A5014334832- Model Reduction and Neural Networks
- Fluid Dynamics and Turbulent Flows
- Quantum chaos and dynamical systems
- Probabilistic and Robust Engineering Design
- Fluid Dynamics and Vibration Analysis
- Nonlinear Dynamics and Pattern Formation
- Microfluidic and Bio-sensing Technologies
- Microfluidic and Capillary Electrophoresis Applications
- Mathematical Dynamics and Fractals
- Lattice Boltzmann Simulation Studies
- Computational Fluid Dynamics and Aerodynamics
- stochastic dynamics and bifurcation
- Chaos control and synchronization
- Power System Optimization and Stability
- Force Microscopy Techniques and Applications
- Numerical methods for differential equations
- Building Energy and Comfort Optimization
- Stability and Controllability of Differential Equations
- Nuclear Engineering Thermal-Hydraulics
- Mechanical and Optical Resonators
- Control Systems and Identification
- Theoretical and Computational Physics
- Neural Networks and Applications
- Advanced Thermodynamics and Statistical Mechanics
- Image and Signal Denoising Methods
University of California, Santa Barbara
2015-2024
University of Rijeka
2017-2021
California Institute of Technology
1994-2021
Johns Hopkins University
2019-2020
California NanoSystems Institute
2019-2020
Osaka Prefecture University
2020
Massachusetts Institute of Technology
2019
University of Namur
2018
Virginia Tech
2017
University of Southampton
2016
It is difficult to mix solutions in microchannels. Under typical operating conditions, flows these channels are laminar—the spontaneous fluctuations of velocity that tend homogenize fluids turbulent absent, and molecular diffusion across the slow. We present a passive method for mixing streams steady pressure-driven microchannels at low Reynolds number. Using this method, length channel required grows only logarithmically with Péclet number, hydrodynamic dispersion along reduced relative...
We present a technique for describing the global behaviour of complex nonlinear flows by decomposing flow into modes determined from spectral analysis Koopman operator, an infinite-dimensional linear operator associated with full system. These modes, referred to as are particular observable, and may be directly data (either numerical or experimental) using variant standard Arnoldi method. They have temporal frequency growth rate viewed generalization eigenmodes linearized provide alternative...
This article reviews theory and applications of Koopman modes in fluid mechanics. mode decomposition is based on the surprising fact, discovered Mezić (2005) , that normal linear oscillations have their natural analogs—Koopman modes—in context nonlinear dynamics. To pursue this analogy, one must change representation system from state-space to dynamics governed by operator an infinite-dimensional space observables. Whereas his original paper dealt only with measure-preserving...
A majority of methods from dynamical system analysis, especially those in applied settings, rely on Poincaré's geometric picture that focuses "dynamics states." While this has fueled our field for a century, it shown difficulties handling high-dimensional, ill-described, and uncertain systems, which are more common engineered systems design analysis "big data" measurements. This overview article presents an alternative framework based the observables" picture. The central object is Koopman...
We propose a novel operator-theoretic framework to study global stability of nonlinear systems. Based on the spectral properties so-called Koopman operator, our approach can be regarded as natural extension classic linear analysis The main results establish (necessary and sufficient) relationship between existence specific eigenfunctions operator property hyperbolic fixed points limit cycles. These are complemented with numerical methods which used estimate region attraction point or prove...
We establish the convergence of a class numerical algorithms, known as Dynamic Mode Decomposition (DMD), for computation eigenvalues and eigenfunctions infinite-dimensional Koopman operator. The algorithms act on data coming from observables state space, arranged in Hankel-type matrices. proofs utilize assumption that underlying dynamical system is ergodic. This includes classical measure-preserving systems, well systems whose attractors support physical measure. Our approach relies...
This work reviews the present position of and surveys future perspectives in physics chaotic advection: field that emerged three decades ago at intersection fluid mechanics nonlinear dynamics, which encompasses a range applications with length scales ranging from micrometers to hundreds kilometers, including systems as diverse mixing thermal processing viscous fluids, microfluidics, biological flows, oceanographic atmospheric flows.
We perform modal analysis of short-term swing dynamics in multi-machine power systems. The is based on the so-called Koopman operator, a linear, infinite-dimensional operator that defined for any nonlinear dynamical system and captures full information system. Modes derived through spectral called modes, provide extension linear oscillatory modes. Computation modes extracts single-frequency, spatial embedded non-stationary data short-term, dynamics, it provides novel technique identification...
Chaotic advection has served as the paradigm for mixing in fluid flows with simple time dependence. Its skeletal structure is based on analysis of invariant attracting and repelling manifolds flows. Here we develop a finite-time theory two-dimensional incompressible arbitrary dependence introduce new diagnostic it. Besides stretching events around manifolds, this allows us to detect hyperbolic zones. We used forecast spatial location timing oil washing ashore Plaquemines Parish Grand Isle,...
The irruption of gas and oil into the Gulf Mexico during Deepwater Horizon event fed a deep sea bacterial bloom that consumed hydrocarbons in affected waters, formed regional oxygen anomaly, altered microbiology region. In this work, we develop coupled physical–metabolic model to assess impact mixing processes on these ocean communities their capacity for hydrocarbon use. We find observed biodegradation patterns are well-described by exponential growth bacteria from seed populations present...
Abstract As building energy modelling becomes more sophisticated, the amount of user input and number parameters used to define models continue grow. There are numerous sources uncertainty in these parameters, especially when process is being performed before construction commissioning. Past efforts perform sensitivity analysis have focused on tens while this work, we increase size by two orders magnitude (by studying influence about 1000 parameters). We extend traditional order decompose...
Concise, accurate descriptions of physical systems through their conserved quantities abound in the natural sciences. In data science, however, current research often focuses on regression problems, without routinely incorporating additional assumptions about system that generated data. Here, we propose to explore a particular type underlying structure data: Hamiltonian systems, where an "energy" is conserved. Given collection observations such over time, extract phase space coordinates and...
The loss of stability-an instability-can become a critical cause emergent cascading outages leading to wide-spread blackouts. Penetration renewable energy sources makes the problem instability more urgent because highly fluctuating nature such sources. Here we show data-based approach stability assessment power systems without models. This is enabled by Koopman mode analysis for nonlinear dynamical systems, which detects an based on properties point spectrum operator. We apply technique data...