Necessary conditions for having wormholes in f(R) gravity

For a generic $f(R)$ which admits a polynomial expansion of at least third order (i.e. $\frac{d^{3}f}{dR^{3}}\neq 0$) we find the near-throat wormhole solution. Necessary conditions for the existence of wormholes in such $f(R)$ theories are derived for both zero and non-zero matter sources. A particular choice of energy-momentum reveals that the wormhole geometry satisfies the weak energy condition (WEC). For a range of parameters even the strong energy condition (SEC) is shown to be satisfied.Comment: 7 pages, 1 figur

Cloud of strings as source in 2+12+1-dimensional f(R)=Rnf( R) = R^n gravity

We present three parameters exact solutions with possible black holes in $2+1-$dimensional $f\left( R\right) =R^{n}$ modified gravity coupled minimally to a cloud of strings. These three parameters are $n,$ the cloud of string coupling constant $\xi$ and an integration constant $C$. Although in general one has to consider each set of parameters separately; for $n$ an even integer greater than one we give a unified picture providing black holes. For $n\geq 1$ we analyze null / timelike geodesic within the context of particle confinement.Comment: 5 pages, no figures. Revised versio

Absence of Buckling in Nerve Fiber

In this study we give a geometrical model which employs the smoothness of nerve fibers as differentiable curves. We show that a nerve fiber may encounter large curvature due to the possible helicial bending and hence it could cause the fiber to buckle. However, its membrane structure provides a mechanism, entirely geometrical to avoid it. To overcome the challenge of emerging helix we project it into a plane.Comment: 7 pages no figure. Final version presented at The 10th International Physics Conference of the Balkan Physical Union (BPU10), 26-30 August 2018. To be published in AIP Conference Proceeding