Constraints on Cosmological Parameters from the 500 deg² SPTPOL Lensing Power Spectrum

We present cosmological constraints based on the cosmic microwave background (CMB) lensing potential power spectrum measurement from the recent 500 deg² SPTPOL survey, the most precise CMB lensing measurement from the ground to date. We fit a flat ΛCDM model to the reconstructed lensing power spectrum alone and in addition with other data sets: baryon acoustic oscillations (BAO), as well as primary CMB spectra from Planck and SPTPOL. The cosmological constraints based on SPTPOL and Planck lensing band powers are in good agreement when analyzed alone and in combination with Planck full-sky primary CMB data. With weak priors on the baryon density and other parameters, the SPTPOL CMB lensing data alone provide a 4% constraint on σ₈Ω^(0.25)_m = 0.593 ± 0.025. Jointly fitting with BAO data, we find σ₈ = 0.779±0.023, Ω_m = 0.368^(+0.032)_(−0.037), and H₀ = 72.0^(+2.1)_(−2.5)kms⁻¹ Mpc⁻¹, up to 2σ away from the central values preferred by Planck lensing + BAO. However, we recover good agreement between SPTPOL and Planck when restricting the analysis to similar scales. We also consider single-parameter extensions to the flat ΛCDM model. The SPTPOL lensing spectrum constrains the spatial curvature to be Ω_K = −0.0007±0.0025 and the sum of the neutrino masses to be ∑m_ν < 0.23 eV at 95% C.L. (with Planck primary CMB and BAO data), in good agreement with the Planck lensing results. With the differences in the signal-to-noise ratio of the lensing modes and the angular scales covered in the lensing spectra, this analysis represents an important independent check on the full-sky Planck lensing measurement

SBV Regularity for Genuinely Nonlinear, Strictly Hyperbolic Systems of Conservation Laws in one space dimension

We prove that if $t \mapsto u(t) \in \mathrm {BV}(\R)$ is the entropy solution to a $N \times N$ strictly hyperbolic system of conservation laws with genuinely nonlinear characteristic fields $$u_t + f(u)_x = 0,$$ then up to a countable set of times $\{t_n\}_{n \in \mathbb N}$ the function $u(t)$ is in $\mathrm {SBV}$, i.e. its distributional derivative $u_x$ is a measure with no Cantorian part. The proof is based on the decomposition of $u_x(t)$ into waves belonging to the characteristic families $$u(t) = \sum_{i=1}^N v_i(t) \tilde r_i(t), \quad v_i(t) \in \mathcal M(\R), \ \tilde r_i(t) \in \mathrm R^N,$$ and the balance of the continuous/jump part of the measures $v_i$ in regions bounded by characteristics. To this aim, a new interaction measure \mu_{i,\jump} is introduced, controlling the creation of atoms in the measure $v_i(t)$. The main argument of the proof is that for all $t$ where the Cantorian part of $v_i$ is not 0, either the Glimm functional has a downward jump, or there is a cancellation of waves or the measure $\mu_{i,\mathrm{jump}}$ is positive

Global Structure of Admissible BV Solutions to Piecewise Genuinely Nonlinear, Strictly Hyperbolic Conservation Laws in One Space Dimension

The paper describes the qualitative structure of an admissible BV solution to a strictly hyperbolic system of conservation laws whose characteristic families are piecewise genuinely nonlinear. More precisely, we prove that there are a countable set of points \u398 and a countable family of Lipschitz curves T{script} such that outside T{script} 2a \u398 the solution is continuous, and for all points in T{script}{set minus}\u398 the solution has left and right limit. This extends the corresponding structural result in [7] for genuinely nonlinear systems. An application of this result is the stability of the wave structure of solution w.r.t. -convergence. The proof is based on the introduction of subdiscontinuities of a shock, whose behavior is qualitatively analogous to the discontinuities of the solution to genuinely nonlinear systems

Quadratic interaction functional for general systems of conservation laws

For the Glimm scheme approximation u_\e to the solution of the system of conservation laws in one space dimension \begin{equation*} u_t + f(u)_x = 0, \qquad u(0,x) = u_0(x) \in \R^n, \end{equation*} with initial data $u_0$ with small total variation, we prove a quadratic (w.r.t. \TV(u_0)) interaction estimate, which has been used in the literature for stability and convergence results. No assumptions on the structure of the flux $f$ are made (apart smoothness), and this estimate is the natural extension of the Glimm type interaction estimate for genuinely nonlinear systems. More precisely we obtain the following results: \begin{itemize} \item a new analysis of the interaction estimates of simple waves; \item a Lagrangian representation of the derivative of the solution, i.e. a map $\mathtt x(t,w)$ which follows the trajectory of each wave $w$ from its creation to its cancellation; \item the introduction of the characteristic interval and partition for couples of waves, representing the common history of the two waves; \item a new functional $\mathfrak Q$ controlling the variation in speed of the waves w.r.t. time. \end{itemize} This last functional is the natural extension of the Glimm functional for genuinely nonlinear systems. The main result is that the distribution $D_{tt} \mathtt x(t,w)$ is a measure with total mass \leq \const \TV(u_0)^2

