16,374 research outputs found
Invariance properties of the multidimensional matching distance in Persistent Topology and Homology
Persistent Topology studies topological features of shapes by analyzing the
lower level sets of suitable functions, called filtering functions, and
encoding the arising information in a parameterized version of the Betti
numbers, i.e. the ranks of persistent homology groups. Initially introduced by
considering real-valued filtering functions, Persistent Topology has been
subsequently generalized to a multidimensional setting, i.e. to the case of
-valued filtering functions, leading to studying the ranks of
multidimensional homology groups. In particular, a multidimensional matching
distance has been defined, in order to compare these ranks. The definition of
the multidimensional matching distance is based on foliating the domain of the
ranks of multidimensional homology groups by a collection of half-planes, and
hence it formally depends on a subset of inducing a
parameterization of these half-planes. It happens that it is possible to choose
this subset in an infinite number of different ways. In this paper we show that
the multidimensional matching distance is actually invariant with respect to
such a choice.Comment: 14 pages, 2 figure
Kinetic cascade in solar-wind turbulence: 3D3V hybrid-kinetic simulations with electron inertia
Understanding the nature of the turbulent fluctuations below the ion
gyroradius in solar-wind turbulence is a great challenge. Recent studies have
been mostly in favor of kinetic Alfv\'en wave (KAW) type of fluctuations, but
other kinds of fluctuations with characteristics typical of magnetosonic,
whistler and ion Bernstein modes, could also play a role depending on the
plasma parameters. Here we investigate the properties of the sub-proton-scale
cascade with high-resolution hybrid-kinetic simulations of freely-decaying
turbulence in 3D3V phase space, including electron inertia effects. Two proton
plasma beta are explored: the "intermediate" and "low"
regimes, both typically observed in solar wind and corona. The
magnetic energy spectum exhibits and power laws
at , while they are slightly steeper at . Nevertheless,
both regimes develop a spectral anisotropy consistent with at , and pronounced small-scale intermittency.
In this context, we find that the kinetic-scale cascade is dominated by
KAW-like fluctuations at , whereas the low- case presents a
more complex scenario suggesting the simultaneous presence of different types
of fluctuations. In both regimes, however, a non-negligible role of ion
Bernstein type of fluctuations at the smallest scales seems to emerge.Comment: 6 pages, 5 figures, final version published in The Astrophysical
Journal Letters: Cerri, Servidio & Califano, ApJL 846, L18 (2017
OPTIMAL HOMEOMORPHISMS BETWEEN CLOSED CURVES
The concept of natural pseudo-distance has proven to be a powerful tool for measuring the dissimilarity between topological spaces endowed with continuous real-valued functions. Roughly speaking, the natural pseudo-distance is defined as the infimum of the change of the functions' values, when moving from one space to the other through homeomorphisms, if possible. In this paper, we prove the first available result about the existence of optimal
homeomorphisms between closed curves, i.e. inducing a change of the function that equals the natural pseudo-distance
About the rapidity and helicity distributions of the W bosons produced at LHC
bosons are produced at LHC from a forward-backward symmetric initial
state. Their decay to a charged lepton and a neutrino has a strong spin
analysing power. The combination of these effects results in characteristic
distributions of the pseudorapidity of the leptons decaying from and
of different helicity. This observation may open the possibility to
measure precisely the and rapidity distributions for the two
transverse polarisation states of bosons produced at small transverse
momentum.Comment: 8 pages, 5 figure
Identification of Long-lived Charged Particles using Time-Of-Flight Systems at the Upgraded LHC detectors
We study the impact of picosecond precision timing detection systems on the
LHC experiments' long-lived particle search program during the HL-LHC era. We
develop algorithms that allow us to reconstruct the mass of such charged
particles and perform particle identification using the time-of-flight
measurement. We investigate the reach for benchmark scenarios as a function of
the timing resolution, and find sensitivity improvement of up to a factor of
ten, depending on the new heavy particle mass.Comment: 20 pages, 13 figure
Automated Setup to Accurately Calibrate Electrical DC Voltage Generators
At National Institute of Metrological Research (INRIM), an automated setup to
calibrate DC Voltage generators, mainly top-level calibrators from 1 mV to 1 kV
has been developed. The heart of the setup is an INRIM-built automated fixed
ratios DC Voltage divider. The significant achievement of this setup is the
possibility to interconnect the divider, a DMM characterized in linearity, a DC
Voltage Standard and a DC Voltage generator under calibration and automatically
to manage the calibration process. This calibration method allows to save a lot
of time, to improve the reliability and to increase the accuracy of the
calibration of generators. The relative uncertainties of the system span from
0.6x10-6 to 1.2x10-4 improving the previous capabilities of the INRIM
laboratory for calibration of programmable multifunction instruments. In
addition, this system allows to avoid the employment of several Standards (some
of them still manually operating) carrying out the entire process without
changing the setup configuration and without the presence of operators. The
concept of this setup can be transferred to secondary high-level electrical
calibration Laboratories that could be consider it useful for their calibration
activities.Comment: 6 pages 8 figure
Pressure anisotropy generation in a magnetized plasma configuration with a shear flow velocity
The nonlinear evolution of the Kelvin Helmholtz instability in a magnetized
plasma with a perpendicular flow close to, or in, the supermagnetosonic regime
can produce a significant parallel-to-perpendicular pressure anisotropy. This
anisotropy, localized inside the flow shear region, can make the configuration
unstable either to the mirror or to the firehose instability and, in general,
can affect the development of the KHI. The interface between the solar wind and
the Earth's magnetospheric plasma at the magnetospheric equatorial flanks
provides a relevant setting for the development of this complex nonlinear
dynamics.Comment: 11 pages, 7 figures, submitted to Plasma Phys. Control. Fusio
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