Abstract:
CeAu2Si2 is a newly discovered pressure-induced heavy fermion superconductor which shows very unusual interplay between superconductivity and magnetism under pressure. Here we compare the results of high-pressure measurements on single crystalline CeAu2Si2 samples with different levels of disorder. It is found that while the magnetic properties are essentially sample independent, superconductivity is rapidly suppressed when the residual resistivity of the sample increases. We show that the depression of bulk Tc can be well understood in terms of pair breaking by nonmagnetic disorder, which strongly suggests an unconventional pairing state in pressurized CeAu2Si2. Furthermore, increasing the level of disorder leads to the emergence of another phase transition at T* within the magnetic phase, which might be in competition with superconductivity.

Abstract:
URu$_2$Si$_2$ is surely one of the most mysterious of the heavy-fermion compounds. Despite more than twenty years of experimental and theoretical works, the order parameter of the transition at $T_0 = 17.5$ K is still unknown. The state below $T_0$ remains called "hidden-order phase" and the stakes are still to identify the energy scales driving the system to this phase. We present new magnetoresistivity and magnetization measurements performed on very-high-quality single crystals in pulsed magnetic fields up to 60 T. We show that the transition to the hidden-order state in URu$_2$Si$_2$ is initially driven by a high-temperature crossover at around 40-50 K, which is a fingerprint of inter-site electronic correlations. In a magnetic field $\mathbf{H}$ applied along the easy-axis $\bf{c}$, the vanishing of this high-temperature scale precedes the polarization of the magnetic moments, as well as it drives the destabilization of the hidden-order phase. Strongly impurity-dependent magnetoresistivity confirms that the Fermi surface is reconstructed below $T_0$ and is strongly modified in a high magnetic field applied along $\mathbf{c}$, i.e. at a sufficiently-high magnetic polarization. The possibility of a sharp crossover in the hidden-order state controlled by a field-induced change of the Fermi surface is pointed out.

Abstract:
The San Andreas fault (SAF) in the USA is one of the most investigated self-organizing systems in nature. In this paper, we studied some geophysical properties of the SAF system in order to analyze the behavior of earthquakes in the context of Tsallis's $q$--Triplet. To that end, we considered 134,573 earthquake events in magnitude interval $2\leq m<8$, taken from the Southern Earthquake Data Center (SCEDC, 1932 - 2012). The values obtained ("$q$--Triplet"$\equiv$$\{$$q$$_{stat}$,$q$$_{sen}$,$q$$_{rel}$$\}$) reveal that the $q_{stat}$--Gaussian behavior of the aforementioned data exhibit long-range temporal correlations. Moreover, $q_{sen}$ exhibits quasi-monofractal behavior with a Hurst exponent of 0.87.

Abstract:
We analyze algorithms that output absolutely normal numbers digit-by-digit with respect to quality of convergence to normality of the output, measured by the discrepancy. We consider explicit variants of algorithms by Sierpinski, by Turing and an adaption of constructive work on normal numbers by Schmidt. There seems to be a trade-off between the complexity of the algorithm and the speed of convergence to normality of the output.

Abstract:
Copeland and Erd\H{o}s showed that the concatenation of primes when written in base $10$ yields a real number that is normal to base $10$. We generalize this result to Pisot number bases in which all integers have finite expansion.

Abstract:
We report magnetization and magnetoresistivity measurements on the isostructural ferromagnetic superconductors UCoGe and URhGe in magnetic fields up to 60 T and temperatures from 1.5 to 80 K. At low-temperature, a moment polarization in UCoGe in a field $\mu_0\mathbf{H}\parallel\mathbf{b}$ of around 50 T leads to well-defined anomalies in both magnetization and magnetoresistivity. These anomalies vanish in temperatures higher than 30-40 K, where maxima in the magnetic susceptibility and the field-induced variation of the magnetoresistivity are found. A comparison is made between UCoGe and URhGe, where a moment reorientation in a magnetic field $\mu_0\mathbf{H}\parallel\mathbf{b}$ of 12 T leads to field-induced reentrant superconductivity.

