In this note, we prove an It^o formula for the isochron map of a reaction-diffusion system. This follows the proof of a new result which states that the second derivative of the isochron map of a reaction-diffusion system is trace class. This result,
in turn, is a corollary of Proposition 2.3, which guarantees that the first and second Frechet derivatives of the flow of a reaction-diffusion system with respect to initial conditions are trace class.
We employ magnetic small-angle neutron scattering to investigate the magnetic interactions in $(Fe_{0.7}Ni_{0.3})_{86}B_{14}$ alloy, a HiB-NANOPERM-type soft magnetic nanocrystalline material, which exhibits an ultrafine microstructure with an averag
e grain size below 10 nm. The neutron data reveal a significant spin-misalignment scattering, which is mainly related to the jump of the longitudinal magnetization at internal particle-matrix interfaces. The field dependence of the neutron data can be well described by the micromagnetic small-angle neutron scattering theory. In particular, the theory explains the clover-leaf-type angular anisotropy observed in the purely magnetic neutron scattering cross section. The presented neutron-data analysis also provides access to the magnetic interaction parameters, such as the exchange-stiffness constant, which plays a crucial role towards the optimization of the magnetic softness of Fe-based nanocrystalline materials.
We present new $ u_murightarrow u_e$, $ u_murightarrow u_mu$, $overline{ u}_murightarrowoverline{ u}_e$, and $overline{ u}_murightarrowoverline{ u}_mu$ oscillation measurements by the NOvA experiment, with a 50% increase in neutrino-mode beam exposur
e over the previously reported results. The additional data, combined with previously published neutrino and antineutrino data, are all analyzed using improved techniques and simulations. A joint fit to the $ u_e$, $ u_mu$, $overline{ u}_e$, and $overline{ u}_mu$ candidate samples within the 3-flavor neutrino oscillation framework continues to yield a best-fit point in the normal mass ordering and the upper octant of the $theta_{23}$ mixing angle, with $Delta m^{2}_{32} = (2.41pm0.07)times 10^{-3}$ eV$^2$ and $sin^2theta_{23} = 0.57^{+0.03}_{-0.04}$. The data disfavor combinations of oscillation parameters that give rise to a large asymmetry in the rates of $ u_e$ and $overline{ u}_e$ appearance. This includes values of the CP-violating phase in the vicinity of $delta_text{CP} = pi/2$ which are excluded by $>3sigma$ for the inverted mass ordering, and values around $delta_text{CP} = 3pi/2$ in the normal ordering which are disfavored at 2$sigma$ confidence.
We study stochastic perturbations of ODE with stable limit cycles -- referred to as stochastic oscillators -- and investigate the response of the asymptotic (in time) frequency of oscillations to changing noise amplitude. Unlike previous studies, we
do not restrict our attention to the small noise limit, and account for the fact that large deviation events may push the system out of its oscillatory regime. To do so, we consider stochastic oscillators conditioned on their remaining in an oscillatory regime for all time. This leads us to use the theory of quasi-ergodic measures, and to define quasi-asymptotic frequencies as conditional, long-time average frequencies. We show that quasi-asymptotic frequencies always exist, though they may or may not be observable in practice. Our discussion recovers previous results on stochastic oscillators in the literature. In particular, existing results imply that the asymptotic frequency of a stochastic oscillator depends quadratically on the noise amplitude. We describe scenarios where this prediction holds, though we also show that it is not true in general -- even for small noise.
A search is performed for supernova-like neutrino interactions coincident with 76 gravitational wave events detected by the LIGO/Virgo Collaboration. For 40 of these events, full readout of the time around the gravitational wave is available from the
NOvA Far Detector. For these events, we set limits on the fluence of the sum of all neutrino flavors of $F < 7(4)times 10^{10}mathrm{cm}^{-2}$ at 90% C.L. assuming energy and time distributions corresponding to the Garching supernova models with masses 9.6(27)$mathrm{M}_odot$. Under the hypothesis that any given gravitational wave event was caused by a supernova, this corresponds to a distance of $r > 29(50)$kpc at 90% C.L. Weaker limits are set for other gravitational wave events with partial Far Detector data and/or Near Detector data.
