The issues of quintessence and cosmic acceleration can be discussed in the framework of higher order curvature and torsion theories of gravity. We can define effective pressure and energy density directly connected to the curvature or to the torsion fields and then ask for the conditions to get an accelerated expansion. Exact accelerated expanding solutions can be achieved for several fourth or...

Electromagnetic processes associated with a charged particle moving in a strong circular magnetic field are considered in cylindrical coordinates. We investigate the relation between the vacuum curvature emission and Cherenkov emission and argue that, for the superluminal motion of a particle in the inhomogeneous magnetic field in a dielectric, the combined effects of magnetic field inhomogenei...

Although wave optics is the standard method of analyzing systems composed of a sequence of lenses separated by arbitrary distances, it is often easier and more intuitive to ascertain the function and properties of such systems by tracing a few rays through them. Determining the location, magnification or scale factor, and field curvature associated with images and Fourier transforms by tracing ...

The transport properties of finite nanotubes placed in a magnetic field parallel to their axes are investigated. Upon including spin-orbit coupling and curvature effects, two main phenomena are analyzed that crucially depend on the tube’s chirality: (i) Finite carbon nanotubes in a parallel magnetic field may present a suppression of current due to the localization at the edges of otherwise con...

This paper proposes a potential field-based method for high speed navigation of unmanned ground vehicles (UGVs) on uneven terrain. A potential field is generated in the two-dimensional “trajectory space” of the UGV path curvature and longitudinal velocity. Dynamic constraints, terrain conditions, and navigation conditions can be expressed in this space. A maneuver is chosen within a set of perf...

We introduce a family of conditions on a simplicial complex that we call local klargeness (k ≥ 6 is an integer). They are simply stated, combinatorial and easily checkable. One of our themes is that local 6-largeness is a good analogue of the nonpositive curvature: locally 6-large spaces have many properties similar to nonpositively curved ones. However, local 6-largeness neither implies nor is...

This paper shows that the continuous shearlet transform, a novel directional multiscale transform recently introduced by the authors and their collaborators, provides a precise geometrical characterization for the boundary curves of very general planar regions. This study is motivated by imaging applications, where such boundary curves represent edges of images. The shearlet approach is able to...

Given the Finsler structure (M, F) on a manifold M, a Riemannian structure (M, h) and a linear connection on M are defined. They are obtained as the " average " of the Finsler structure and the Chern connection. This linear connection is the Levi-Civita connection of the Riemannian metric h. The relation between parallel transport of the Chern connection and the Levi-Civita connection of h are ...

We discuss second-order cosmological perturbations on super-Hubble scales, in a scalar field dominated universe, such as during single field inflation. In this contest we show that the gauge-invariant curvature perturbations defined on the uniform density and comoving hypersurfaces coincide and that perturbations are adiabatic in the large scale limit. Since it has been recently shown that the ...