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The existence of time-periodic stochastic motions of an incompressible fluid is obtained. Here the fluid is subject to a time-periodic body force and an additional time-periodic stochastic force that is produced by a rigid body moves periodically stochastically with the same period in the fluid.
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We have examined the effect of V doping on the electronic and optical properties of epitaxial hematite (α-Fe{sub 2}O{sub 3}) thin films, by employing several characterization techniques and computational modeling. The conductivity of α-(Fe{sub 1-x}V{sub x}){sub 2}O{sub 3} (0 ≤ x ≤ ∼0.5) is enhanced by several orders of magnitude as x is increased, as evidenced by electrical resistivity measurements and x-ray photoelectron spectroscopy core-level and valence-band spectra. Optical absorption shows a reduction in the direct band gap by as much as 0.64 eV for x = 0.53 (E{sub g} = 1.46 eV) relative to that of α-Fe{sub 2}O{sub 3} (E{sub g} = 2.10 eV). Detailed understanding of the character of the optical transitions in the alloys is achieved using first-principles calculations of the ground and excited states. These calculations reveal that V doping results in occupied V 3d orbitals hybridized with Fe orbitals and located at approximately mid-gap in α-Fe{sub 2}O{sub 3}. The lowest energy transitions involve charge transfer from occupied V 3d to unoccupied Fe 3d* orbitals. With a low band gap and high conductivity, α-(Fe{sub 1-x}V{sub x}){sub 2}O{sub 3} is a promising material for photovoltaic and photoelectrochemical applications.
In order to characterize the Madison Symmetric Torus (MST) reversed-field pinch(RFP)plasmas that bifurcate to a helical equilibrium, the V3FIT equilibrium reconstruction code was modified to include a conducting boundary. RFPplasmas become helical at a high plasma current, which induces large eddy currents in MST's thick aluminum shell. The V3FIT conducting boundary accounts for the contribution from these eddy currents to external magnetic diagnostic coil signals. This implementation of V3FIT was benchmarked against MSTFit, a 2D Grad-Shafranov solver, for axisymmetric plasmas. The two codes both fit B measurement loops around the plasma minor diameter with qualitative agreement between each other and the measured field. Fits in the 3D case converge well, with q-profile and plasma shape agreement between two distinct toroidal locking phases. Greater than 60% of the measured n = 5 component of B at r = a is due to eddy currents in the shell, as calculated by the conducting boundary model.
We attempt to explain simultaneously the Galactic center gamma-ray excess and the 3.5 keV X-ray line from the Perseus cluster based on a class of non-abelian SU(2) DM models, in which the dark matter and an excited state comprise a “dark” SU(2) doublet. The non-abelian group kinetically mixes with the standard model gauge group via dimensions-5 operators. The dark matter particles annihilate into standard model fermions, followed by fragmentation and bremsstrahlung, and thus producing a continuous spectrum of gamma-rays. On the other hand, the dark matter particles can annihilate into a pair of excited states, each of which decays back into the dark matter particle and an X-ray photon, which has an energy equal to the mass difference between the dark matter and the excited state, which is set to be 3.5 keV. The large hierarchy between the required X-ray and γ-ray annihilation cross-sections can be achieved by a very small kinetic mixing between the SM and dark sector, which effectively suppresses the annihilation into the standard model fermions but not into the excited state.
Observations with the Fermi Large Area Telescope (LAT) indicate a possible small photon signal originating from the dwarf galaxy Reticulum II that exceeds the expected background between 2 GeV and 10 GeV. We have investigated two specific scenarios for annihilating WIMP dark matter within the phenomenological Minimal Supersymmetric Standard Model (pMSSM) framework as a possible source for these photons. We find that the same parameter ranges in pMSSM as reported by an earlier paper to be consistent with the Galactic Center excess, are also consistent with the excess observed in Reticulum II, resulting in a J-factor of log{sub 10} (J(α{sub int}=0.5{sup ∘}))≃(20.3−20.5){sub −0.3}{sup +0.2} GeV{sup 2}cm{sup −5}. This J-factor is consistent with log{sub 10} (J(α{sub int}=0.5{sup ∘}))=19.6{sub −0.7}{sup +1.0} GeV{sup 2}cm{sup −5}, which was derived using an optimized spherical Jeans analysis of kinematic data obtained from the Michigan/Magellan Fiber System (M2FS)
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