Inequalities for Light Nuclei in the Wigner Symmetry Limit

Using effective field theory we derive inequalities for light nuclei in the Wigner symmetry limit. This is the limit where isospin and spin degrees of freedom can be interchanged. We prove that the energy of any three-nucleon state is bounded below by the average energy of the lowest two-nucleon and four-nucleon states. We show how this is modified by lowest-order terms breaking Wigner symmetry and prove general energy convexity results for SU(N). We also discuss the inclusion of Wigner-symmetric three and four-nucleon force terms.Comment: 10 page

Non-linear Weibel-type Soliton Modes

Discussion is given of non-linear soliton behavior including coupling between electrostatic and electromagnetic potentials for non-relativistic, weakly relativistic, and fully relativistic plasmas. For plasma distribution functions that are independent of the canonical momenta perpendicular to the soliton spatial structure direction there are, in fact, no soliton behaviors allowed because transverse currents are zero. Dependence on the transverse canonical momenta is necessary. When such is the case, it is shown that the presence or absence of a soliton is intimately connected to the functional form assumed for the particle distribution functions. Except for simple situations, the coupled non-linear equations for the electrostatic and electromagnetic potentials would seem to require numerical solution procedures. Examples are given to illustrate all of these points for non-relativistic, weakly relativistic, and fully relativistic plasmas.Comment: Accepted for publication at Journal of Physics A: Mathematical and Theoretica

Benchmarking the performance of controllers for power grid transient stability

As the energy transition transforms power grids across the globe, it poses several challenges regarding grid design and control. In particular, high levels of intermittent renewable generation complicate the task of continuously balancing power supply and demand, requiring sufficient control actions. Although there exist several proposals to control the grid, most of them have not demonstrated to be cost efficient in terms of optimal control theory. Here, we mathematically formulate an optimal centralized (therefore non-local) control problem for stable operation of power grids and determine the minimal amount of active power necessary to guarantee a stable service within the operational constraints, minimizing a suitable cost function at the same time. This optimal control can be used to benchmark control proposals and we demonstrate this benchmarking process by investigating the performance of three distributed controllers, two of which are fully decentralized, that have been recently studied in the physics and power systems engineering literature. Our results show that cost efficient controllers distribute the controlled response amongst all nodes in the power grid. Additionally, superior performance can be achieved by incorporating sufficient information about the disturbance causing the instability. Overall, our results can help design and benchmark secure and cost-efficient controllers

The evaluation of liquefaction potential of oil-containing sand under cyclic loading

Risk and Reliability in Geotechnical Engineerin

Magnetic light

In this paper we report on the observation of novel and highly unusual magnetic state of light. It appears that in small holes light quanta behave as small magnets so that light propagation through such holes may be affected by magnetic field. When arrays of such holes are made, magnetic light of the individual holes forms novel and highly unusual two-dimensional magnetic light material. Magnetic light may soon become a great new tool for quantum communication and computing.Comment: Submitted to Phys.Rev.Lett., 3 figure