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Register a new userSome consequences of $mathrm{TD}$ and $mathrm{sTD}$
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Strongly Turing determinacy, or $mathrm{sTD}$, says that for any set $A$ of reals, if $forall xexists ygeq_T x (yin A)$, then there is a pointed set $Psubseteq A$. We prove the following consequences of Turing determinacy ($mathrm{TD}$) and $mathrm{sTD}$: (1). $mathrm{ZF+TD}$ implies weakly dependent choice ($mathrm{wDC}$). (2). $mathrm{ZF+sTD}$ implies that every set of reals is measurable and has Baire property. (3). $mathrm{ZF+sTD}$ implies that every uncountable set of reals has a perfect subset. (4). $mathrm{ZF+sTD}$ implies that for any set of reals $A$ and any $epsilon>0$, (a) there is a closed set $Fsubseteq A$ so that $mathrm{Dim_H}(F)geq mathrm{Dim_H}(A)-epsilon$. (b) there is a closed set $Fsubseteq A$ so that $mathrm{Dim_P}(F)geq mathrm{Dim_P}(A)-epsilon$.
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The iron-based superconductors are characterized by strong fluctuations due to high transition temperatures and small coherence lengths. We investigate fluctuation behavior in the magnetic iron-pnictide superconductor $mathrm{Rb}mathrm{Eu}mathrm{Fe}_{4}mathrm{As}_{4}$ by calorimetry and transport. We find that the broadening of the specific-heat transition in magnetic fields is very well described by the lowest-Landau-level scaling. We report calorimetric and transport observations for vortex-lattice melting, which is seen as a sharp drop of the resistivity and a step of the specific heat at the magnetic-field-dependent temperature. The melting line in the temperature/magnetic-field plane lies noticeably below the upper-critical-field line and its location is in quantitative agreement with theoretical predictions without fitting parameters. Finally, we compare the melting behavior of $mathrm{Rb}mathrm{Eu}mathrm{Fe}_{4}mathrm{As}_{4}$ with other superconducting materials showing that thermal fluctuations of vortices are not as prevalent as in the high-temperature superconducting cuprates, yet they still noticeably influence the properties of the vortex matter.
We study the seasonal evolution of Titans lower stratosphere (around 15~mbar) in order to better understand the atmospheric dynamics and chemistry in this part of the atmosphere. We analysed Cassini/CIRS far-IR observations from 2006 to 2016 in order to measure the seasonal variations of three photochemical by-products: $mathrm{C_4H_2}$, $mathrm{C_3H_4}$, and $mathrm{C_2N_2}$. We show that the abundances of these three gases have evolved significantly at northern and southern high latitudes since 2006. We measure a sudden and steep increase of the volume mixing ratios of $mathrm{C_4H_2}$, $mathrm{C_3H_4}$, and $mathrm{C_2N_2}$ at the south pole from 2012 to 2013, whereas the abundances of these gases remained approximately constant at the north pole over the same period. At northern mid-latitudes, $mathrm{C_2N_2}$ and $mathrm{C_4H_2}$ abundances decrease after 2012 while $mathrm{C_3H_4}$ abundances stay constant. The comparison of these volume mixing ratio variations with the predictions of photochemical and dynamical models provides constraints on the seasonal evolution of atmospheric circulation and chemical processes at play.
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The existence of a new force beyond the Standard Model is compelling because it could explain several striking astrophysical observations which fail standard interpretations. We searched for the light vector mediator of this dark force, the $mathrm{U}$ boson, with the KLOE detector at the DA$Phi$NE $mathrm{e}^{+}mathrm{e}^{-}$ collider. Using an integrated luminosity of 1.54 fb$^{-1}$, we studied the process $mathrm{e}^{+}mathrm{e}^{-} to mathrm{U}gamma$, with $mathrm{U} to mathrm{e}^{+}mathrm{e}^{-}$, using radiative-return to search for a resonant peak in the dielectron invariant-mass distribution. We did not find evidence for a signal, and set a 90%~CL upper limit on the mixing strength between the Standard Model photon and the dark photon, $varepsilon^2$, at $10^{-6}$--$10^{-4}$ in the 5--520~MeV/c$^2$ mass range.
The ${}^{12}mathrm{C}(alpha,gamma){}^{16}mathrm{O}$ reaction plays a key role in the evolution of stars with masses of $M >$ 0.55 $M_odot$. The cross-section of the ${}^{12}mathrm{C}(alpha,gamma){}^{16}mathrm{O}$ reaction within the Gamow window ($E_textrm{c.m.}$ = 300 keV, $T_textrm9$ = 0.2) is extremely small (about $10^{-17}$ barn), which makes the direct measurement in a ground-based laboratory with existing techniques unfeasible. Up until now, the cross-sections at lower energies can only be extrapolated from the data at higher energies. However, two subthreshold resonances, located at $E_x$ = 7.117 MeV and $E_x$ = 6.917 MeV, make this extrapolation more complicated. In this work, the 6.917 MeV subthreshold resonance in the ${}^{12}mathrm{C}(alpha,gamma){}^{16}mathrm{O}$ reaction was investigated via the ${}^{12}mathrm{C}({}^{11}mathrm{B},{}^{7}mathrm{Li}){}^{16}mathrm{O}$ reaction. The experiment was performed using the Q3D magnetic spectrograph at the HI-13 tandem accelerator. We measured the angular distribution of the ${}^{12}mathrm{C}({}^{11}mathrm{B},{}^{7}mathrm{Li}){}^{16}mathrm{O}$ transfer reaction leading to the 6.917 MeV state. Based on the FRDWBA analysis, we derived the asymptotic normalization coefficient (ANC) of the 6.917 MeV level in $^{16}$O to be (1.10 $pm$ 0.29) $times 10^{10}$ fm$^{-1}$, with which the reduced $alpha$ width was computed to be $18.0pm4.7$ keV at the channel radius of 6.5 fm. Finally, we calculated the astrophysical $S_{E2}(300)$ factor of the ground-state transitions to be 46.2 $pm$ 7.7 keV b. The result for the astrophysical $S_{E2}(300)$ factor confirms the values obtained in various direct and indirect measurements and presents an independent examination of the most important data in nuclear astrophysics.
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