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Center for Nonlinear Studies |
Numerous natural and engineered systems that consist of ensembles of isolated or interacting dynamical components exhibit levels of complexity that are beyond human comprehension. These complex systems often require an appropriate excitation, an optimal hierarchical organization, or a periodic dynamical structure, such as synchrony, to function as desired or operate optimally. Many of them can be regulated by the application of external inputs, or may be coupled by a topology of connections whose strength can be tuned, in order to alter their dynamic configurations or to modify their rhythmic behavior. Such complex systems can be tremendously large in scale, while their dynamics can only be influenced by a limited number of external inputs. For example, in nuclear magnetic resonance spectroscopy and imaging, billions of spins are excited by using a common pulse sequence, and in brain stimulation for neurological disorders, thousands of neurons are affected by a single electrode. In this talk, I will address theoretical and computational challenges for engineering dynamic structures in ensemble systems through various compelling applications arising from the quantum and biological domains. In particular, I will present recent results in controllability and each ability of ensembles and introduce novel computational methods for optimal control synthesis for ensemble systems. Practical ensemble control designs, including optimal pulses in quantum control and entrainment waveforms for pattern formation in a network of nonlinear oscillators, will be illustrated along with their experimental realizations.
Host: Anatoly Zlotnik