Optimizing resonator shapes for maximizing the ratio of maximum to minimum gas pressure at an end of the resonator is investigated numerically. It is well known that the resonant frequencies and the nonlinear standing waveform in an acoustical resonator strongly depend on the resonator geometry. A quasi-Newton type scheme was used to find optimized axisymmetric resonator shapes achieving the ma...

We demonstrate all-optical switching action in a nonlinear photonic crystal cross-waveguide geometry with instantaneous Kerr nonlinearity, in which the transmission of a signal can be reversibly switched on and off by a control input. Our geometry accomplishes both spatial and spectral separation between the signal and the control in the nonlinear regime. The device occupies a small footprint o...

The Saffman–Taylor viscous fingering instability occurs when a less viscous fluid displaces a more viscous one between narrowly spaced parallel plates in a Hele–Shaw cell. Experiments in radial flow geometry form fan-like patterns, in which fingers of different lengths compete, spread and split. Our weakly nonlinear analysis of the instability predicts these phenomena, which are beyond the scop...

In recent years, many traditional optimization methods have been successfully generalized to minimize objective functions on manifolds. In this paper, we first extend the general traditional constrained optimization problem to a nonlinear programming problem built upon a general Riemannian manifold M , and discuss the first-order and the second-order optimality conditions. By exploiting the dif...

Complex wave dynamics in microlasers and nonlocal maps. Abstract The optical implementation of complex network is considered for laser cavity formed by active mirrors deposited on the surface of plane-parallel slice, ellipsoidal microball , whose eccentricity is close to 0.5 and equivalent optical circuit, containing amplifying and absorbing media in Fourier-conjugated planes. In this types of ...

As an attempt to bridge between numerical analysis and algebraic geometry, this paper formulates the multiplicity for the general nonlinear system at an isolated zero, presents an algorithm for computing the multiplicity structure, proposes a depth-deflation method for accurate computation of multiple zeros, and introduces the basic algebraic theory of the multiplicity. Furthermore, this paper ...

Studies have shown that computations of visual kinematics relations are highly complicated and do require a considerable amount of time. This is due to dependent on Jacobians and massive inter-related relations. This hinders even complicated visual servo algorithm for real-time applications. In this respect, the proposed methodology is based on approximating the highly nonlinear relations and e...

Some forty years ago Per Enflo introduced the nonlinear notions of roundness and generalized roundness for general metric spaces in order to study (a) uniform homeomorphisms between (quasi-) Banach spaces, and (b) Hilbert’s Fifth Problem in the context of non locally compact topological groups (see [24], [25], [26], and [27]). Since then the concepts of roundness and generalized roundness have ...

A multi-mode nonlinear constitutive model for mucus is constructed directly from micro- and macro-rheology experimental data on cell culture mucus, and a numerical algorithm is developed for the culture geometry and idealized cilia driving conditions. This study investigates the roles that mucus rheology, wall effects, and HBE culture geometry play in the development of flow profiles and the sh...