Singularities of equidistants and global centre symmetry sets of Lagrangian submanifolds

We define the Global Centre Symmetry set (GCS) of a smooth closed m-dimensional submanifold M of R^n, $n \leq 2m$, which is an affinely invariant generalization of the centre of a k-sphere in R^{k+1}. The GCS includes both the centre symmetry set defined by Janeczko and the Wigner caustic defined by Berry. We develop a new method for studying generic singularities of the GCS which is suited to the case when M is lagrangian in R^{2m} with canonical symplectic form. The definition of the GCS, which slightly generalizes one by Giblin and Zakalyukin, is based on the notion of affine equidistants, so, we first study singularities of affine equidistants of Lagrangian submanifolds, classifying all the stable ones. Then, we classify the affine-Lagrangian stable singularities of the GCS of Lagrangian submanifolds and show that, already for smooth closed convex curves in R^2, many singularities of the GCS which are affine stable are not affine-Lagrangian stable.Comment: 26 pages, 2 figure

Observation of a superconducting glass state in granular superconducting diamond

The magnetic field dependence of the superconductivity in nanocrystalline boron doped diamond thin films is reported. Evidence of a glass state in the phase diagram is presented, as demonstrated by electrical resistance and magnetic relaxation measurements. The position of the phase boundary in the H-T plane is determined from resistance data by detailed fitting to zero-dimensional fluctuation conductivity theory. This allows determination of the boundary between resistive and non-resistive behavior to be made with greater precision than the standard ad hoc onset/midpoint/offset criterion

Fluctuation spectroscopy as a probe of granular superconducting diamond films

We present resistance versus temperature data for a series of boron-doped nanocrystalline diamond films whose grain size is varied by changing the film thickness. Upon extracting the fluctuation conductivity near to the critical temperature we observe three distinct scaling regions -- 3D intragrain, quasi-0D, and 3D intergrain -- in confirmation of the prediction of Lerner, Varlamov and Vinokur. The location of the dimensional crossovers between these scaling regions allows us to determine the tunnelling energy and the Thouless energy for each film. This is a demonstration of the use of \emph{fluctuation spectroscopy} to determine the properties of a superconducting granular system

Dynamic behavior of magnetic avalanches in the spin-ice compound Dy2_2Ti2_2O7_7

Avalanches of the magnetization, that is to say an abrupt reversal of the magnetization at a given field, have been previously reported in the spin-ice compound Dy$_{2}$Ti$_{2}$O$_{7}$. This out-of-equilibrium process, induced by magneto-thermal heating, is quite usual in low temperature magnetization studies. A key point is to determine the physical origin of the avalanche process. In particular, in spin-ice compounds, the origin of the avalanches might be related to the monopole physics inherent to the system. We have performed a detailed study of the avalanche phenomena in three single crystals, with the field oriented along the [111] direction, perpendicular to [111] and along the [100] directions. We have measured the changing magnetization during the avalanches and conclude that avalanches in spin ice are quite slow compared to the avalanches reported in other systems such as molecular magnets. Our measurements show that the avalanches trigger after a delay of about 500 ms and that the reversal of the magnetization then occurs in a few hundreds of milliseconds. These features suggest an unusual propagation of the reversal, which might be due to the monopole motion. The avalanche fields seem to be reproducible in a given direction for different samples, but they strongly depend on the initial state of magnetization and on how the initial state was achieved.Comment: 11 pages, 14 figure

Magnetic order and the electronic ground state in the pyrochlore iridate Nd2Ir2O7

We report a combined muon spin relaxation/rotation, bulk magnetization, neutron scattering, and transport study of the electronic properties of the pyrochlore iridate Nd2Ir2O7. We observe the onset of strongly hysteretic behavior in the temperature dependent magnetization below 120 K, and an abrupt increase in the temperature dependent resistivity below 8 K. Zero field muon spin relaxation measurements show that the hysteretic magnetization is driven by a transition to a magnetically disordered state, and that below 8 K a complex magnetically ordered ground state sets in, as evidenced by the onset of heavily damped spontaneous muon precession. Our measurements point toward the absence of a true metal-to-insulator phase transition in this material and suggest that Nd2Ir2O7 lies either within or on the metallic side of the boundary of the Dirac semimetal regime within its topological phase diagram.Comment: 21 pages, 7 figure

Precession of a Freely Rotating Rigid Body. Inelastic Relaxation in the Vicinity of Poles

When a solid body is freely rotating at an angular velocity ${\bf \Omega}$, the ellipsoid of constant angular momentum, in the space $\Omega_1, \Omega_2, \Omega_3$, has poles corresponding to spinning about the minimal-inertia and maximal-inertia axes. The first pole may be considered stable if we neglect the inner dissipation, but becomes unstable if the dissipation is taken into account. This happens because the bodies dissipate energy when they rotate about any axis different from principal. In the case of an oblate symmetrical body, the angular velocity describes a circular cone about the vector of (conserved) angular momentum. In the course of relaxation, the angle of this cone decreases, so that both the angular velocity and the maximal-inertia axis of the body align along the angular momentum. The generic case of an asymmetric body is far more involved. Even the symmetrical prolate body exhibits a sophisticated behaviour, because an infinitesimally small deviation of the body's shape from a rotational symmetry (i.e., a small difference between the largest and second largest moments of inertia) yields libration: the precession trajectory is not a circle but an ellipse. In this article we show that often the most effective internal dissipation takes place at twice the frequency of the body's precession. Applications to precessing asteroids, cosmic-dust alignment, and rotating satellites are discussed.Comment: 47 pages, 1 figur