Research Interests:

We work on applying mathematical ideas to problems in science and engineering. Our work may be broadly divided into the Biological and Physical, although there is often some overlap.

Specific Biological Areas of focus:
Our interests in biology are recent, and as a consequence somewhat desultory. A basic question is to understand "how things work" which leads naturally to physiology. We believe that a practical approach requires a comparative study of extremes in biology and offers many beautiful examples of the interconversion of matter, energy and information in non-equilibrium systems. Much recent activity in the field focuses on information: however, our own interests are at one natural interface between physical and biological systems that arises in the context of collective biophysical and biomechanical behavior over a range of scales, from O(nm) to a O(cm). Almost all our work in biology involves both theory and experiments, with the latter done both in our own lab and elsewhere through close collaboration.

Cellular and Developmental Physiology: Some of the questions that interest us are: How is cell shape determined? How does a cell move? How does it stick? Can one think about the cell as a material with evolving properties? Can one reconstitute aspects of the behavior of a cell using its parts? How do tissues form? change? What is the role of force in regulating the growth and shape of organs and organisms? We have few answers, but are working on sharpening our questions using a combination of experiments and theory.

Plant Physiology: The adaptations that plants and fungi have engineering through evolution are truly exquisite, from the ability to silently haul water to the top of a giant Sequoia to the myriad mechanisms for seed and spore dispersal, pollination, drought resistance etc. The adaptive designs seen raise a host of physical and physico-chemical questions, few of which seem to have been studied quantitatively either from an experimental or a theoretical perspective. Our preliminary studies are currently focused on aspects of movements in plants and fungi, using the specific to illustrate the general, and revolve around understanding passive and active mechanisms of water movements in these hydraulic engineering marvels.

Locomotion and Behavior: Our current focus involves aspects of biological and biomimetic locomotion, and thus involves both trying to understand gait and speed selection and transition in different modes of locomotion such as crawling, inch-worming, reptation, swimming and in building simple physical models to study these. An outstanding question in this regard is a theory of locomotion that couples the internal and external dynamics to sensory feedback.

Specific Physical Areas of focus:
In terms of more physical research areas, the behavior of matter at the mesoscopic/macroscopic scale is a theme of central interest, particularly in understanding how matter is shaped and how it flows. This leads naturally to questions of the organization and self-organization of matter in space and time as manifest in the rich range of patterns that surround us, from the ripples seen on the surface of a moving liquid to the dynamics of drapery, from the settling of yogurt under its weight to the cracking of drying mud, from the mechanics of plate subduction to the flow of sand on a beach. We use a combination of experiential, experimental, analytical and computational approaches to study these sometimes frivolous and sometimes serious (the difference is often not clear a priori!) questions with the aim (although it is only rarely realized!) of stripping the complexity of the underlying phenomenon to its minimal essence. Indeed a goal is thus to get at a qualitative understanding using quantitative methods.

Geometry and Elasticity: Characterizing the shape of a solid is inherently a geometrical problem in that one is interested in defining the distances, angles (and changes therein) of material points near and far, relative to each other. In the past, we have studied aspects of this problem in the context of the low-dimensional behavior of filaments and membranes in the context of their equilibrium, and nonequilibrium behavior to understand how these objects fold, wrinkle, and pattern often driven by simple packing constraints. The rich experimental phenomenology combined with the host of mathematical questions that these lead to have kept us occupied for longer than one might think. The contrast is self-evident in an experiment that is the result of many a failed calculation: how easy it is to crumple a piece of paper, and yet how hard it is to understand it! We continue to work on variants of these problems with applications to a range of problems, from origami to tectonics.

Natural and Artificial Microstructured Materials: The study of these materials cuts across the traditional boundaries of solids, fluids and gases. Theoretical and experimental approaches to these problems at a macroscopic level use a combination of ideas from continuum and statistical mechanics, physical chemistry and various simulation methods. We are interested in the simple properties of these complex materials with the goal of understanding their qualitative behaviors, manifest as their mechanical and transport properties, and their stability in the presence of external stimuli. A particular interest is the appearance and role of order and/or disorder in determining these properties. More recently, we have become interested in learning from Nature, i.e. in trying to understand the solutions that evolution has stumbled upon, in such instances as clever adhesion mechanisms, locomotory designs, and various self-organized and self-assembled material systems.

Interfaces: Interfaces and boundaries are distinguished by crises, chaos and creativity. Instabilities are often nucleated at boundaries, as are new phases, and interfaces often have a Janus-like life of their own, unable to completely forget one or the other material that they separate. Unusual capillary phenomena have been of long standing interest to us. We got started by thinking about flows that involve the deposition of thin films of liquid onto surfaces as a result of external forces associated with inertia, viscosity, gravity, for example in a horizontally rotating cylinder. We have also studied the unusual statics and dynamics of non-wetting droplets, and uncovered a solution in biology for making perfect non-wetting droplets have been used by insects for more than 200 million years as a means of keeping themselves and their environment clean. We continue to be interested in various applied aspects of non-wetting droplets in physiology and chemical physics. More recently, we have been looking at elastocapillarity, the physics of soft objects at fluid interfaces, revisiting the problem of capillary rise between soft sheets, the way in which particulate materials aggregate, break and buckle at interfaces, and how filaments fold, and self-pack themselves when placed at interfaces.

Selected Publications:

A. Upadhyaya, M. Baraban, J. Wong, P. Matsudaira, A. van Oudenaarden and L. Mahadevan (2008). Power-limited contraction dynamics of Vorticella convallaria: an ultrafast biological spring. Biophysical Journal 94: 265.

G. Charras, M. Coughlin, T. Mitchison and L. Mahadevan (2008). Life and times of a cellular bleb. Biophysical Journal 94: 1836.

P. Bendix, G. Koenderink, D. Cuvelier, Z. Dogic, B. Koeleman, W. Brieher, C. Field, L. Mahadevan and D. Weitz (2008). A quantitative analysis of contractility in active cytoskeletal protein networks. Biophysical Journal 94: 3126.

P. Hersen, M. McClean, L. Mahadevan, and S. Ramanathan (2008). Signal processing by HOG MAP kinase pathway. Proc. Natl. Acad. Sci. USA 105: 7165.