Nonlinear hyperbolic systems: Non-degenerate flux, inner speed variation, and graph solutions

We study the Cauchy problem for general, nonlinear, strictly hyperbolic systems of partial differential equations in one space variable. First, we re-visit the construction of the solution to the Riemann problem and introduce the notion of a nondegenerate (ND) system. This is the optimal condition guaranteeing, as we show it, that the Riemann problem can be solved with finitely many waves, only; we establish that the ND condition is generic in the sense of Baire (for the Whitney topology), so that any system can be approached by a ND system. Second, we introduce the concept of inner speed variation and we derive new interaction estimates on wave speeds. Third, we design a wave front tracking scheme and establish its strong convergence to the entropy solution of the Cauchy problem; this provides a new existence proof as well as an approximation algorithm. As an application, we investigate the time-regularity of the graph solutions $(X,U)$ introduced by the second author, and propose a geometric version of our scheme; in turn, the spatial component $X$ of a graph solution can be chosen to be continuous in both time and space, while its component $U$ is continuous in space and has bounded variation in time.Comment: 74 page

Auto-oscillation threshold and line narrowing in MgO-based spin-torque oscillators

We present an experimental study of the power spectrum of current-driven magnetization oscillations in MgO tunnel junctions under low bias. We find the existence of narrow spectral lines, down to 8 MHz in width at a frequency of 10.7 GHz, for small applied fields with clear evidence of an auto-oscillation threshold. Micromagnetics simulations indicate that the excited mode corresponds to an edge mode of the synthetic antiferromagnet

Auto-oscillation threshold, narrow spectral lines, and line jitter in spin-torque oscillators based on MgO magnetic tunnel junctions

We demonstrate spin torque induced auto-oscillation in MgO-based magnetic tunnel junctions. At the generation threshold, we observe a strong line narrowing down to 6 MHz at 300K and a dramatic increase in oscillator power, yielding spectrally pure oscillations free of flicker noise. Setting the synthetic antiferromagnet into autooscillation requires the same current polarity as the one needed to switch the free layer magnetization. The induced auto-oscillations are observed even at zero applied field, which is believed to be the acoustic mode of the synthetic antiferromagnet. While the phase coherence of the auto-oscillation is of the order of microseconds, the power autocorrelation time is of the order of milliseconds and can be strongly influenced by the free layer dynamics

Detecting slope and urban potential unstable areas by means of multi-platform remote sensing techniques: the Volterra (Italy) case study

Volterra (Central Italy) is a town of great historical interest, due to its vast and well-preserved cultural heritage, including a 2.6 km long Etruscan-medieval wall enclosure representing one of the most important elements. Volterra is located on a clayey hilltop prone to landsliding, soil erosion, therefore the town is subject to structural deterioration. During 2014, two impressive collapses occurred on the wall enclosure in the southwestern urban sector. Following these events, a monitoring campaign was carried out by means of remote sensing techniques, such as space-borne (PS-InSAR) and ground-based (GB-InSAR) radar interferometry, in order to analyze the displacements occurring both in the urban area and the surrounding slopes, and therefore to detect possible critical sectors with respect to instability phenomena. Infrared thermography (IRT) was also applied with the aim of detecting possible criticalities on the wall-enclosure, with special regards to moisture and seepage areas. PS-InSAR data allowed a stability back-monitoring on the area, revealing 19 active clusters displaying ground velocity higher than 10 mm/year in the period 2011–2015. The GB-InSAR system detected an acceleration up to 1.7 mm/h in near-real time as the March 2014 failure precursor. The IRT technique, employed on a double survey campaign, in both dry and rainy conditions, permitted to acquire 65 thermograms covering 23 sectors of the town wall, highlighting four thermal anomalies. The outcomes of this work demonstrate the usefulness of different remote sensing technologies for deriving information in risk prevention and management, and the importance of choosing the appropriate technology depending on the target, time sampling and investigation scale. In this paper, the use of a multi-platform remote sensing system permitted technical support of the local authorities and conservators, providing a comprehensive overview of the Volterra site, its cultural heritage and landscape, both in near-real time and back-analysis and at different scales of investigation