We consider an inflationary model inspired in the low energy limit of string theory. In this model, the scale factor grows exponentially with time. A perturbation study is performed, and we show that there is a mode which displays an exponential growth in the perturbation of the scalar field.

Numerical simulations of large aspect ratio, three-dimensional rotating Rayleigh-Bénard convection for no-slip boundary conditions have been performed in both cylinders and periodic boxes. We have focused near the threshold for the supercritical bifurcation from the conducting state to a convecting state exhibiting domain chaos. A detailed analysis of these simulations has been carried out and ...

Recent work on gravitational geons is extended to examine the stability properties of gravitational and electromagnetic geon constructs. All types of geons must possess the property of regularity, self-consistency and quasistability on a time-scale much longer than the period of the comprising waves. Standard perturbation theory, modified to accommodate timeaveraged fields, is used to test the ...

Our starting point is the set of eigenstates n of the unperturbed Hamiltonian 0 n H n E n = , notice we are not labeling with a zero, no 0 n E , because with a time-dependent Hamiltonian, energy will not be conserved, so it is pointless to look for energy corrections. What happens instead, provided the perturbation is not too large, is that the system makes transitions between the eigenstates n...

We consider a nonoscillatory second-order linear dynamic equation on a time scale together with a linear perturbation of this equation and give conditions on the perturbation that guarantee that the perturbed equation is also nonoscillatory and has solutions that behave asymptotically like a recessive and dominant solutions of the unperturbed equation. As the theory of time scales unifies conti...

An estimate of the one-loop correction to the power spectrum of the primordial curvature perturbation is given, assuming it is generated during a phase of single-field, slow-roll inflation. The loop correction splits into two parts, which can be calculated separately: a purely quantum-mechanical contribution which is generated from the interference among quantized field modes around the time wh...

Motivated by its broad applications in machine learning and reinforcement learning, we study the linear two-time-scale stochastic approximation, an iterative method using two different step sizes f...

This work focuses on time-inhomogeneous Markov chains with two time scales. Our motivations stem from applications in reliability and dependability, queueing networks, financial engineering and manufacturing systems, where two-time-scale scenarios naturally arise. One of the important questions is: As the rate of fluctuation of the Markov chain goes to infinity, if the limit distributions of su...

This paper presents a singular perturbation stability analysis for a nonlinear three-time-scale autonomous helicopter model in vertical flight. The presented time-scale analysis permits to conduct a stability analysis for the singular perturbed threetime-scale system, and allows to construct a composite Lyapunov function for the resultant closed-loop system using time-scale separation. The meth...

mineral dust is produced from both natural and anthropogenic sources. dust aerosols can be transported over long distances in the atmosphere. they reduce the incident shortwave radiation to the surface by absorbing and scattering the solar radiation; thereby leading to a cooling effect at the surface and lower tropospheric temperature. on the other hand, by absorption and re-emission of longwav...