Our research direcions are summarized below. In each case, technical details can be found in the original research articles. (The reference numbers in the brackets correspond to the numbers of the articles in the list in the publications page.)
We developed highly sensitive methods for measuring small mechanical fluctuations and tiny pressures, and applied these techniques to problems in biological science. We recently used a non-invasive micro-opto-fluidic technique to measure the extremely small mechanical distensions and pressures in a microvessel [41,43]. The physical principle underlying this measurement can be summarized as follows : the flow exerts pressure upon the confining walls of the microchannel (microvessel), which are compliant; the response of the walls, in turn, provides information about the flow itself. We are interested in extending this technique in order to characterize blood flow in arteries and smaller vessels, where flow-structure interactions are critical in determining functionality.
In another study , we used an optical measurement technique to detect the tiny mechanical oscillations of a microcantilever with bacteria adhered to its surface (figure). Without bacteria, only thermal fluctuations excited the cantilever motion. We used surface chemistry to attach live Escherichia coli to the microcantilever. The added noise by the bacteria was significantly above the thermal fluctuations and allowed us to monitor the small colony's reactions to various stimuli in real time. The response to administered antibiotics was particularly interesting from an applications perspective: when the antibiotic was effective, the bacteria died and the bacterial fluctuations subsided. This approach could allow for rapidly determining the susceptibility of bacteria to various antibiotics. Currently used methods of assessing the antibiotic susceptibility of bacteria involves culturing bacteria in administered antibiotics and waiting up to a day for the results. We are currently continuing this line of research.
Newtonian fluid dynamics, which describes everyday macroscopic flows, is accurate when the length and time scales of the flow are large. At this limit, one can in principle solve the Navier-Stokes equations subject to boundary conditions and obtain the desired flow field. Fluid flows in or around modern nanodevices, however, can attain extreme parameters , and the Navier-Stokes equations eventually break down. The failure of the Navier-Stokes equations can take place via different physical mechanisms: for instance, the continuum hypothesis may break down due to a size effect; or the local equilibrium may be violated due to the high rate of strain. In this body of work, we explore experimentally , theoretically  and numerically  how the Navier-Stokes equations break down, leading to the limit of nanofluidics. We formulate the problem in terms of the dimensionless Knudsen (Kn) and Weissenberg (Wi) numbers. When both Kn and Wi are small, the Newtonian fluid dynamics is recovered; when either or both approach one, a kinetic description of the flow becomes more appropriate. Our experiments are based on micro- and nanomechanical resonators oscillating in a near-ideal gas . By independently tuning the linear dimensions and the frequencies of the resonators, we experimentally cover the limits 0 < Kn < ∞ and 0 < Wi < ∞. All our experimental data, regardless of the specifics, can be collapsed using our theory (figure). In currently active projects, we are exploring the effects of the surface structure and composition of the resonator on the accommodation of gases. We are also pushing the limits of nanofluidics in water .
Transition to turbulence is a very complicated problem that has attracted a great deal of attention from the scientific community since the time of O. Reynolds. Much of the past work has focused on idealized situations, where a perfect channel flow is perturbed by well-controlled disturbances (either at the inlet or by mid-stream jets, etc.). In contrast, we performed experiments  in an imperfect channel by choice; we further added artificial inlet noise to see how the transitional flow evolved. We measured the near-wall fluctuations using an ultrasensitive mechanical technique based upon a microcantilever sensor (figure inset). Our observations were quite surprising and pointed to two very different paths to turbulence: In the first with no inlet perturbations, wall effects led to an extremely intermittent transitional flow. In the second, the inlet noise gave rise to a less intermittent and homogeneous-like turbulence. Surprisingly, however, we were able to find similarities between these seemingly different flows when we treated the effects of noise properly (figure). Our theoretical analysis, based upon the Landau theory of transition, culminated in a simple but remarkable result . The noise, regardless of its origin, regularized the Landau singularity of the relaxation time and made transitions driven by different noise sources appear similar. We believe that these fundamental experimental and theoretical results will have significant downstream applications. For instance, the possibility of modulating and increasing wall bursts by inlet perturbations may increase heat and mass transfer by orders of magnitude in transitional flows in the arteries, chemical reactors, and so on.
Nanomechanics and NEMS:
One of the central themes in our research is the development of transducers for nanomechanical resonators or NEMS . This is challenging for both electronic and optical transducers: For most electronic transducers (e.g., capacitive transducers) in the NEMS domain, the motional modulation of the impedance becomes very small while parasitic embedding impedances become very large. Free-space optical techniques (e.g., optical interferometry) in small structures are limited by the diffraction of light. Up to date, we have successfully adapted capacitive detection to NEMS by using careful impedance matching . We have also had some success with free-space optical techniques, ranging from interferometry [16, 24] to optical knife edge technique . Recently, we have started developing near field optical transducers to read-out arrays of NEMS . We are also looking at possibilities of coupling NEMS to optical cavities in order to enhance the detection sensitivity and study cavity opto-mechanics .
We are also interested in fundamental processes in nanomechanics. These include fluctuations and dissipation at the nanoscale. We are interested in exploring the dissipation in a nanomechanical resonator in order to distinguish between different dissipation scales and processes. Another recent direction is the study of interactions between resonators coupled by a variety of mutual forces, including optical and surface forces .
Radio-frequency Scanning Tunneling Microscopy (RF-STM):
The scanning tunneling microscope (STM) is a ubiquitous tool in nanoscience. In the 25-year period since its invention, the STM has helped uncover a wealth of phenomena in diverse physical systems, ranging from semiconductors to superconductors to atomic and molecular nanosystems. A major limitation of existing STMs is the 1 ms range time resolution. This is due to the high tip-sample tunnel impedance combined with instrumentation capacitance (cables and amplifiers), which results in an audio-frequency low-pass filter. The fundamental bandwidth limit in STM is in the 1 ns -100 ps range. In order to improve the STM bandwidth, we have used an impedance transformation with a high frequency resonant circuit . Our simple modification to an existing STM head is shown in the figure: the three inductors (coils) resonate with the chip capacitance and provide access to the tunnel resistance. We have demonstrated three applications of the RF-STM technique. First, we have obtained STM images at high scan rates. Second, we have shown that fast thermometry is possible by measuring the high frequency noise of the tunneling electrons. Third, we have detected radio-frequency nanomechanical motion with very high sensitivity.