Extinction controlled adaptive phase-mask coronagraph

Context. Phase-mask coronagraphy is advantageous in terms of inner working angle and discovery space. It is however still plagued by drawbacks such as sensitivity to tip-tilt errors and chromatism. A nulling stellar coronagraph based on the adaptive phase-mask concept using polarization interferometry is presented in this paper. Aims. Our concept aims at dynamically and achromatically optimizing the nulling efficiency of the coronagraph, making it more immune to fast low-order aberrations (tip-tilt errors, focus, ...). Methods. We performed numerical simulations to demonstrate the value of the proposed method. The active control system will correct for the detrimental effects of image instabilities on the destructive interference. The mask adaptability both in size, phase and amplitude also compensates for manufacturing errors of the mask itself, and potentially for chromatic effects. Liquid-crystal properties are used to provide variable transmission of an annulus around the phase mask, but also to achieve the achromatic {\pi} phase shift in the core of the PSF by rotating the polarization by 180 degrees. Results. We developed a new concept and showed its practical advantages using numerical simulations. This new adaptive implementation of the phase-mask coronagraph could advantageously be used on current and next-generation adaptive optics systems, enabling small inner working angles without compromising contrast.Comment: 7 pages, 6 figure

A generalization of the Heine--Stieltjes theorem

We extend the Heine-Stieltjes Theorem to concern all (non-degenerate) differential operators preserving the property of having only real zeros. This solves a conjecture of B. Shapiro. The new methods developed are used to describe intricate interlacing relations between the zeros of different pairs of solutions. This extends recent results of Bourget, McMillen and Vargas for the Heun equation and answers their question on how to generalize their results to higher degrees. Many of the results are new even for the classical case.Comment: 12 pages, typos corrected and refined the interlacing theorem

Towards Deconstruction of the Type D (2,0) Theory

We propose a four-dimensional supersymmetric theory that deconstructs, in a particular limit, the six-dimensional $(2,0)$ theory of type $D_k$. This 4d theory is defined by a necklace quiver with alternating gauge nodes $\mathrm{O}(2k)$ and $\mathrm{Sp}(k)$. We test this proposal by comparing the 6d half-BPS index to the Higgs branch Hilbert series of the 4d theory. In the process, we overcome several technical difficulties, such as Hilbert series calculations for non-complete intersections, and the choice of $\mathrm{O}$ versus $\mathrm{SO}$ gauge groups. Consistently, the result matches the Coulomb branch formula for the mirror theory upon reduction to 3d

Extinction controlled Adaptive Mask Coronagraph Lyot and Phase Mask dual concept for wide extinction area

A dual coronagraph based on the Adaptive Mask concept is presented in this paper. A Lyot coronagraph with a variable diameter occulting disk and a nulling stellar coronagraph based on the Adaptive Phase Mask concept using polarization interferometry are presented in this work. Observations on sky and numerical simulations show the usefulness of the proposed method to optimize the nulling efficiency of the coronagraphs. In the case of the phase mask, the active control system will correct for the detrimental effects of image instabilities on the destructive interference (low-order aberrations such as tip-tilt and focus). The phase mask adaptability both in size, phase and amplitude also compensate for manufacturing errors of the mask itself, and potentially for chromatic effects. Liquid-crystal properties are used to provide variable transmission of an annulus around the phase mask, but also to achieve the achromatic π phase shift in the core of the PSF by rotating the polarization by 180°.A compressed mercury (Hg) drop is used as an occulting disk for the Lyot mask, its size control offers an adaptation to the seeing conditions and provides an optimization of the Tip-tilt correction

Eigenvalue distributions from a star product approach

We use the well-known isomorphism between operator algebras and function spaces equipped with a star product to study the asymptotic properties of certain matrix sequences in which the matrix dimension $D$ tends to infinity. Our approach is based on the $su(2)$ coherent states which allow for a systematic 1/D expansion of the star product. This produces a trace formula for functions of the matrix sequence elements in the large-$D$ limit which includes higher order (finite-$D$) corrections. From this a variety of analytic results pertaining to the asymptotic properties of the density of states, eigenstates and expectation values associated with the matrix sequence follows. It is shown how new and existing results in the settings of collective spin systems and orthogonal polynomial sequences can be readily obtained as special cases. In particular, this approach allows for the calculation of higher order corrections to the zero distributions of a large class of orthogonal polynomials.Comment: 25 pages, 8 figure

On the energy growth of some periodically driven quantum systems with shrinking gaps in the spectrum

We consider quantum Hamiltonians of the form H(t)=H+V(t) where the spectrum of H is semibounded and discrete, and the eigenvalues behave as E_n~n^\alpha, with 0<\alpha<1. In particular, the gaps between successive eigenvalues decay as n^{\alpha-1}. V(t) is supposed to be periodic, bounded, continuously differentiable in the strong sense and such that the matrix entries with respect to the spectral decomposition of H obey the estimate |V(t)_{m,n}|0, p>=1 and \gamma=(1-\alpha)/2. We show that the energy diffusion exponent can be arbitrarily small provided p is sufficiently large and \epsilon is small enough. More precisely, for any initial condition \Psi\in Dom(H^{1/2}), the diffusion of energy is bounded from above as _\Psi(t)=O(t^\sigma) where \sigma=\alpha/(2\ceil{p-1}\gamma-1/2). As an application we consider the Hamiltonian H(t)=|p|^\alpha+\epsilon*v(\theta,t) on L^2(S^1,d\theta) which was discussed earlier in the literature by Howland

MODELING OF HYDROTHERMAL FLUID CIRCULATION AS A TOOL FOR VOLCANIC HAZARD ASSESSMENT

Monitoring of geophysical and geochemical observ¬ables at the surface plays a main role in the under¬standing of—and the hazard evaluation of— active volcanoes. Measurable changes in these parameters should occur when a volcano approches eruptive con¬ditions. Hydrothermal activity is commonly studied as an efficient carrier of signals from the magmatic system. As the magmatic system evolves, the amount, temperature, and composition of magmatic fluids that feed the hydrothermal system change, in turn affecting the parameters that are monitored at the surface. Modeling of hydrothermal circulation, as shown in the past, may cause measurable gravity changes and ground deformation. In this work, we extend our previous studies and increase the number of observable parameters to include gas temperature, the rate of diffuse degassing, the extent of the degassing area, and electrical conductivity. The possibility of nonmagmatic disturbance needs to be carefully addressed to ensure a proper estimate of volcanic hazard