Pieri's Formula for Generalized Schur Polynomials

Young's lattice, the lattice of all Young diagrams, has the Robinson-Schensted-Knuth correspondence, the correspondence between certain matrices and pairs of semi-standard Young tableaux with the same shape. Fomin introduced generalized Schur operators to generalize the Robinson-Schensted-Knuth correspondence. In this sense, generalized Schur operators are generalizations of semi-standard Young tableaux. We define a generalization of Schur polynomials as expansion coefficients of generalized Schur operators. We show that the commutating relation of generalized Schur operators implies Pieri's formula to generalized Schur polynomials

Parametric instabilities in the LCGT arm cavity

We evaluated the parametric instabilities of LCGT (Japanese interferometric gravitational wave detector project) arm cavity. The number of unstable modes of LCGT is 10-times smaller than that of Advanced LIGO (U.S.A.). Since the strength of the instabilities of LCGT depends on the mirror curvature more weakly than that of Advanced LIGO, the requirement of the mirror curvature accuracy is easier to be achieved. The difference in the parametric instabilities between LCGT and Advanced LIGO is because of the thermal noise reduction methods (LCGT, cooling sapphire mirrors; Advanced LIGO, fused silica mirrors with larger laser beams), which are the main strategies of the projects. Elastic Q reduction by the barrel surface (0.2 mm thickness Ta$_2$O$_5$) coating is effective to suppress instabilities in the LCGT arm cavity. Therefore, the cryogenic interferometer is a smart solution for the parametric instabilities in addition to thermal noise and thermal lensing.Comment: 6 pages,3 figures. Amaldi7 proceedings, J. Phys.: Conf. Ser. (accepted

Gyrokinetic simulation of entropy cascade in two-dimensional electrostatic turbulence

Two-dimensional electrostatic turbulence in magnetized weakly-collisional plasmas exhibits a cascade of entropy in phase space [Phys. Rev. Lett. 103, 015003 (2009)]. At scales smaller than the gyroradius, this cascade is characterized by the dimensionless ratio D of the collision time to the eddy turnover time measured at the scale of the thermal Larmor radius. When D >> 1, a broad spectrum of fluctuations at sub-Larmor scales is found in both position and velocity space. The distribution function develops structure as a function of v_{perp}, the velocity coordinate perpendicular to the local magnetic field. The cascade shows a local-scale nonlinear interaction in both position and velocity spaces, and Kolmogorov's scaling theory can be extended into phase space.Comment: 8 pages, 10 figures, Conference paper presented at 2009 Asia-Pacific Plasma Theory Conference. Ver.2 includes corrected typos & updated reference

A Precision Angle Sensor using an Optical Lever inside a Sagnac Interferometer

We built an ultra low noise angle sensor by combining a folded optical lever and a Sagnac interferometer. The instrument has a measured noise floor of 1.3 prad / Hz^(1/2) at 2.4 kHz. We achieve this record angle sensitivity using a proof-of-concept apparatus with a conservative N=11 bounces in the optical lever. This technique could be extended to reach sub-picoradian / Hz^(1/2) sensitivities with an optimized design.Comment: 3 pages, 4 figure

Fire and edge effects in a fragmented tropical forest landscape in the southwestern Amazon.

The Amazon holds the largest tropical rain forest formation in the world but this natural ecosystem has been altered by both anthropogenic and natural disturbances since the 1970s (Davidson et al., 2012). The Brazilian Amazon experienced the highest annual tropical deforestation rates until the mid-2000s when rates began to decline dramatically due to the government?s environmental law enforcement. Conversely, other forest disturbances, such as understory fire, selective logging, and fragmentation (Aragao et al., 2014; Arima et al., 2014) have gained more importance in terms of their impacts on remnant forests. The degree of forest degradation varies as functions of disturbance type, the intensity and frequency of disturbance events, and the time since occurrence (Cochrane and Schulze, 1999; Barlow and Peres, 2004; Brando et al., 2014). Additionally, the impacts of these disturbances may vary across the region due to different gradients of physical conditions including rainfall, edaphic and geological properties (Hoorn et al., 2010; Malhi et al., 2004)

Satellite-based characterization of climatic conditions before large-scale general flowering events in Peninsular Malaysia

General flowering (GF) is a unique phenomenon wherein, at irregular intervals, taxonomically diverse trees in Southeast Asian dipterocarp forests synchronize their reproduction at the community level. Triggers of GF, including drought and low minimum temperatures a few months previously has been limitedly observed across large regional scales due to lack of meteorological stations. Here, we aim to identify the climatic conditions that trigger large-scale GF in Peninsular Malaysia using satellite sensors, Tropical Rainfall Measuring Mission (TRMM) and Moderate Resolution Imaging Spectroradiometer (MODIS), to evaluate the climatic conditions of focal forests. We observed antecedent drought, low temperature and high photosynthetic radiation conditions before large-scale GF events, suggesting that large-scale GF events could be triggered by these factors. In contrast, we found higher-magnitude GF in forests where lower precipitation preceded large-scale GF events. GF magnitude was also negatively influenced by land surface temperature (LST) for a large-scale GF event. Therefore, we suggest that spatial extent of drought may be related to that of GF forests, and that the spatial pattern of LST may be related to that of GF occurrence. With significant new findings and other results that were consistent with previous research we clarified complicated environmental correlates with the GF phenomenon

A study for reduction of radiation pressure noise in gravitational wave detectors

We describe an experimental conceptual design for observation and reduction of radiation pressure noise. The radiation pressure noise is increased in a high finesse cavity with a small mass mirror. In our experiment a Fabry-Perot Michelson interferometer with a homodyne detection scheme will be built with Fabry-Perot cavities of finesse of 10000 containing suspended mirrors of 23 mg. To observe the radiation pressure noise, the goal sensitivity is set to 1×10^(-17) [m/√Hz] at 1 kHz. Then the radiation pressure noise is reduced by adjusting the homodyne phase. To achieve the sensitivity, the other noise sources such as thermal noises, seismic noise and laser frequency noise should be suppressed below 1×10^(-18) [m/√Hz] at 1kHz. The whole interferometer is suspended as a double pendulum on double-layer stacks. As a preliminary setup, a Fabry-Perot cavity of finesse of 800 with a suspended mirror of 100 mg was locked. The current best sensitivity is 1×10^(-15) [m/√Hz] at 1 kHz