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Recent research shows that supervised learning can be an effective tool for designing near-optimal feedback controllers for high-dimensional nonlinear dynamic systems. But the behavior of neural network controllers is still not well…
In turbulence modeling, we are concerned with finding closure models that represent the effect of the subgrid scales on the resolved scales. Recent approaches gravitate towards machine learning techniques to construct such models. However,…
Wave turbulence in a thin elastic plate is experimentally investigated. By using a Fourier transform profilometry technique, the deformation field of the plate surface is measured simultaneously in time and space. This enables us to compute…
We discover an instability mechanism in suspensions of self-propelled particles that does not involve active stress. Instead, it is driven by a subtle interplay of inertia, swimmer motility, and concentration fluctuations, through a crucial…
We investigate various boundary conditions in two dimensional turbulence systematically in the context of conformal field theory. Keeping the conformal invariance, we can either change the shape of boundaries through finite conformal…
Energy cascades lie at the heart of the dynamics of turbulent flows. In a recent study of turbulence in fluids with odd-viscosity [de Wit \textit{et al.}, Nature \textbf{627}, 515 (2024)], the two-dimensionalization of the flow at small…
The paper describes a novel method of sampled-data in space (spatial variable) control of scalar semilinear systems of parabolic and hyperbolic type with unknown parameters and distributed disturbances. A finite set of sampled-data in the…
The statistical behavior of scalars passively advected by random flows exhibits intermittency in the form of anomalous multiscaling, in many ways similar to the patterns commonly observed in incompressible high-Reynolds fluids. This…
The random Fourier method (RFM) is widely employed for synthetic turbulence due to its mathematical clarity and simplicity. However, deviations remain between prescribed inputs and synthetic results, and the origin of these errors has not…
Based upon the formalism of conformal field theory with a boundary, we give a description of the boundary effect on fully developed two dimensional turbulence. Exact one and two point velocity correlation functions and energy power spectrum…
We consider the determination of the optimal stationary singular stochastic control of a linear diffusion for a class of average cumulative cost minimization problems arising in various financial and economic applications of stochastic…
This paper deals with the control of a kind of turbulent flows. We consider a simplified k-e model with distributed controls, locally supported in space. We proof that the system is partially locally null-controllable, in the sense that the…
We report numerical investigations of wave turbulence in a vibrating plate. The possibility to implement advanced measurement techniques and long time numerical simulations makes this system extremely valuable for wave turbulence studies.…
The methods of conformal field theory are used to obtain the series of exact solutions of the fundamental equations of the theory of turbulence. The basic conjecture, proved to be self-consistent ,is the conformal invariance of the inertial…
This paper is concerned with the problem of Model Predictive Control and Rolling Horizon Control of discrete-time systems subject to possibly unbounded random noise inputs, while satisfying hard bounds on the control inputs. We use a…
We study the problem of co-designing control barrier functions (CBF) and linear state feedback controllers for continuous-time linear systems. We achieve this by means of a single semi-definite optimization program. Our formulation can…
In this work, we will investigate the question of optimal control for bilinear systems with constrained endpoint. The optimal control will be characterized through a set of unconstrained minimization problems that approximate the former.…
We study a control problem governed by a semilinear parabolic equation. The control is a measure that acts as the kernel of a possibly nonlocal time delay term and the functional includes a non-differentiable term with the measure-norm of…
Hydrodynamic turbulence is studied as a constrained system from the point of view of metafluid dynamics. We present a Lagrangian description for this new theory of turbulence inspired from the analogy with electromagnetism. Consequently it…
One-dimensional models are presented for transitional shear flows. The models have two variables corresponding to turbulence intensity and mean shear. These variables evolve according to simple equations based on known properties of…