Our research addresses fundamental issues that represent roadblocks in critical technologies towards engineering our physical environment. The members of our faculty lead dynamic research groups that are funded from diverse sources. The research is often interdisciplinary and projects range from focused individual focused to large centers of collaboration.
Actuation remains a significant challenge in soft robotics. Actuation by light has important advantages such as tether-free, minimum radio interference, and significant power transmission over long distance. The Bhattacharya group has built theoretical and numerical models for photomechanical actuation in photoactive materials. Combining statistical mechanics and continuum theory, photomechanical coupling is explored for photoactive nematic elastomers under both light illumination and mechanical stress. The microscopic information is further integrated to build a simple macroscopic modeling framework to study a series of examples. Of particular interest is the generation of cyclic or periodic motion under steady illumination, which emerges as a result of a coupling between light absorption and structure deformation. These photomechanical couplings from micro- to macro-scale can be exploited in new material design as well as utilizing structure instabilities to generate cyclic motion.
(a) Microscale photomechanical coupling in nematic elastomers (Bai, Bhattacharya, JMPS, 2020): actuation, domain formation, and energy landscape. (b) Crystallization in photomechanical semi-crystalline polymers under light illumination (Bai, Bhattacharya, et al., in preparation). (c)&(d) Macroscale coupling (Korner, Bhattacharya, et al., PNAS, 2020): flapping beam and rolling ring as cyclic motions under steady illumination.
High-density epidural spinal stimulation, uses sheet-like arrays of numerous electrodes to stimulate neurons. The goal of the system, is to stimulate the native standing and stepping control circuitry in the lower spinal cord so as to coordinate sensory-motor activity and partially replace the missing signals from the brain to the nerves. Using a combination of experimentation, computational models of the array and spinal cord, and machine-learning algorithms, Burdick and his colleagues are trying to optimize the stimulation pattern to achieve the best effects, and to improve the design of the electrode array.
A recent research interest for Professor Rosakis is Hypervelocity Impact. Hypervelocity impact is a rising concern in spacecraft missions where man-made debris in low Earth orbit (LEO) and meteoroids are capable of compromising or depleting the structural integrity of spacecraft. To address these concerns, the goal of current research is to experimentally investigate the underlying mechanisms responsible for deformation and damage evolution during hypervelocity impact utilizing Caltech/JPL's Small Particle Hypervelocity Impact Range (SPHIR) facility. By combining high speed photography, optical techniques, including Coherent Gradient Sensing (CGS) interferometry, the dynamic perforation behavior involving crater morphology, debris and ejecta formation and solid/fluid/plasma transitions and interactions have been examined.
Biomolecular Feedback Circuits for Modular, Robust and Rapid Response
We are working to develop a new class of feedback circuits that makes use of synthetic biological components to implement rapid response to input signals in a more robust and modular fashion. Our approach is to make use of biological processes that operate on timescales of seconds to minutes, primarily through feedback mechanisms using allosteric and covalent modifications that affect protein function. We are exploring the use of the modularity of protein domains to design circuit elements that can be reused more easily than existing components, and we will test our circuits across a variety of cellular contexts to assess robustness as a fundamental property of the design.
Block diagram of the proposed control architecture.
The (slow) transcriptional regulation is used to maintain an appro- priate concentration of protein whose activity can be modulated via a conformation change. An allosteric regulation mechanism is then used to produce an active protein (or protein complex) at a much faster timescale. The protein must both have the desired function (e.g., fluorescence) and allow a mechanism to compare its concentration to that of a reference species (inducer).
Substantial research challenges exist in the design and verification of large-scale, complex, distributed sensing, actuation and control systems. Three topics of particular interest are the design in information flows, cooperative behavior between distributed agents, and verification of distributed, asynchronous control systems. Each of these topics relates to a difficult aspect in the proper operation of large-scale distributed system in which the temporal scales of the underlying dynamics of the systems, the rate of communications between agents, and the latency in computation and multi-threaded execution cannot be separated. The additional need to be able to rapidly design, implement and commission such systems requires new techniques in modeling, analysis, design and verification.
