In this work we construct and analyze exact solutions describing Ricci flows and nonholonomic deformations of four dimensional (4D) Taub-NUT spacetimes. It is outlined a new geometric techniques of constructing Ricci flow solutions. Some conceptual issues on spacetimes provided with generic off–diagonal metrics and associated nonlinear connection structures are analyzed. The limit from gravity/...

It is now well known that the focussing nonlinear Schrödinger equation allows plane waves to be modulationally unstable, and at the same time supports breather solutions which are often invoked as models for rogue waves. This suggests a direct connection between modulation instability and the existence of rogue waves. In this chapter we review this connection for a suite of long wave models, su...

We elucidate the connection between the Kolmogorov-Sinai entropy rate k and the time evolution of the physical or statistical entropy S. For a large family of chaotic conservative dynamical systems including the simplest ones, the evolution of Sstd for far-from-equilibrium processes includes a stage during which S is a simple linear function of time whose slope is k. We present numerical confir...

Recurrent neural networks are often used for learning time-series data. Based on a few assumptions we model this learning task as a minimization problem of a nonlinear least-squares cost function. The special structure of the cost function allows us to build a connection to reinforcement learning. We exploit this connection and derive a convergent, policy iteration-based algorithm. Furthermore,...

One of the typically damaged steel beam-column connection during the Northridge earthquake of 1994 was bolted-web, welded-flange (BWWF), now known as “pre-Northridge” connection. Proposed post-Northridge connections are more ductile and capable of dissipating more energy, thus improving the behavior of steel moment resisting frames (SMRF). The post-Northridge connections with added ductility wi...

We consider a framework for nonlinear operators on functions evaluated on graphs via stacks of level sets. We investigate family of transformations which includes adaptive flat and non-flat erosions and dilations. Additionally, we note the connection to mean motion curvature on graphs. Proposed operators are illustrated in the cases of functions on graphs, textured meshes and graphs of images.

A solution of the nonlinear Klein-Gordon equation perturbed by a parametric driver is studied. The frequency of the parametric perturbation varies slowly and passes through a resonant value. It yields a change in a solution. We obtain a connection formula for the asymptotic solution before and after the resonance.

To enhance installation security, a LNG storage in Rudong of Jiangsu province was adopted as a practical work, and it was analyzed by nonlinear finite element method to research overall and local stability performance, as well as the stress and deformation under the action of wind load and self-weight. Results indicate that deformation is tiny when steel mesh maintains as an overall ring, and s...

Stochastic quantization provides a connection between quantum field theory and statistical mechanics, with applications especially in gauge field theories. Euclidean quantum field theory is viewed as the equilibrium limit of a statistical system coupled to a thermal reservoir. Nonlinear phenomena in stochastic quantization arise when employing nonlinear Brownian motion as an underlying stochast...

The periodic forcing of nonlinear oscillations can often be cast as a problem involving self-maps of the circle. Consideration of the effects of changes in the frequency and amplitude of the periodic forcing leads to a problem involving the bifurcations of circle maps in a two-dimensional parameter space. The global bifurcations in this two-dimensional parameter space is described for periodic ...