Norm inequalities for vector functions

We study vector functions of ${\mathbb R}^n$ into itself, which are of the form $x \mapsto g(|x|)x\,,$ where $g : (0,\infty) \to (0,\infty)$ is a continuous function and call these radial functions. In the case when $g(t) = t^c$ for some $c \in {\mathbb R}\,,$ we find upper bounds for the distance of image points under such a radial function. Some of our results refine recent results of L. Maligranda and S. Dragomir. In particular, we study quasiconformal mappings of this simple type and obtain norm inequalities for such mappings.Comment: 19 page

Alien Registration- Lundell, Matti A. (Paris, Oxford County)

https://digitalmaine.com/alien_docs/21113/thumbnail.jp

The Electroweak Phase Transition in Ultra Minimal Technicolor

We unveil the temperature-dependent electroweak phase transition in new extensions of the Standard Model in which the electroweak symmetry is spontaneously broken via strongly coupled, nearly-conformal dynamics achieved by the means of multiple matter representations. In particular, we focus on the low energy effective theory introduced to describe Ultra Minimal Walking Technicolor at the phase transition. Using the one-loop effective potential with ring improvement, we identify regions of parameter space which yield a strong first order transition. A striking feature of the model is the existence of a second phase transition associated to the electroweak-singlet sector. The interplay between these two transitions leads to an extremely rich phase diagram.Comment: 38 RevTeX pages, 9 figure

Electromagnetic wormholes and virtual magnetic monopoles

We describe new configurations of electromagnetic (EM) material parameters, the electric permittivity $\epsilon$ and magnetic permeability $\mu$, that allow one to construct from metamaterials objects that function as invisible tunnels. These allow EM wave propagation between two points, but the tunnels and the regions they enclose are not detectable to EM observations. Such devices function as wormholes with respect to Maxwell's equations and effectively change the topology of space vis-a-vis EM wave propagation. We suggest several applications, including devices behaving as virtual magnetic monopoles.Comment: 4 pages, 3 figure

Optimization in random field Ising models by quantum annealing

We investigate the properties of quantum annealing applied to the random field Ising model in one, two and three dimensions. The decay rate of the residual energy, defined as the energy excess from the ground state, is find to be $e_{res}\sim \log(N_{MC})^{-\zeta}$ with $\zeta$ in the range $2...6$, depending on the strength of the random field. Systems with ``large clusters'' are harder to optimize as measured by $\zeta$. Our numerical results suggest that in the ordered phase $\zeta=2$ whereas in the paramagnetic phase the annealing procedure can be tuned so that $\zeta\to6$.Comment: 7 pages (2 columns), 9 figures, published with minor changes, one reference updated after the publicatio

Elastic lines on splayed columnar defects studied numerically

We investigate by exact optimization method properties of two- and three-dimensional systems of elastic lines in presence of splayed columnar disorder. The ground state of many lines is separable both in 2d and 3d leading to a random walk -like roughening in 2d and ballistic behavior in 3d. Furthermore, we find that in the case of pure splayed columnar disorder in contrast to point disorder there is no entanglement transition in 3d. Entanglement can be triggered by perturbing the pure splay system with point defects.Comment: 9 pages, 11 figures. Accepted for publication in PR