To approach the interlinked challenges of information flow, cooperative behavior and verification, we plan to combine tools and recent advances from control theory, networked systems and computer science. The primary tools that we expect to build on are graph theory, partial order theory, temporal logic, graph grammars, formal methods and optimization-based control. This combination of tools allows us to model and analyze complex, protocol-based control systems by using temporal logic to specify desired behavior, graph theory (in particular the graph Laplacian and other associated matrices) to model and design the information flow, graph grammars to design cooperative behavior, lattice theory and Lyapunov theory to understand convergence properties via invariant sets, and model-checking and receding horizon control to design systems whose asynchronous execution sequences satisfy a given specification. Previous results in each of these areas has demonstrated the efficacy of modeling and analysis of distributed, asynchronous sensing, actuation and control systems; future work will focus on advances required to support large-scale systems and modularity.
Our lab is interested in computational mechanics with applications to granular and porous materials. We develop basic computational tools that allow us to model and predict the behavior of these ubiquitous materials with significant impact on engineering science and industry. Current applications of our research include: mars rover explorations, landslide modeling, liquefaction modeling, CO₂ geologic sequestration. Though our emphasis is in computational procedures, we perform basic experiments and collaborate with top experimentalists around the world to make our models useful and predictive.
The combustion of hydrogen and high hydrogen content (HHC) fuels in real burners is controlled by complex interactions between chemical kinetics, molecular transport, and turbulence. Modeling and predicting the combustion of hydrogen remains challenging. More specifically, current state-of-the-art models are not capable of capturing satisfactorily the unique combustion characteristics of fuel-lean hydrogen/air or HHC-fuels/air mixtures under high pressures. Under fuel-lean conditions, the Lewis number of the reacting mixture is significantly less than one, promoting thus the development of thermo-diffusional instabilities. These instabilities might lead ultimately to unstable combustion, flashback, blow-off, and noise.
Example of thermo-diffusive instabilities.
Experimental picture of a spherical flame in a bomb chamber (left). Detailed numerical simulation of the initial growth of the thermo-diffusive instabilities (right).
Rayleigh-Taylor instabilities appear when a heavy fluid is placed on top of a light fluid. The light fluid rises as a result of buoyancy forces, and in many cases, the flow transitions rapidly to turbulence. Due to their intrinsic nature, Rayleigh-Taylor instabilities are found in a large diversity of engineering applications and natural phenomena (inertial confinement fusion, furnaces, accidental fires, heat transfer within stars, supernova formation, underwater hot vents, oil spill…). A lot of work has been done on the initial and long term growth of Rayleigh-Taylor instabilities. However, little is known about the structure of the turbulence inside buoyant mixing layers. A perfect example is the observed anisotropy of scales in direct contradiction with the well-established Kolmogorov theory and which remains currently unexplained by any theoretical models.
Turbulent buoyant helium plume.
Bubbles of helium (black) rise and spikes of air (white) fall (left). These spikes and bubbles grow into a large scale puffing phenomenon with a well-defined frequency (right).
Isolated hot surfaces surrounded by a flammable mixture, such as a pipe carrying hot gas in a flammable leakage zone in an aircraft or the overheating of a failing electrical or mechanical device, are potential ignition sources. To study these phenomena, a new experimental procedure has been setup in which a hot glow-plug is surrounded by a flammable hydrocarbon/air mixture. Heated gases rise up due to buoyancy and a thermal plume is established. At the right location in the plume, the mixture ignites and a laminar flame starts to propagate through the vessel. During the investigation of the dependence of hot surface ignition temperature on various parameters, such as pressure, equivalence ratio, and surface size, it was observed that periodic flames (puffing) develop at higher equivalence ratios. Puffing behavior has been encountered already in non-premixed (diffusion) flames such as fires. The present results may be the first evidence of a puffing premixed flame. Preliminary results suggest that the puffing behavior in these premixed flames is a direct outcome of the interaction between buoyancy forces and vorticity generation near the flame front.
Snapshots (at different times) of a numerical simulation of the puffing premixed flame (left). Comparison between experimental schlieren pictures and density profiles from the simulation highlighting the location of the flame front (right).
Earthquake Early Warning System (EEWS) only provides few seconds to a minute of early warning, which is not enough for human decision-making in many engineering applications. Automated Decision-making System (ADS) is developed to make fast and rational decision based on the most updated EEWS information. The decision is based on a probabilistic estimation of economic loss using PEER performance-based earthquake engineering (PBEE) methodology. Action Function (AF) is defined such that mitigation action is taken when expected value of AF is greater than zero. Concept of surrogate model is used to speed up calculation process in order to achieve real-time decision-making. Time constraint is also considered to make sure the chosen mitigation action can be completed within limited warning time.