Abstract:
Superconductivity in underdoped cuprates emerges from an unusual electronic state characterised by nodal quasiparticles and an antinodal pseudogap. The relation between this state and superconductivity is intensely studied but remains controversial. The discrimination between competing theoretical models is hindered by a lack of electronic structure data from related doped Mott insulators. Here we report the doping evolution of the Heisenberg antiferromagnet Sr$_2$IrO$_4$, a close analogue to underdoped cuprates. We demonstrate that metallicity emerges from a rapid collapse of the Mott gap with doping, resulting in lens-like Fermi contours rather than disconnected Fermi arcs as observed in cuprates. Intriguingly though, the emerging electron liquid shows nodal quasiparticles with an antinodal pseudogap and thus bares strong similarities with underdoped cuprates. We conclude that anisotropic pseudogaps are a generic property of two-dimensional doped Mott insulators rather than a unique hallmark of cuprate high-temperature superconductivity.

Abstract:
We present measurements of the resistivity $\rho_{x,x}$ of URu2Si2 high-quality single crystals in pulsed high magnetic fields up to 81~T at a temperature of 1.4~K and up to 60~T at temperatures down to 100~mK. For a field \textbf{H} applied along the magnetic easy-axis \textbf{c}, a strong sample-dependence of the low-temperature resistivity in the hidden-order phase is attributed to a high carrier mobility. The interplay between the magnetic and orbital properties is emphasized by the angle-dependence of the phase diagram, where magnetic transition fields and crossover fields related to the Fermi surface properties follow a 1/$\cos\theta$-law, $\theta$ being the angle between \textbf{H} and \textbf{c}. For $\mathbf{H}\parallel\mathbf{c}$, a crossover defined at a kink of $\rho_{x,x}$, as initially reported in [Shishido et al., Phys. Rev. Lett. \textbf{102}, 156403 (2009)], is found to be strongly sample-dependent: its characteristic field $\mu_0H^*$ varies from $\simeq20$~T in our best sample with a residual resistivity ratio RRR of $225$ to $\simeq25$~T in a sample with a RRR of $90$. A second crossover is defined at the maximum of $\rho_{x,x}$ at the sample-independent characteristic field $\mu_0H_{\rho,max}^{LT}\simeq30$~T. Fourier analyzes of SdH oscillations show that $H_{\rho,max}^{LT}$ coincides with a sudden modification of the Fermi surface, while $H^*$ lies in a regime where the Fermi surface is smoothly modified. For $\mathbf{H}\parallel\mathbf{a}$, i) no phase transition is observed at low temperature and the system remains in the hidden-order phase up to 81~T, ii) quantum oscillations surviving up to 7~K are related to a new and almost-spherical orbit - for the first time observed here - at the frequency $F_\lambda\simeq1400$~T and associated with a low effective mass $m^*_\lambda=(1\pm0.5)\cdot m_0$, and iii) no Fermi surface modification occurs up to 81~T.

Abstract:
We present measurements of the magnetoresistivity RHOxx of URu2Si2 single crystals in high magnetic fields up to 60 T and at temperatures from 1.4 K to 40 K. Different orientations of the magnetic field have been investigated permitting to follow the dependence on Q of all magnetic phase transitions and crossovers, where Q is the angle between the magnetic field and the easy-axis c. We find out that all magnetic transitions and crossovers follow a simple 1/cos(Q) -law, indicating that they are controlled by the projection of the field on the c-axis.

Abstract:
In this work, we compare the two approximations of a path-connected space $X$, by the Ganea spaces $G_n(X)$ and by the realizations $\|\Lambda_\bullet X\|_{n}$ of the truncated simplicial resolutions emerging from the loop-suspension cotriple $\Sigma\Omega$. For a simply connected space $X$, we construct maps $\|\Lambda_\bullet X\|_{n-1}\to G_n(X)\to \|\Lambda_\bullet X\|_{n}$ over $X$, up to homotopy. In the case $n=2$, we prove the existence of a map $G_2(X)\to\|\Lambda_\bullet X\|_{1}$ over $X$ (up to homotopy) and conjecture that this map exists for any $n$.