Discontinuity induced bifurcations of non-hyperbolic cycles in nonsmooth systems

We analyse three codimension-two bifurcations occurring in nonsmooth systems, when a non-hyperbolic cycle (fold, flip, and Neimark-Sacker cases, both in continuous- and discrete-time) interacts with one of the discontinuity boundaries characterising the system's dynamics. Rather than aiming at a complete unfolding of the three cases, which would require specific assumptions on both the class of nonsmooth system and the geometry of the involved boundary, we concentrate on the geometric features that are common to all scenarios. We show that, at a generic intersection between the smooth and discontinuity induced bifurcation curves, a third curve generically emanates tangentially to the former. This is the discontinuity induced bifurcation curve of the secondary invariant set (the other cycle, the double-period cycle, or the torus, respectively) involved in the smooth bifurcation. The result can be explained intuitively, but its validity is proven here rigorously under very general conditions. Three examples from different fields of science and engineering are also reported

Japan as a Victim of Comparative Law

Article published in the Michigan State International Law Review

Uncertainty Quantification of geochemical and mechanical compaction in layered sedimentary basins

In this work we propose an Uncertainty Quantification methodology for sedimentary basins evolution under mechanical and geochemical compaction processes, which we model as a coupled, time-dependent, non-linear, monodimensional (depth-only) system of PDEs with uncertain parameters. While in previous works (Formaggia et al. 2013, Porta et al., 2014) we assumed a simplified depositional history with only one material, in this work we consider multi-layered basins, in which each layer is characterized by a different material, and hence by different properties. This setting requires several improvements with respect to our earlier works, both concerning the deterministic solver and the stochastic discretization. On the deterministic side, we replace the previous fixed-point iterative solver with a more efficient Newton solver at each step of the time-discretization. On the stochastic side, the multi-layered structure gives rise to discontinuities in the dependence of the state variables on the uncertain parameters, that need an appropriate treatment for surrogate modeling techniques, such as sparse grids, to be effective. We propose an innovative methodology to this end which relies on a change of coordinate system to align the discontinuities of the target function within the random parameter space. The reference coordinate system is built upon exploiting physical features of the problem at hand. We employ the locations of material interfaces, which display a smooth dependence on the random parameters and are therefore amenable to sparse grid polynomial approximations. We showcase the capabilities of our numerical methodologies through two synthetic test cases. In particular, we show that our methodology reproduces with high accuracy multi-modal probability density functions displayed by target state variables (e.g., porosity).Comment: 25 pages, 30 figure

Impacts of fragmented accretion streams onto Classical T Tauri Stars: UV and X-ray emission lines

Context. The accretion process in Classical T Tauri Stars (CTTSs) can be studied through the analysis of some UV and X-ray emission lines which trace hot gas flows and act as diagnostics of the post-shock downfalling plasma. In the UV band, where higher spectral resolution is available, these lines are characterized by rather complex profiles whose origin is still not clear. Aims. We investigate the origin of UV and X-ray emission at impact regions of density structured (fragmented) accretion streams.We study if and how the stream fragmentation and the resulting structure of the post-shock region determine the observed profiles of UV and X-ray emission lines. Methods. We model the impact of an accretion stream consisting of a series of dense blobs onto the chromosphere of a CTTS through 2D MHD simulations. We explore different levels of stream fragmentation and accretion rates. From the model results, we synthesize C IV (1550 {\AA}) and OVIII (18.97 {\AA}) line profiles. Results. The impacts of accreting blobs onto the stellar chromosphere produce reverse shocks propagating through the blobs and shocked upflows. These upflows, in turn, hit and shock the subsequent downfalling fragments. As a result, several plasma components differing for the downfalling velocity, density, and temperature are present altoghether. The profiles of C IV doublet are characterized by two main components: one narrow and redshifted to speed $\approx$ 50 km s$^{-1}$ and the other broader and consisting of subcomponents with redshift to speed in the range 200 $\approx$ 400 km s$^{-1}$. The profiles of OVIII lines appear more symmetric than C IV and are redshifted to speed $\approx$ 150 km s$^{-1}$. Conclusions. Our model predicts profiles of C IV line remarkably similar to those observed and explains their origin in a natural way as due to stream fragmentation.Comment: 11 pages, 10 figure

Is there anything new to say about SIFT matching?

SIFT is a classical hand-crafted, histogram-based descriptor that has deeply influenced research on image matching for more than a decade. In this paper, a critical review of the aspects that affect SIFT matching performance is carried out, and novel descriptor design strategies are introduced and individually evaluated. These encompass quantization, binarization and hierarchical cascade filtering as means to reduce data storage and increase matching efficiency, with no significant loss of accuracy. An original contextual matching strategy based on a symmetrical variant of the usual nearest-neighbor ratio is discussed as well, that can increase the discriminative power of any descriptor. The paper then undertakes a comprehensive experimental evaluation of state-of-the-art hand-crafted and data-driven descriptors, also including the most recent deep descriptors. Comparisons are carried out according to several performance parameters, among which accuracy and space-time efficiency. Results are provided for both planar and non-planar scenes, the latter being evaluated with a new benchmark based on the concept of approximated patch overlap. Experimental evidence shows that, despite their age, SIFT and other hand-crafted descriptors, once enhanced through the proposed strategies, are ready to meet the future image matching challenges. We also believe that the lessons learned from this work will inspire the design of better hand-crafted and data-driven descriptors

Relevance of electron spin dissipative processes to dynamic nuclear polarization via thermal mixing

The available theoretical approaches aiming at describing Dynamic Nuclear spin Polarization (DNP) in solutions containing molecules of biomedical interest and paramagnetic centers are not able to model the behaviour observed upon varying the concentration of trityl radicals or the polarization enhancement caused by moderate addition of gadolinium complexes. In this manuscript, we first show experimentally that the nuclear steady state polarization reached in solutions of pyruvic acid with 15 mM trityl radicals is substantially independent from the average internuclear distance. This evidences a leading role of electron (over nuclear) spin relaxation processes in determining the ultimate performances of DNP. Accordingly, we have devised a variant of the Thermal Mixing model for inhomogenously broadened electron resonance lines which includes a relaxation term describing the exchange of magnetic anisotropy energy of the electron spin system with the lattice. Thanks to this additional term, the dependence of the nuclear polarization on the electron concentration can be properly accounted for. Moreover, the model predicts a strong increase of the final polarization on shortening the electron spin-lattice relaxation time, providing a possible explanation for the effect of gadolinium doping.Comment: 13 pages, 12 figure