Fluid mixing controls many natural and industrial processes, including the spread of air pollution1, mass transfer and reactions in microfluidic devices2,3 and the detection of odours or other chemical signals4. Strongly nonlinear flows enhance mixing by chaotic advection5,6, stretching and folding7,8 fluid volumes. Though these processes have been studied in simple models9,10, stretching and f...

This paper considers least squares estimators for regression problems over convex, uniformly bounded, uniformly Lipschitz function classes minimizing the empirical risk over max-affine functions (the maximum of finitely many affine functions). Based on new results on nonlinear nonparametric regression and on the approximation accuracy of maxaffine functions, these estimators are proved to achie...

The paper extends the use of multichannel filtered-x affine projection algorithms suitable for feed-forward active noise control to a broad class of nonlinear filter structures, which comprises also Volterra filters and Functional Link Artificial Neural Networks (FLANN). An analysis of the transient and steady-state behavior of the resulting algorithms is provided. Some experimental results tha...

In this paper, a nonlinear active noise control (ANC) is proposed using adaptive Volterra filtering with a variable step-size Gauss-Seidel pseudo affine projection (VSSGSPAP) algorithm. In particular, it requires a lower computational burden than the VSS affine projection (VSSAP) algorithm, and provides an improved convergence as the VSSAP algorithm does. Simulation results show that the propos...

In this paper we discuss the algebraic construction of the mKdV hierarchy in terms of an affine Lie algebra ŝl(2). An interesting novelty araises from the negative even grade sector of the affine algebra leading to nonlinear integro-differential equations admiting non-trivial vacuum configuration. These solitons solutions are constructed systematically from generalization of the dressing method...

The key in applying energy-based control approach is to be able to express the system under consideration as a dissipative Hamiltonian system, i.e., to obtain Dissipative Hamiltonian Realization (DHR) for the system. In general, the precise DHR form is hard to obtain for nonlinear dynamic systems. When a precise DHR does not exist for a dynamic system or such a precise realization is difficulty...

Nonlinear permutations (S-boxes) are key components in block ciphers. Differential branch number measures the diffusion power of a permutation. Differential branch number of nonlinear permutations of F2 has not been analyzed, although it is well studied for linear permutations. In this paper we obtain a bound on differential branch number of permutations (both linear and nonlinear) of F2 . We a...

This paper develops the theory for tracking control using the nonlinear H1 control design methodology for a class of nonlinear input affine systems. The authors use a two-step process of first designing the feedforward part of the controller to design for perfect trajectory following and then design the feedback part of the controller using nonlinear H1 regulator theory. Results for infinite-ti...

Optimal Control and Estimation Strategies for Nonlinear and Switched Systems Mehdi Abedinpour Fallah This dissertation includes two main parts. In the first part, the main contribution is to use an inverse optimality approach to analytically solve the Hamilton-Jacobi-Bellman equation of a third order nonlinear optimal control problem for which the dynamics are affine and the cost is quadratic i...

A closed bosonic string in a curved affine--metric spacetime is considered as an example of dissipative quantum field theory. The eonformal anomaly of the trace of the energy--momentum tensor for the string on the affine--metrie manifold is investigated. The two-loop metric beta function for the two-dimensional nonlinear dissipative sigma model is calculated. Examples of nonflat manifolds that ...