Synchronization measures have become an important tool for exploring the relationships between time series. We review three recently proposed nonlinear synchronization measures and expand their definitions in a straightforward way to apply to an ensemble of measurements. We also develop a synchronization measure in which nearest neighbors are determined across the ensemble. We compare these fou...

Despite the steady increase in computing power many nonlinear partial differential equations still cannot be solved by brute-force numerical methods in acceptable time. However, often the method of multiple scales resulting in so-called amplitude equations can be used to first reduce the complexity of the problem. The amplitude equations give valuable mathematical insight and, moreover, can be ...

Abst rac t . Recent experiments (Weisberg, Kevrekidis & Smits 1997) have demonstrated that the centrifugal instability leading to Taylor vortex flow can be controlled by harmonic oscillations of the inner cylinder in the axial direction. Marques & Lopez (1997) used linear Floquet analysis to study the control of the instability for the flow between two infinite length co-axial cylinders. Howeve...

This paper presents a novel 2D shape deformation algorithm based on nonlinear least squares optimization. The algorithm aims to preserve two local shape properties: Laplacian coordinates of the boundary curve and local area of the shape interior, which are together represented in a non-quadric energy function. An iterative Gauss-Newton method is used to minimize this nonlinear energy function. ...

We report an algorithm of constructing linear and nonlinear potentials in the two-dimensional Gross-Pitaevskii equation subject to given boundary conditions, which allow for exact analytic solutions. The obtained solutions represent superfluid flows in inhomogeneous Bose-Einstein condensates. The method is based on the combination of the similarity reduction of the two-dimensional Gross-Pitaevs...

This paper shows how globally attractive limit cycle oscillations can be induced in a system with a nonlinear feedback element. Based on the same principle as the Van der Pol oscillator, the feedback behaves as a negative damping for low velocities but as an ordinary damper for high velocities. This nonlinear damper can be physically implemented with a continuous variable transmission and a spr...

We present exact analytical results for the statistics of nonlinear coupled oscillators under the influence of additive white noise. We suggest a perturbative approach for analysing the statistics of such systems under the action of a determanistic perturbation, based on the exact expressions for probability density functions for noise-driven oscillators. Using our perturbation technique we sho...

Abstract Mathematical models of planar physically nonlinear inhomogeneous plates with rectangular cuts are constructed based on the three-dimensional (3D) theory elasticity, Mises plasticity criterion, and Birger’s method variable parameters. The is developed for arbitrary deformation diagrams, boundary conditions, transverse loads, material inhomogeneities. Additionally, inhomogeneities in for...

Physically-based animation techniques enable more realistic and accurate animation to be created. We present a fully physically-based approach for efficiently producing realisticlooking, natural animations of facial movement, including animation of expressive wrinkles. This involves simulation of detailed models using a GPU-based total Lagrangian explicit dynamic finite element (TLED FE) system...