Bifurcation of heteroclinic cycle near 1:4 resonance in a self-excited parametrically forced oscillator with quadratic nonlinearity is investigated analytically in this paper. This bifurcation mechanism leads to the disappearance of a slow flow limit cycle giving rise to frequency-locking near the resonance. The analytical approach used to approximate the bifurcation is based on a collision cri...

We study the dynamics of a thermo-mechanical model for a forced disc shaped, micromechanical limit cycle oscillator. The forcing can be accomplished either parametrically, by modulating the laser beam incident on the oscillator, or nonparametrically, using inertial driving. The system exhibits both 2:1 and 1:1 resonances, as well as quasiperiodic motions and hysteresis. A perturbation method is...

Large-scale features of a randomly isotropically forced incompressible and unbounded rotating fluid are examined in perturbation theory. At first order in both the random force amplitude and the angular velocity, we find two types of modifications to the fluid equation of motion. The first correction transforms the molecular shear viscosity into a (rotation independent) effective viscosity. The...

Dispersive effects induced by weak hydrostatic imbalance in the presence of topography and stratification are incorporated into a new model of barotropic (vertically integrated) mesoscale ocean dynamics. This barotropic model is obtained by first expanding the solutions of three dimensional Euler-Boussinesq equations in a regular perturbation expansion in terms of the several small dimensionles...

This paper presents Lyapunov functions for proving stability of steady gliding motions for vehicles with hydrodynamic or aerodynamic forces and moments. Because of lifting forces and moments, system energy cannot be used as a Lyapunov function candidate. A Lyapunov function is constructed using a conservation law discovered by Lanchester in his classical work on phugoid-mode dynamics of an airp...

Adult bone marrow-derived stem cells (BMDC) have been shown to contribute to numerous tissues after transplantation into a new host. However, whether the participation of these cells is part of the normal response to injury remains a matter of debate. Using parabiotically joined pairs of genetically labeled and wildtype mice, we show here that irradiation-induced damage of the target tissue, in...

The renormalization group method of Goldenfeld, Oono and their collaborators is applied to asymptotic analysis of vector fields. The method is formulated on the basis of the theory of envelopes, as was done for scalar fields. This formulation actually completes the discussion of the previous work for scalar equations. It is shown in a generic way that the method applied to equations with a bifu...

Mathematical modeling of thermal effects on steady state dynamics of microresonators, utilizing an analytical approach is studied. Thermal phenomena has two distinct effects, which in this report are called, thermal damping and temperature relaxation. In this part of a two-part report we investigate the thermal damping and its effects on microresonator dynamics. To do this, first the reduced or...

In this article, we consider a small SO(2)-equivariant perturbation of a reaction-diffusion system on the sphere, which is equivariant with respect to the group SO(3) of all rigid rotations. We consider a normally hyperbolic SO(3)-group orbit of a rotating wave on the sphere that persists to a normally hyperbolic SO(2)-invariant manifold M(ε). We investigate the effects of this forced symmetry ...