ADS framework (left). Sample result of expected-AF (E[AF]) calculation based on PBEE methodology and earthquake magnitude estimation from EEWS (right).
In the late eighties, Rosakis introduced the concept of "Laboratory Earthquakes" and since then his research interests have mainly focused on the mechanics of seismology, the physics of dynamic shear rupture and frictional sliding and on laboratory seismology. The goal of this body of work is to create, in a controlled and repeatable environment, surrogate laboratory earthquake scenarios mimicking various dynamic shear rupture process occurring in natural earthquake events. Such, highly instrumented, experiments are used to observe new physical phenomena and to also create benchmark comparisons with existing analysis and field observations. The experiments use high-speed photography, full-field photoelasticity, and laser velocimetry as diagnostics. The fault systems are simulated using two photoelastic plates held together in frictional contact. The far field tectonic loading is simulated by pre-compression while the triggering of dynamic rupture (spontaneous nucleation) is achieved by suddenly dropping the normal stress in a small region along the interface. The frictional interface (fault) forms various angles with the compression axis to provide the shear driving force necessary for continued rupturing. Rosakis and his co-workers, investigate the characteristics of rupture, such as rupture speed, rupture mode, associated ground motion under various conditions such as tectonic load, interface complexity and roughness. Both homogeneous and bimaterial interfaces (abutted by various elastic and damaged media) are investigated. Rosakis and his coworkers have been credited with the experimental discovery of the "intersonic" or "supershear rupture" phenomenon. Indeed they have investigated this new phenomenon in various engineering and geophysical settings involving shear dominated rupture in the presence of weak interfaces or faults. Their experimental discoveries of supershear rupture has refocused the attention of the geophysics community to the study of supershear earthquakes.
Quantum Mechanics at the Macroscopic Scale: Coarse-graining Density Functional Theory
Defects play a critical role in determining the macroscopic properties of solids. Dislocations mediate plasticity, vacancies mediate creep, and grain boundaries affect dislocations and vacancy migration. However, defects present a particularly daunting challenge since the (quantum) chemistry of the core, the atomistic halo and macroscopic (elastic) fields are intimately coupled. Density Functional Theory (DFT) describes the quantum mechanics, but is much too complex to directly use at the macroscopic scales. This has motivated a number of approaches for multiscale modeling, but they often use specific and ad hoc assumptions about the interactions. Bhattacharya and Ortiz groups have pursed an approach where they solve the equations of DFT on macroscopic domains by exploiting the structure of the solution to systematically eliminate degrees of freedom. Keys ideas include a reformulation of DFT in terms of local variables, efficient methods of solution and a nested discretization that resolves all details near the core but only samples representative points away from it. This has been used to study vacancy binding in Aluminum and surface energies of Magnesium, and current work addresses dislocations in metals and domain walls in ferroelectric materials.
The electronic density at the (0001) surface of Magnesium.
Suryanarayana, Bhattacharya and Ortiz, In preparation.
The Bhattacharya group studies a wide range of active materials including shape-memory alloys, ferroelectrics, electro-active materials and liquid crystal elastomers. The materials have unusual properties that couple mechanical, electrical, magnetic and thermal phenomena. A key issue that is addresses is understanding the link between microstructure and macroscopic properties, and then using this understanding (i) to develop ideas for improved materials, (ii) to propose novel applications and (iii) to build high-fidelity macroscopic models.
Fundamental problems involving the interaction of shock waves with drops and bubbles arise in numerous applications. In underwater explosions, the blast wave can interact with underwater structures to form cavitation bubbles whose violent collapse generates secondary shock waves. Similar processes occur in medical procedures involving shock and ultrasonic waves, such as lithotripsy (pulverization of kidney stones with shock waves) and historipsy (tissue fractionation for treatment of cancer), and in two-phase flow in turbomachinery. We are developing robust and accurate numerical simulations of the interactions of shock waves with a disperse phase, and using the simulations to characterize the stresses occurring in nearby solid and fluid structures. The methodology has so far been applied to study the collapse of cavitation bubbles near a kidney stone in lithotripsy, and the deformation of a target during a high-speed droplet impact. We are also modeling the growth and collapse of cavitation bubbles in micro-vessels as a model for the tissue injury that occurs in lithotripsy.
