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We present a wide class of differential systems in any dimension that are either integrable or complete integrable. In particular, our result enlarges a known family of planar integrable systems. We give an extensive list of examples that illustrates the applicability of our approach. For instance, in the plane this list includes some Li\'enard, Lotka--Volterra and quadratic systems; in the space, some Kolmogorov, Rikitake and R\"ossler systems. Examples of complete integrable systems in higher dimensions are also provided., Comment: 18 pages

We prove that star-like limit cycles of any planar polynomial system can also be seen either as solutions defined on a given interval of a new associated planar non-autonomous polynomial system or as heteroclinic solutions of a 3-dimensional polynomial system. We illustrate these points of view with several examples. One of the key ideas in our approach is to decompose the periodic solutions as the sum of two suitable functions. As a first application we use these new approaches to prove that all star-like reversible limit cycles are algebraic. As a second application we introduce a function whose zeroes control the periodic orbits that persist as limit cycles when we perturb a star-like reversible center. As far as we know this is the first time that this question is solved in full generality. Somehow, this function plays a similar role that an Abelian integral for studying perturbations of Hamiltonian systems., Comment: 20 pages, 1 figure

Using double quantum dots as the weak link of a Josephson junction, we realize the superconducting analog of the celebrated two-impurity Kondo model. The device shows a cusped current-voltage characteristic, which can be modelled by an overdamped circuit relating the observed cusp current to the Josephson critical current. The gate dependence of the cusp current and of the subgap spectra are used as complementary ground-state indicators to demonstrate gate-tuned changes of the ground state from an inter-dot singlet to independently screened Yu-Shiba-Rusinov (YSR) singlets. In contrast to the two-impurity Kondo effect in normal-state systems, the crossover between these two singlets is heralded by quantum phase boundaries to nearby doublet YSR phases in which only a single spin is screened., Comment: 16 pages, 17 figures

The effect of isothermal pre-oxidation treatments on the \b{eta}-(Ni,Pt)Al + Ren\'e N5 system degradation is here reported. The oxidation treatments were carried out from 900 (mostly {\theta}-Al2O3 growing conditions) to 1200{\deg}C (mainly {\alpha}-Al2O3 growing conditions) for 5 h, under a purified Ar-stream with a fixed pO2= 1 x 10-5 atm. Results are discussed based on the correlation between the structural, microstructural and chemical properties of the \b{eta}-(Ni,Pt)Al BC showing that pre-oxidation parameters have an important effect on the multi-elemental counter diffusion phenomena along BC. For instance, a significant BC+IDZ thickness increase of 55% at 1200 {\deg}C was observed with respect to as-received sample just after 5 h of oxidation resulting in a severe BC degradation., Comment: 18 pages, 7 Figures

An experimental approach based on design of experiments, process maps and the analysis of deposition first stages to improve the biocompatibility of High-Velocity Oxygen Fuel (HVOF) hydroxyapatite (HAp) coatings is here presented. A two-level design of three factors (23) was performed using the stand-off distance (SOD), the fuel-oxygen ratio (F/O) and the powder feed rate (PFR). The effect of these experimental factors on the first stages of the coating formation was investigated to study the physical state of the particles before and after impacting the substrate. This study allowed the selection of the most suitable deposition parameter combinations to obtain HAp coatings with optimal crystallinity (> 45%), Ca/P ratio (approx. 1.67), phase content (> 95% of HAp), which guarantee the coatings mechanical stability and biocompatibility. The behavior of the coating within simulated body fluid (SBF) and cell culture (hFOB) was studied to analyze the apatite layer formation and the extracts cytotoxicity on human osteoblasts, respectively. The results show that the F/O ratio is the most influential factor on temperature and velocity on the in-flight particles and therefore on the coating properties. The SBF results confirmed the formation of an apatite layer after 14 days of immersion. Finally, the mitochondrial activity, measured by the MTS assay, and cell membrane integrity measures by LDH liberation assays, show that the coating released material does not induce toxicity on the exposed cells., Comment: Keywords: HAp coatings, HVOF, Process maps, Design of experiments, in vitro behavior

We demonstrate the Josephson effect in a serial double quantum dot defined in a nanowire with epitaxial superconducting leads. The supercurrent stability diagram adopts a honeycomb pattern with electron-hole and left-right reflection symmetry. We observe sharp discontinuities in the magnitude of the critical current, $I_c$, as a function of dot occupation, related to doublet to singlet ground state transitions. Detuning of the energy levels offers a tuning knob for $I_c$, which attains a maximum at zero detuning. The consistency between experiment and theory indicates that our device is a faithful realization of the two-impurity Anderson model., Comment: 6 pages, 5 figures, Supplemental Material available as ancillary file

We study the superconducting proximity effect in an InAs nanowire contacted by Ta-based superconducting electrodes. Using local bottom gates, we control the potential landscape along the nanowire, tuning its conductance to a quasi-ballistic regime. At high magnetic field ($B$), we observe approximately quantized conductance plateaus associated with the first two spin-polarized one-dimensional modes. For $B < 1$ T, the onset of superconductivity occurs in concomitance with the development of sizeable charge localization leading to a 0.7-type conductance anomaly. In this regime, the proximity supercurrent exhibits an unusual, non-monotonic $B$ dependence. We interpret this finding in terms of a competition between the Kondo effect, dominating near $B=0$, and the Zeeman effect, enforcing spin polarization and the emergence of a $\pi$ phase shift in the Josephson relation at higher $B$.

We report an experimental study of one-dimensional (1D) electronic transport in an InSb semiconducting nanowire. Three bottom gates are used to locally deplete the nanowire creating a ballistic quantum point contact with only a few conducting channels. In a magnetic field, the Zeeman splitting of the corresponding 1D subbands is revealed by the emergence of conductance plateaus at multiples of $e^2$/h, yet we find a quantized conductance pattern largely dependent on the configuration of voltages applied to the bottom gates. In particular, we can make the first plateau disappear leaving a first conductance step of 2$e^2/h$, which is indicative of a remarkable two-fold subband degeneracy that can persist up to several Tesla. For certain gate voltage settings, we also observe the presence of discrete resonant states producing conductance features that can resemble those expected from the opening of a helical gap in the subband structure. We explain our experimental findings through the formation of two spatially separated 1D conduction channels.

We study the number of limit cycles and the bifurcation diagram in the Poincar\'{e} sphere of a one-parameter family of planar differential equations of degree five $\dot {\bf x}=X_b({\bf x})$ which has been already considered in previous papers. We prove that there is a value $b^*>0$ such that the limit cycle exists only when $b\in(0,b^*)$ and that it is unique and hyperbolic by using a rational Dulac function. Moreover we provide an interval of length 27/1000 where $b^*$ lies. As far as we know the tools used to determine this interval are new and are based on the construction of algebraic curves without contact for the flow of the differential equation. These curves are obtained using analytic information about the separatrices of the infinite critical points of the vector field. To prove that the Bendixson-Dulac Theorem works we develop a method for studying whether one-parameter families of polynomials in two variables do not vanish based on the computation of the so called double discriminant., Comment: 33 pages, 14 figures