Could MT2 be a singularity variable?

The algebraic singularity method is a framework for analyzing collider events with missing energy. It provides a way to draw out a set of singularity variables that can catch singular features originating from the projection of full phase space onto the observable phase space of measured particle momenta. It is a promising approach applicable to various physics processes with missing energy but still requires more studies for use in practice. Meanwhile, in the double-sided decay topology with an invisible particle on each side, the MT2 variable has been known to be a useful collider observable for measuring particle masses from missing energy events or setting signal regions of collider searches. We investigate the relation between the two different types of kinematic variables in double-sided decay topology. We find that the singularity variables contain the MT2 variable in many cases, although the former is not a strict superset of the latter.

Serial-robot Wrist-singularity Mitigation Along Alternative Optimally Adjusted Paths

Adjusting the displacement path of a serial robot encountering the wrist singularity to pass either through the singularity or around it mitigates its adverse effects. Both such path adjustments are commonly called singularity avoidance and are applied here to either a spherical or an offset wrist. These adjustments avoid high joint rates that can occur at singularity encounter. A recent through-the singularity method limits joint rates and accelerations in the robot with either a spherical or offset wrist when conducting a constant rate of traversal of the tool manipulated by the robot. A kinematic model adding multiple virtual joints allows a modified high-order path-following algorithm to maintain accurate tool position while achieving an optimal level of tool deviation in orientation. Whereas a path reversal resulting from a turning-point type singularity had been revealed for an offset wrist over a finite range of close-approach, these conditions are met when connecting the isolated path segments. Procedures are developed here with this capability for an around-the-singularity path. Choosing between the through and around-singularity alternatives offers the overall optimum.

Software for hydraulic design of axial-flow pump impellers and its manufacturing documentations

This article presents a hydraulic design procedure for axial-flow pump impellers, followed by their manufacturing documentations, all in one easy-to-use software named AXPHD V2.0 (AXial Pump Hydraulic Design) developed by one of the authors (Kalmár). After the user determined pump duty, the software offers input data which may be changed interactively. The hydrodynamic singularity method is used to compute the blade profiles on cylindrical surfaces. If the velocity and pressure distributions are accepted, then the body model of the impeller is produced by AUTODESK INVENTOR PROFESSIONAL 2019. Full manufacturing documentation is prepared including shop-drawings for traditional production, numeric modules for CAM, and files for 3D printing. A photo of an impeller made by 3D printing closes the paper.

Detection of Thermal Changes Related to the 2011 Shinmoedake Volcano Activity, Japan: Spatiotemporal Variation of Singularity of MODIS Data after Discriminating False Changes Due to Cloud

We proposed a cloud discrimination method applicable in Japan using MODIS nighttime data, monitored the singularity of the spatiotemporal correlation of surface temperature anomalies and investigated the possibility of detecting and monitoring lava activity in Shinmoedake. With the aim to detect lava eruption activity in 2011, nine years of data from 2003 to 2011 were analyzed. As a result, the first anomalous singularity in brightness temperature was detected on 26 January 2011. Moreover, the maximum value was detected on 30 January 2011. The values showed larger ones until early February 2011. When an anomalous singularity appeared, it was the only period with the magma-related volcanic activity for Shinmoedake over the analyzed period of nine years. The above facts indicate the effectiveness of the proposed singularity method to monitor the lava activity for Shinmoedake. Therefore, it is concluded that if cloud discrimination is realized with high accuracy, no spurious changes will come to arise, and no false detection of hotspots will be given.

Bifurcation Analysis for a Simple Dual-Rotor System with Nonlinear Intershaft Bearing Based on the Singularity Method

This paper aims to classify bifurcation modes for two interrelated primary resonances of a simple dual-rotor system under double frequency excitations. The four degree-of-freedom (4DOF) dynamic equations of the system considering the nonlinearity of the intershaft bearing can be obtained by using the assumed mode method (AMM) and Lagrange’s equation. A simplified method for dynamic equations is developed due to the symmetry of rotors, based on which the amplitude frequency equations for two interrelated primary resonances are obtained by using the multiple scales method. Furthermore, the validity of the simplified method for dynamic equations and the amplitude frequency equations solved by the multiple scales method are confirmed by numerical verification. Afterwards, the bifurcation analysis for two interrelated primary resonances is carried out according to the two-state-variable singularity method. There exist a total of three different types of bifurcation modes because of double frequency excitations of the dual-rotor system and the nonlinearity of the intershaft bearing. The second primary resonance is more prone to have nonlinear dynamic characteristics than the first primary resonance. This discovery indicates that two interrelated primary resonances of the dual-rotor system may have different bifurcation modes under the same dynamic parameters.

On the Calculation of 2D Green's Functions Via Sommerfeld Integrals and the Spatial Singularity Method

<p>We provide a low-level review of the computation of Sommerfeld integration theory using the singularity expansion method (SEM) to analytically estimate the short-wavelength components of the 2-dimensional Green's function. The SEM is employed to replace the infinite tail of the spectral integral by a closed-form evaluation. The various steps in the SEM substitution and the calculations are elaborately presented and discussed with emphasis on giving the missing details often not included in the published literature.<b></b></p>

On the Calculation of 2D Green's Functions Via Sommerfeld Integrals and the Spatial Singularity Method

<p>We provide a low-level review of the computation of Sommerfeld integration theory using the singularity expansion method (SEM) to analytically estimate the short-wavelength components of the 2-dimensional Green's function. The SEM is employed to replace the infinite tail of the spectral integral by a closed-form evaluation. The various steps in the SEM substitution and the calculations are elaborately presented and discussed with emphasis on giving the missing details often not included in the published literature.<b></b></p>