Control of Universal Scaling, Noise Strength, and Pattern Formation in Critical Dynamics
Abstract
The objective of our current and planned research program is to build on a powerful and highly successful theory for non-linear stochastic dynamics of cooperative multi-component systems, namely critical dynamics, and upon drawing on considerable available experience in control theory, develop novel efficient protocols for: (1) steering multi-critical complex interacting dynamical systems toward certain desired universal scaling behavior; (2) externally controlling the strength of stochastic fluctuations and intrinsic noise in systems that are driven far from thermal equilibrium and display generic scale invariance; (3) selectively targeting and stabilizing specific self-generated spatio-temporal patterns in strongly fluctuating reaction-diffusion systems and epidemic models. These ambitious research projects presently involve one undergraduate and seven doctoral students. In addition, we are currently advertising postdoctoral research associate positions at Virginia Tech and the University of Maryland. From this interdisciplinary research, the emergence of new concepts and innovative mathematical tools is anticipated. Our research team has begun to explore a wide range of potential applications that span from materials science such as magnetism and surface growth, to synthetic biology, neuroscience, epidemiology, ecology, and social system dynamics. In this brief report period, we have initiated detailed numerical investigations of various important model systems. In this interdisciplinary theoretical research project, we aim to combine our respective thorough expertise critical dynamics and control theory to identify tools and methods to exert control over complex cooperative stochastic dynamical systems both near or far away from thermal equilibrium that display scale invariant properties. Specifically, we intend to pursue, through the study of carefully selected model systems, the following five central and fundamental questions: (i) Can we design efficient control mechanisms that would allow us to influence and drive scale-invariant critical dynamics towards certain targeted universality classes? (ii) Is it possible to externally control the strength of system-imminent fluctuations and even intrinsic reaction noise amplitudes to achieve desired observable output? (iii) May one exploit large-scale collective behavior of near-critical multiple-agent dynamical systems to exert global control through correlation-facilitated spreading of carefully posited local perturbations? (iv) Can we construct control schemes to specifically select for certain fluctuation-induced and noise-stabilized spatio-temporal patterns to generate desired morphologies in interacting many-particle and reaction-diffusion systems? (v) Is it feasible to extend powerful renormalization group ideas and techniques to systematically describe and classify control schemes in near-critical dynamical systems?
Document Details
- Document Type
- DoD Grant Award
- Publication Date
- Sep 11, 2018
- Source ID
- W911NF1710156
Entities
People
- Uwe C. Täuber
Organizations
- Army Contracting Command
- United States Army
- Virginia Tech