Numerical Schlieren (top) and pressure (bottom) contours illustrate the non-spherical deformation of the bubble and the generation of shockwaves during the collapse. The high pressure thereby produced during can lead to significant structural damage to neighboring structures. This phenomenon is exhibited in many applications, ranging from the erosion of propeller blades and pump impellers to the comminution of kidney stones.
Together with colleagues at the Illinois Institute of Technology and Princeton and Northeastern Universities, we are developing integrated closed-loop flow and flight control for stabilization and regulation of separated flows occurring on unmanned and micro air vehicle (UAV/MAV) wings. Inspired by the remarkable performance of birds and insects, increased lift associated with the controlled flows will lead to dramatic improvements in maneuverability, gust resistance, and a wider flight envelope. We are also studying how energy can be effectively extracted from wind gradients, in order to minimize power requirements and thereby reduce the weight of MAV. Our approach utilizes model-based, real-time control of unsteady mass injection along the wing's leading edge in order to dynamically alter the aerodynamic forces and moments, potentially eliminating traditional control surfaces whose inertia and structural limitations preclude real-time disturbance rejection algorithms. The methodology, so far demonstrated on model wings in laboratory and simulation environments, also delivers high-lift flow states that would be otherwise unstable without sensing and actuation. Specific laboratory demonstrations include the ability to dynamically cancel lift fluctuations associated with gusting flows on a time scale approaching the fast, intrinsic fluid-dynamic time scales associated with small-scale wings. A significant aspect of the work is the development of general model reduction theory and algorithms suitable for robust flow control that can be applied to a wide variety of flow control problems.
Top view of separated flow over low aspect ratio wings of elliptical, semi-circular, and delta-shaped planform at Re=300 and 30 degrees angle of attack. The flow is visualized with surfaces of constant vorticity magnitude (dark grey) and "Q-criterion" (light grey) which highlight the leading-edge and tip vortices. See Taira and Colonius (Journal of Fluid Mechanics, 623:187-207, 2009) for further details.
Simulation, Modeling, and Control of Turbulent Jet Noise
Since the 1950s, significant reductions in aircraft noise have been made by increasing the bypass ratio of the turbofan engine. However, the bypass ratio is reaching a practical upper bound, and significant further reductions in jet noise will require more subtle interactions with the turbulent flow field and better understanding of the mechanisms of sound generation. To date, only passive devices such as serrated nozzles have proven robust and effective enough for deployment on commercial aircraft, but recent advances in simulation and modeling promise new insights into mechanisms that can be exploited in active and, perhaps ultimately, closed-loop control. We are performing large-scale computations of turbulent jets and their radiated noise in order to provide detailed databases through which reduced-order modeling and control concepts can be evaluated. These simulations utilize new methods that permit better scalability for parallel simulations on very large numbers of processors. We are also developing reduced-order models based on Parabolized Stability Equations (PSE) and utilizing data from advanced diagnostic techniques such as large microphone arrays in order to isolate specific turbulent structures responsible for the loudest noise.
Analysis of jets from standard round and serrated nozzles shows the impact of the serrations on the basic instabilities of the flow field. Contours of pressure in a cross section of the jet two diameters downstream of the nozzle lip are shown. See Gudmundsson and Colonius (AIAA Paper 2007-3599).
Booming sand dunes have intrigued travelers since Marco Polo and puzzled scientists for long. Some dunes emit a persistent, low-frequency sound during a slumping event or a natural avalanche on the leeward face of the dune. The sound can last for several minutes and is audible from miles away. The resulting acoustic emission is characterized by a dominant audible frequency (70 - 105 Hz) and several higher harmonics. Seismic refraction experiments by Caltech ME proved the existence of a multi-layer internal structure in the dune that acts as a waveguide for the acoustic energy. Constructive interference between the reflecting waves enables the amplification and sets the frequency of each boom. Continuing work focuses on additional geophysical measurements and finite difference simulations supporting the waveguide model for booming sand dunes.
Ground penetrating radar image of a large sand dune at Eureka Dunes, Death Valley, California. The image shows parallel layering on either side of the dune crest; this layering structure is a key ingredient in the phenomena of booming dunes.