We present results for a digital holography experiment with anisoplanatic image correction through two discrete planes of phase errors. Using a nonlinear optimization technique, we maximize a modified sharpness metric to solve for estimates of the phase errors in the system in the multiple planes where they physically exist. We show that correcting for phase errors in multiple planes gives a su...

Abstract. We show that the fourth-order nonlinear ODE which controls the pole dynamics in the general solution of equation P 2 I compatible with the KdV equation exhibits two remarkable properties: (1) it governs the isomonodromy deformations of a 2× 2 matrix linear ODE with polynomial coefficients, and (2) it does not possess the Painlevé property. We also study the properties of the Riemann–H...

In this paper, based on a Lax pair of the Riccati form for the general KdV equation, a new auto-Bäcklund transformation (ABT) is presented. As an application of this ABT, since only integration is needed, a series of explicit and exact solutions can be obtained which contain soliton-like solutions. This approach is important for finding more new and physically significant exact solutions of non...

This paper presents the results of the parameter estimation procedure for the primary circuit dynamics of a VVER-type nuclear power plant. The model structure is a low dimensional lumped nonlinear model published previously in Fazekas et al. [2007a]. The parameter estimation method uses the modular decomposition of the system model for obtaining physically meaningful initial parameter estimates...

We derive an analytic formula for the lateral dynamics of solitons in a general inhomogeneous nonlinear media, and show that it can be valid over tens of diffraction lengths. In particular, we show that solitons centered at a lattice maximum can be "mathematically unstable" but "physically stable." We also derive an analytic upper bound for the critical velocity for tunneling, which is valid ev...

Nonlinear reaction-diffusion systems are known to exhibit very many novel spatiotemporal patterns. Fisher equation is a prototype of diffusive equations. In this contribution we investigate the integrability properties of the generalized Fisher type equation to obtain physically interesting solutions using Lie symmetry analysis. In particular, we report several travelling wave patterns, static ...

Modeling and numerical approximation of two-phase incompressible flows with different densities and viscosities are considered. A physically consistent phase-field model that admits an energy law is proposed, and several energy stable, efficient, and accurate time discretization schemes for the coupled nonlinear phase-field model are constructed and analyzed. Ample numerical experiments are car...

where: x is position in one or more spatial dimensions; u(x, t) is some scalar or vector field, such as fluid velocity and pressure; L is a dissipative linear operator, such as ∇; f(u) includes other autonomous terms representing nonlinear advection, reaction, etc.; and q(u, t) is some time dependent control or possibly stochastic forcing [22]. Among many physically relevant examples are Burger...

In this survey, we provide an overview of model order reduction (MOR) methods applied to coupled systems. The coupling can be linear or nonlinear, weak or strong. Physically, the coupling may come from structurestructure coupling, fluid-structure or fluid-fluid interaction, electro-thermal coupling, electroor thermal-mechanical coupling, or circuit-device coupling. Different MOR methods for cou...

We present a class of nonlinear dynamic viscoelastic models for materials subjected to shear stress. The model equations are based on a continuum variation of a reptation model in which chemically cross-linked (CC) systems of molecules act as constraint boxes per unit volume for physically constrained (PC) systems of molecules. Results from validating the model with dynamic shear experiments ar...