of blood cells
and other synthetic particles. In addition to solving biologically motivated ques-
tions, there is tremendous interest in the development and application of advanced
computational techniques to solve these fluid-structure interaction problems.
Given the widespread interest among mathematicians, biologists, and engineers
in fluid-structure interaction problems, we believe that this volume is both timely
and valuable; this is particularly true because of recent algorithmic improvements.
The focus of this volume will be on three main themes: (i) formulation and analy-
sis of mathematical equations that describe fluid-structure interactions in biological
systems, (ii) algorithmic and computational issues related to increasing accuracy
and efficiency through use of adaptivity, time-stepping scheme, and regularization,
and (iii) applications to problems in biological and physical sciences, and interpre-
tation of model results.
This volume is organized as follows. It begins with two review articles that dis-
cuss the numerical and computational aspects of fluid-structure interaction prob-
lems. Specifically, these articles focus on the mathematical equations describing
the fluid and structure, as well they describe state of the art computational ap-
proaches to solve the coupled system of equations. Next are original articles that
study small-scale fluid motion driven by cilia and flagella. Biological questions are
addressed in terms of transport of fluid as well as the development and extension
of new numerical methods. Also included are articles that consider a wide vari-
ety of physiological examples, including peristalsis, platelet adhesion and cohesion,
upside-down jellyfish, and dynamics in the rat kidney.
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