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Register a new userAn experimental design for the control and assembly of magnetic microwheels
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Superparamagnetic colloidal particles can be reversibly assembled into wheel-like structures called microwheels ($mu$wheels) which roll on surfaces due to friction and can be driven at user-controlled speeds and directions using rotating magnetic fields. Here, we describe the hardware and software to create and control the magnetic fields that assemble and direct wheel motion and the optics to visualize them. Motivated by portability, adaptability and low-cost, an extruded aluminum heat dissipating frame incorporating open optics and audio speaker coils outfitted with high magnetic permeability cores was constructed. Open-source software was developed to define the magnitude, frequency, and orientation of the magnetic field, allowing for real time joystick control of $mu$wheels through two-dimensional (2D) and three-dimensional (3D) fluidic environments. With this combination of hardware and software, $mu$wheels translate at speeds up to 50 $mu$m/s through sample sizes up to 5 cm x 5 cm x 5 cm using 0.75-2.5 mT magnetic fields with rotation frequencies of 5-40 Hz. Heat dissipation by aluminum coil clamps maintained sample temperatures within 3 C of ambient temperature, a range conducive for biological applications. With this design, $mu$wheels can be manipulated and imaged in 2D and 3D networks at length scales of micrometers to centimeters
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We consider a dynamical system with two sources of uncertainties: (1) parameterized input with a known probability distribution and (2) stochastic input-to-response (ItR) function with heteroscedastic randomness. Our purpose is to efficiently quantify the extreme response probability when the ItR function is expensive to evaluate. The problem setup arises often in physics and engineering problems, with randomness in ItR coming from either intrinsic uncertainties (say, as a solution to a stochastic equation) or additional (critical) uncertainties that are not incorporated in the input parameter space. To reduce the required sampling numbers, we develop a sequential Bayesian experimental design method leveraging the variational heteroscedastic Gaussian process regression (VHGPR) to account for the stochastic ItR, along with a new criterion to select the next-best samples sequentially. The validity of our new method is first tested in two synthetic problems with the stochastic ItR functions defined artificially. Finally, we demonstrate the application of our method to an engineering problem of estimating the extreme ship motion probability in ensemble of wave groups, where the uncertainty in ItR naturally originates from the uncertain initial condition of ship motion in each wave group.
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We consider estimation and control of the cylinder wake at low Reynolds numbers. A particular focus is on the development of efficient numerical algorithms to design optimal linear feedback controllers when there are many inputs (disturbances applied everywhere) and many outputs (perturbations measured everywhere). We propose a resolvent-based iterative algorithm to perform i) optimal estimation of the flow using a limited number of sensors; and ii) optimal control of the flow when the entire flow is known but only a limited number of actuators are available for control. The method uses resolvent analysis to take advantage of the low-rank characteristics of the cylinder wake and solutions are obtained without any model-order reduction. Optimal feedback controllers are also obtained by combining the solutions of the estimation and control problems. We show that the performance of the estimators and controllers converges to the true global optima, indicating that the important physical mechanisms for estimation and control are of low rank.
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