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Borexino detector is composed of 2214 photomultipliers (PMTs) collecting the scintillation light produced by the liquid scintillator. Phototubes are partially immersed in the scintillator and partially in high purity water. A proper electrical and mechanical selection of the devices as well as a custom-made encapsulation was mandatory for a long-term immersion in these two aggressive liquid. Underwater cables and connectors and optical fibers are also described in detail.

We consider here nonalternating knots and their properties. Specifically, we show certain classes of knots have nontrivial Jones polynomials.

We compute the bridge spectra of cables of 2-bridge knots. We also give some results about bridge spectra and distance of Montesinos knots.

We compute Kauffman's potential function (equivalent to the Conway polynomial) for any solvable fibered link. Solvable links are links that can be built from the unknot by iterated cabling and summing. Links that arise in complex algebraic geometry are generally of this type.

This paper developed a new Hamiltonian nodal position finite element method (FEM) to treat the nonlinear dynamics of cable system in which the large rigid-body motion is coupled with small elastic cable elongation. The FEM is derived from the Hamiltonian theory using canonical coordinates. The resulting Hamiltonian finite element model of cable contains low frequency mode of rigid-body motion and high frequency mode of axial elastic deformation, which is prone to numerical instability due to error accumulation over a very long period. A second-order explicit Symplectic integration scheme is used naturally to enforce the conservation of energy and momentum of the Hamiltonian finite element system. Numerical analyses are conducted and compared with theoretical and experimental results as well as the commercial software LS-DYNA. The comparisons demonstrate that the new Hamiltonian nodal position FEM is numerically efficient, stable and robust for simulation of long-period motion of cable systems.