Symmetry2016, 8(5), 29; doi:10.3390/sym8050029 - published 28 April 2016 Show/Hide Abstract
Abstract: For more than 35 years theorists have studied quantum or Casimir friction, which occurs when two smooth bodies move transversely to each other, experiencing a frictional dissipative force due to quantum electromagnetic fluctuations, which break time-reversal symmetry. These forces are typically very small, unless the bodies are nearly touching, and consequently such effects have never been observed, although lateral Casimir forces have been seen for corrugated surfaces. Partly because of the lack of contact with observations, theoretical predictions for the frictional force between parallel plates, or between a polarizable atom and a metallic plate, have varied widely. Here, we review the history of these calculations, show that theoretical consensus is emerging, and offer some hope that it might be possible to experimentally confirm this phenomenon of dissipative quantum electrodynamics.
Symmetry2016, 8(4), 28; doi:10.3390/sym8040028 - published 21 April 2016 Show/Hide Abstract
Abstract: The improvement in focusing capabilities of a set of annular scatterers arranged in a fractal geometry is theoretically quantified in this work by means of the finite element method (FEM). Two different arrangements of rigid rings in water are used in the analysis. Thus, both a Fresnel ultrasonic lens and an arrangement of rigid rings based on Cantor prefractals are analyzed. Results show that the focusing capacity of the modified fractal lens is better than the Fresnel lens. This new lens is believed to have potential applications for ultrasonic imaging and medical ultrasound fields.
Symmetry2016, 8(4), 25; doi:10.3390/sym8040025 - published 20 April 2016 Show/Hide Abstract
Abstract: The role of the environment initial conditions in the breaking of the time reversal symmetry of effective theories and in generating the soft irreversibility is studied by the help of Closed Time Path formalism. The initial conditions break the time reversal symmetry of the solution of the equation of motion in a trivial manner. When open systems are considered then the initial conditions of the environment must be included in the effective dynamics. This is achieved by means of a generalized ϵ-prescription where the non-uniform convergence of the limit 0 leaves behind a spontaneous breakdown of the time reversal symmetry.
Symmetry2016, 8(4), 27; doi:10.3390/sym8040027 - published 20 April 2016 Show/Hide Abstract
Abstract: In this article, we introduce special divisors (root, line, ruling, exceptional system and rational quartic) in smooth rational surfaces and study their correspondences to subpolytopes in Gosset polytopes . We also show that the sets of rulings and exceptional systems correspond equivariantly to the vertices of and via E-type Weyl action.
Symmetry2016, 8(4), 26; doi:10.3390/sym8040026 - published 20 April 2016 Show/Hide Abstract
Abstract: We review how nuclear forces emerge from low-energy quantum chromodynamics (QCD) via chiral effective field theory (EFT). During the past two decades, this approach has evolved into a powerful tool to derive nuclear two- and many-body forces in a systematic and model-independent way. We then focus on the nucleon-nucleon () interaction and show in detail how, governed by chiral symmetry, the long- and intermediate-range of the potential builds up order by order. We proceed up to sixth order in small momenta, where convergence is achieved. The final result allows for a full assessment of the validity of the chiral EFT approach to the interaction.
Symmetry2016, 8(4), 23; doi:10.3390/sym8040023 - published 18 April 2016 Show/Hide Abstract
Abstract: The recent systematic study by Janocha et al.  to determine all possible Lie-point symmetries for the functional Hopf–Burgers equation is re-examined. From a more consistent theoretical framework, however, some of the proposed symmetry transformations of the considered Hopf–Burgers equation are in fact rejected. Three out of eight proposed symmetry transformations are invalidated, while two of them should be replaced by their correct intermediate formulations, but which ultimately violate internal consistency constraints of the governing equation. It is concluded that the recently proposed symmetry analysis method for functional integro-differential equations should not be adopted when aiming at a consistent and complete approach.