Relationship between Interplanetary Conditions and Changes in the Geomagnetic Field to Understand the Causes of Geomagnetically Induced Currents

Geomagnetically Induced Currents (GICs) are electrical currents induced in ground-level conductive networks, like power lines and pipelines, which can cause costly damage to infrastructure. GICs are induced in response to fast changes in the geomagnetic field (GMF) according to Faraday’s Law of Electromagnetic Induction. The purpose of this study was to identify the parameters of the solar wind and interplanetary shocks which are most strongly correlated with large, fast changes in the magnitude of the GMF. GMF data is 1-min averaged time series of mid- and high-latitude magnetometer measurements in the Sym/H and AL indices, respectively. For solar wind data, I used an existing database of fast-forward interplanetary shocks compiled from measurements made by the WIND spacecraft. I performed t-tests, and created linear fits to determine which parameter(s) are likely responsible for large 1-min changes in the Sym/H and AL indices. Large changes in Sym/H are most strongly correlated with speed jump at the shock and the change in the square root of dynamic pressure and large changes in AL with speed jump at the shock. To determine the causes of events with larger 1-min changes than the fit, I created a subset of shocks which follow the trend with the same distribution as the outliers to find causes for the outliers. This revealed that faster shock and stronger upstream magnetic field are associated with stronger GMF changes

Factorizing FF-matrices and the XXZ spin-1/2 chain: A diagrammatic perspective

Using notation inherited from the six-vertex model, we construct diagrams that represent the action of the factorizing $F$-matrices associated to the finite length XXZ spin-1/2 chain. We prove that these $F$-matrices factorize the tensor $R^{\sigma}_{1... n}$ corresponding with elements of the permutation group. We consider in particular the diagram for the tensor $R^{\sigma_c}_{1... n}$, which cyclically permutes the spin chain. This leads us to a diagrammatic construction of the local spin operators $S_i^{\pm}$ and $S_i^{z}$ in terms of the monodromy matrix operators.Comment: 26 pages, extra references added, typographical errors correcte

Integrability of the Wess_Zumino-Witten model as a non-ultralocal theory

We consider the 2--dimensional Wess--Zumino--Witten (WZW) model in the canonical formalism introduced in a previous paper by two of us. Using an $r$--$s$ matrix approach to non--ultralocal field theories we find the Poisson algebra of monodromy matrices and of conserved quantities with a new, non--dynamical, $r$ matrix.Comment: Revised version. 3 references added. 13 pages, latex, no figure

Open spin chains with generic integrable boundaries: Baxter equation and Bethe ansatz completeness from SOV

We solve the longstanding problem to define a functional characterization of the spectrum of the transfer matrix associated to the most general spin-1/2 representations of the 6-vertex reflection algebra for general inhomogeneous chains. The corresponding homogeneous limit reproduces the spectrum of the Hamiltonian of the spin-1/2 open XXZ and XXX quantum chains with the most general integrable boundaries. The spectrum is characterized by a second order finite difference functional equation of Baxter type with an inhomogeneous term which vanishes only for some special but yet interesting non-diagonal boundary conditions. This functional equation is shown to be equivalent to the known separation of variable (SOV) representation hence proving that it defines a complete characterization of the transfer matrix spectrum. The polynomial character of the Q-function allows us then to show that a finite system of equations of generalized Bethe type can be similarly used to describe the complete transfer matrix spectrum.Comment: 28 page

Local density dependent potential for compressible mesoparticles

We focus on finding a coarse grained description able to reproduce the thermodynamic behavior of a molecular system by using mesoparticles representing several molecules. Interactions between mesoparticles are modelled by an interparticle potential, and an additional internal equation of state is used to account for the thermic contribution of coarse grained internal degrees of freedom. Moreover, as strong non-equilibrium situations over a wide range of pressure and density are targeted, the internal compressibility of these mesoparticles has to be considered. This is done by introducing a dependence of the potential on the local environment of the mesoparticles, either by defining a spherical local density or by means of a Voronoi tessellation. As an example, a local density dependent potential is fitted to reproduce the Hugoniot curve of a model of nitromethane, where each mesoparticle represents one thousand molecules