Enumeration of chord diagrams on many intervals and their non-orientable analogs

Two types of connected chord diagrams with chord endpoints lying in a collection of ordered and oriented real segments are considered here: the real segments may contain additional bivalent vertices in one model but not in the other. In the former case, we record in a generating function the number of fatgraph boundary cycles containing a fixed number of bivalent vertices while in the latter, we instead record the number of boundary cycles of each fixed length. Second order, non-linear, algebraic partial differential equations are derived which are satisfied by these generating functions in each case giving efficient enumerative schemes. Moreover, these generating functions provide multi-parameter families of solutions to the KP hierarchy. For each model, there is furthermore a non-orientable analog, and each such model likewise has its own associated differential equation. The enumerative problems we solve are interpreted in terms of certain polygon gluings. As specific applications, we discuss models of several interacting RNA molecules. We also study a matrix integral which computes numbers of chord diagrams in both orientable and non-orientable cases in the model with bivalent vertices, and the large-N limit is computed using techniques of free probability.Comment: 23 pages, 7 figures; revised and extended versio

Cluster PEACE observations of electron pressure tensor divergence in the magnetotail

Cluster crossed the magnetotail neutral sheet on four occasions between 16: 38 and 16: 43 UT on 08/17/2003. The four-spacecraft capabilities of Cluster are used to determine spatial gradients from the magnetic field vectors and, for the first time, full electron pressure tensors. We find that the contribution to the electric field from the Hall term (max of similar to 6 mV/m) pointed towards the neutral sheet, whereas that from the electron pressure divergence ( max of similar to 1 mV/m) pointed away from the neutral sheet. The electric field contributions in this direction were closely anti-correlated. During this period Clusters 1 and 4 were sometimes above and below the neutral sheet respectively. This allowed the simultaneous observation of magnetic fields that are interpreted as two quadrants of the Hall magnetic field system. An associated field-aligned current system was detected using the curlometer and moments of the particle distributions

Electric dipole moment oscillations in Aharonov-Bohm quantum rings

Copyright © 2012 American Physical SocietyMagneto-oscillations of the electric dipole moment are predicted and analyzed for a single-electron nanoscale ring pierced by a magnetic flux (an Aharonov-Bohm ring) and subjected to an electric field in the ring's plane. These oscillations are accompanied by periodic changes in the selection rules for interlevel optical transitions in the ring allowing control of polarization properties of the associated terahertz radiation

Saturn's aurora in the January 2004 events

International audienceDifferences in the solar wind interaction with the magnetosphere of Saturn relative to the Earth result from the decrease in the solar wind plasma density and magnetic field strength with distance from the Sun, and from the change in the average angle of the IMF at Saturn's orbit. Other reasons are related to Saturn's rapid rotation and internal magnetospheric plasma sources. Moreover, the IMF structure observed by Cassini in 2003?2004 during the approach to Saturn is consistent with corotating interaction regions (CIRs) existing during the declining phase of the solar cycle. Two cases on 16 and 26 January 2004 are considered when disturbances in the solar wind passed Cassini and then Saturn. After the solar wind shock encountered the kronian magnetosphere, the auroral oval became brighter (especially at dawn) with a reduced radius. In these cases the auroral power was anti-correlated with the radius of the oval. Possible mechanisms responsible for such unexpected behavior are presented and discussed in detail

Measurement of the neutron electric dipole moment by crystal diffraction

An experiment using a prototype setup to search for the neutron electric dipole moment by measuring spin-rotation in a non-centrosymmetric crystal (quartz) was carried out to investigate statistical sensitivity and systematic effects of the method. It has been demonstrated that the concept of the method works. The preliminary result of the experiment is $d_{\rm n}=(2.5\pm 6.5)\cdot 10^{-24}$ e$\cdot$cm. The experiment showed that an accuracy of $\sim 2.5\cdot 10^{-26}$ e$\cdot$cm can be obtained in 100 days data taking, using available quartz crystals and neutron beams.Comment: 13 pages, 4 figure

Patch Antenna for Measuring the Internal Temperature of Biological Objects Using the Near-Field Microwave Radiometric Method

The near-field microwave antenna with central frequency of 2.23 GHz has been designed and manufactured to be used as a part of the medical microwave radiometric system. Experimental studies of the reflection coefficient in different parts of the human body were conducted using the developed antenna. The experimental studies were carried out in a group of volunteers with normal somatic growth. The results of the experiments were used to perform the analysis of the potential errors in the measurements obtained via the developed antenna

Aharonov-Bohm quantum rings in high-Q microcavities

Copyright © 2013 American Physical SocietyA single-mode microcavity with an embedded Aharonov-Bohm quantum ring, which is pierced by a magnetic flux and subjected to a lateral electric field, is studied theoretically. It is shown that external electric and magnetic fields provide additional means of control of the emission spectrum of the system. In particular, when the magnetic flux through the quantum ring is equal to a half-integer number of the magnetic flux quantum, a small change in the lateral electric field allows tuning of the energy levels of the quantum ring into resonance with the microcavity mode providing an efficient way to control the quantum ring-microcavity coupling strength. Emission spectra of the system are calculated for several combinations of the applied magnetic and electric fields