This Letter reports results from the first long-baseline search for sterile antineutrinos mixing in an accelerator-based antineutrino-dominated beam. The rate of neutral-current interactions in the two NOvA detectors, at distances of 1 km and 810 km
from the beam source, is analyzed using an exposure of $12.51times10^{20}$ protons-on-target from the NuMI beam at Fermilab running in antineutrino mode. A total of $121$ of neutral-current candidates are observed at the Far Detector, compared to a prediction of $122pm11$(stat.)$pm15$(syst.) assuming mixing between three active flavors. No evidence for $bar{ u}_{mu}rightarrowbar{ u}_{s}$ oscillation is observed. Interpreting this result within a 3+1 model, constraints are placed on the mixing angles ${theta}_{24} < 25^{circ}$ and ${theta}_{34} < 32^{circ}$ at the 90% C.L. for $0.05$eV$^{2} leq Delta m^{2}_{41} leq 0.5$eV$^{2}$, the range of mass splittings that produces no significant oscillations at the Near Detector. These are the first 3+1 confidence limits set using long-baseline accelerator antineutrinos.
We report the rate of cosmic ray air showers with multiplicities exceeding 15 muon tracks recorded in the NOvA Far Detector between May 2016 and May 2018. The detector is located on the surface under an overburden of 3.6 meters water equivalent. We o
bserve a seasonal dependence in the rate of multiple-muon showers, which varies in magnitude with multiplicity and zenith angle. During this period, the effective atmospheric temperature and surface pressure ranged between 210 K to 230 K and 940mbar to 990mbar, respectively; the shower rates are anti-correlated with the variation in the effective temperature. The variations are about 30% larger for the highest multiplicities than the lowest multiplicities and 20% larger for showers near the horizon than vertical showers.
The main goal of this paper is to analyse the influence of cracks on the azimuthal variations of amplitude. We restrict our investigation to a single set of vertical, circular, and flat cavities aligned along a horizontal axis. Such cracks are embedd
ed in either isotropic surroundings or transversely isotropic background with a vertical symmetry axis. We employ the effective medium theory to obtain either transversely-isotropic material with a horizontal symmetry axis or an orthotropic medium, respectively. To consider the amplitudes, we focus on a Vavrycuk-Psencik approximation of the PP-wave reflection coefficient. We assume that cracks are situated in one of the halfspaces being in welded contact. Azimuthal variations depend on the background stiffnesses, incidence angle, and crack density parameter. Upon analytical analysis, we indicate which factors (such as backgrounds saturation) cause the reflection coefficient to have maximum absolute value in the direction parallel or perpendicular to cracks. We discuss the irregular cases, where such extreme values appear in the other than the aforementioned directions. Due to the support of numerical simulations, we propose graphic patterns of two-dimensional amplitude variations with azimuth. The patterns consist of a series of shapes that change with the increasing value of the crack density parameter. Schemes appear to differ depending on the incidence angle and the saturation. Finally, we extract these shapes that are characteristic of gas-bearing rocks. They may be treated as gas indicators. We support the findings and verify our patterns using real values of stiffnesses extracted from the sedimentary rocks samples.
We report a search for a magnetic monopole component of the cosmic-ray flux in a 95-day exposure of the NOvA experiments Far Detector, a 14 kt segmented liquid scintillator detector designed primarily to observe GeV-scale electron neutrinos. No event
s consistent with monopoles were observed, setting an upper limit on the flux of $2times 10^{-14} mathrm{cm^{-2}s^{-1}sr^{-1}}$ at 90% C.L. for monopole speed $6times 10^{-4} < beta < 5times 10^{-3}$ and mass greater than $5times 10^{8}$ GeV. Because of NOvAs small overburden of 3 meters-water equivalent, this constraint covers a previously unexplored low-mass region.
We report the final measurement of the neutrino oscillation parameters $Delta m^2_{32}$ and $sin^2theta_{23}$ using all data from the MINOS and MINOS+ experiments. These data were collected using a total exposure of $23.76 times 10^{20}$ protons on t
arget producing $ u_{mu}$ and $overline{ u_mu}$ beams and 60.75 kt$cdot$yr exposure to atmospheric neutrinos. The measurement of the disappearance of $ u_{mu}$ and the appearance of $ u_e$ events between the Near and Far detectors yields $|Delta m^2_{32}|=2.40^{+0.08}_{-0.09}~(2.45^{+0.07}_{-0.08}) times 10^{-3}$ eV$^2$ and $sin^2theta_{23} = 0.43^{+0.20}_{-0.04} ~(0.42^{+0.07}_{-0.03})$ at 68% C.L. for Normal (Inverted) Hierarchy.
