Enforcing state constraints in dynamical systems modelled with neural networks

Deep neural networks (NNs) are usually trained with unconstrained optimisation algorithms. With a reasoning similar to the constrained Kalman filter, incorporating known information in the form of equality constraints at certain checkpoints can potentially improve prediction accuracy. For continuous-time dynamical systems, the state constraints should be enforced in an ordinary differential equation (ODE) model which embeds NNs to represent a learned part of dynamics or a control policy. To this end, incremental correction methods are developed for post-processing of the dynamical systems modelled with NNs for which the parameters are determined by previous optimisation process. The proposed approach is to find a small amount of local correction needed to satisfy given state constraints with the updated solution. Algorithms for updating the neural network parameters and the control function are considered

Evidence for spin liquid ground state in SrDy2_2O4_4 frustrated magnet probed by muSR

Muon spin relaxation ($\mu$SR) measurements were carried out on SrDy$_2$O$_4$, a frustrated magnet featuring short range magnetic correlations at low temperatures. Zero-field muon spin depolarization measurements demonstrate that fast magnetic fluctuations are present from $T=300$ K down to 20 mK. The coexistence of short range magnetic correlations and fluctuations at $T=20$ mK indicates that SrDy$_2$O$_4$ features a spin liquid ground state. Large longitudinal fields affect weakly the muon spin depolarization, also suggesting the presence of fast fluctuations. For a longitudinal field of $\mu_0H=2$ T, a non-relaxing asymmetry contribution appears below $T=6$ K, indicating considerable slowing down of the magnetic fluctuations as field-induced magnetically-ordered phases are approached.Comment: 6 pages, 4 figures, to be published as a proceeding of HFM2016 in Journal of Physics: Conference Series (JPCS

High pressure magnetic state of MnP probed by means of muon-spin rotation

We report a detailed $\mu$SR study of the pressure evolution of the magnetic order in the manganese based pnictide MnP, which has been recently found to undergo a superconducting transition under pressure once the magnetic ground state is suppressed. Using the muon as a volume sensitive local magnetic probe, we identify a ferromagnetic state as well as two incommensurate helical states (with propagation vectors ${\bf Q}$ aligned along the crystallographic $c-$ and $b-$directions, respectively) which transform into each other through first order phase transitions as a function of pressure and temperature. Our data appear to support that the magnetic state from which superconductivity develops at higher pressures is an incommensurate helical phase.Comment: 11 pages, 9 figure

Magnetic quantum critical point and superconductivity in UPt3 doped with Pd

Transverse-field muon spin relaxation measurements have been carried out on the heavy-fermion superconductor UPt3 doped with small amounts of Pd. We find that the critical Pd concentration for the emergence of the large-moment antiferromagnetic phase is ~0.6 at.%Pd. At the same Pd content, superconductivity is completely suppressed. The existence of a magnetic quantum critical point in the phase diagram, which coincides with the critical point for superconductivity, provides evidence for ferromagnetic spin-fluctuation mediated odd-parity superconductivity, which competes with antiferromagnetic order.Comment: 4 pages (includes 3 figures); postscript fil

Magnetic quantum critical point and superconductivity in UPt3 doped with Pd

Transverse-field muon spin relaxation measurements have been carried out on the heavy-fermion superconductor UPt3 doped with small amounts of Pd. We find that the critical Pd concentration for the emergence of the large-moment antiferromagnetic phase is ~0.6 at.%Pd. At the same Pd content, superconductivity is completely suppressed. The existence of a magnetic quantum critical point in the phase diagram, which coincides with the critical point for superconductivity, provides evidence for ferromagnetic spin-fluctuation mediated odd-parity superconductivity, which competes with antiferromagnetic order.Comment: 4 pages (includes 3 figures); postscript fil

The Anti-Coincidence Detector for the GLAST Large Area Telescope

This paper describes the design, fabrication and testing of the Anti-Coincidence Detector (ACD) for the Gamma-ray Large Area Space Telescope (GLAST) Large Area Telescope (LAT). The ACD is LAT first-level defense against the charged cosmic ray background that outnumbers the gamma rays by 3-5 orders of magnitude. The ACD covers the top and 4 sides of the LAT tracking detector, requiring a total active area of ~8.3 square meters. The ACD detector utilizes plastic scintillator tiles with wave-length shifting fiber readout. In order to suppress self-veto by shower particles at high gamma-ray energies, the ACD is segmented into 89 tiles of different sizes. The overall ACD efficiency for detection of singly charged relativistic particles entering the tracking detector from the top or sides of the LAT exceeds the required 0.9997.Comment: 33 pages, 19 figure

Muon spin rotation and relaxation in the superconducting ferromagnet UCoGe

We report zero-field muon spin rotation and relaxation measurements on the superconducting ferromagnet UCoGe. Weak itinerant ferromagnetic order is detected by a spontaneous muon spin precession frequency below the Curie temperature $T_C = 3$ K. The $\mu^+$ precession frequency persists below the bulk superconducting transition temperature $T_{sc} = 0.5$ K, where it measures a local magnetic field $B_{loc} = 0.015$ T. The amplitude of the $\mu$SR signal provides unambiguous proof for ferromagnetism present in the whole sample volume. We conclude ferromagnetism coexists with superconductivity on the microscopic scale.Comment: 4 pages, 3 figures, accepted for publication in PR