2,267 research outputs found
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
50 km s and the other broader and consisting of subcomponents
with redshift to speed in the range 200 400 km s. The profiles
of OVIII lines appear more symmetric than C IV and are redshifted to speed
150 km s.
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
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