We describe techniques to generate useful reachability information for nonlinear dynamical systems. These techniques can be automated for polynomial systems using algorithms from computational algebraic geometry. The generated information can be incorporated into other approaches for doing reachability computation. It can also be used when abstracting hybrid systems that contain modes with nonl...

We demonstrate a novel mechanism for low power optical detection and modulation in a slotted waveguide geometry filled with nonlinear electro-optic polymers. The nanoscale confinement of the optical mode, combined with its close proximity to electrical contacts, enables the direct conversion of optical energy to electrical energy, without external bias, via optical rectification, and also enhan...

We use various nonlinear geometric partial differential equations to efficiently solve several surface modelling problems, including surface blending, N -sided hole filling and free-form surface fitting. The nonlinear equations used include two second order flows (mean curvature flow and average mean curvature flow), one fourth order flow (surface diffusion flow) and a sixth order flow. These n...

The goal of this paper is to improve the performance of an electric motor by modifying the geometry of a specific part of the iron core of its rotor. To be more precise, the objective is to smooth the rotation pattern of the rotor. A shape optimization problem is formulated by introducing a tracking-type cost functional to match a desired rotation pattern. The magnetic field generated by perman...

This paper presents a new nonlinear multivariate statistical process control technique for identifying and isolating the root cause of abnormal process behavior. The new technique is a nonlinear extension to the variables reconstruction technique by (Dunia et al., 1996), based on nonlinear principal component analysis (NLPCA). This work demonstrates that the variable reconstruction (i) affects ...

In this work a theory is developed for unifying large classes of nonlinear discrete-time dynamical systems obeying a superposition of a weighted maximum or minimum type. The state vectors and input-output signals evolve on nonlinear spaces which we call complete weighted lattices and include as special cases the nonlinear vector spaces of minimax algebra. Their algebraic structure has a polygon...

The lattice evolution method for solving the nonlinear Poisson-Boltzmann equation in confined domain is developed by introducing the second-order accurate Dirichlet and Neumann boundary implements, which are consistent with the non-slip model in lattice Boltzmann method for fluid flows. The lattice evolution method is validated by comparing with various analytical solutions and shows superior t...

The geometry of constrained Lagrangian systems is developed using the Lagrange-d’Alembert principle, extending the variational approach of Marsden, Shkoller, and Patrick, Comm. Math. Phys. 199:351–395 from holonomic to nonholonomic systems. It emerges that the instrinsic geometry of nonholonomic systems corresponds to the geometry of the distributional Hamiltonian systems of Sniatycki, Rep. Mat...

Information geometry enables a deeper understanding of the methods of statistical inference. In this paper, the problem of nonlinear parameter estimation is considered from a geometric viewpoint using a natural gradient descent on statistical manifolds. It is demonstrated that the nonlinear estimation for curved exponential families can be simply viewed as a deterministic optimization problem w...