The Moments of the Hydrogen Atom by the Method of Brackets

Expectation values of powers of the radial coordinate in arbitrary hydrogen states are given, in the quantum case, by an integral involving the associated Laguerre function. The method of brackets is used to evaluate the integral in closed-form and to produce an expression for this average value as a finite sum

Hybrid Open-Loop Closed-Loop Control of Coupled Human-Robot Balance During Assisted Stance Transition with Extra Robotic Legs

A new approach to the human-robot shared control of the Extra Robotic Legs (XRL) wearable augmentation system is presented. The XRL system consists of two extra legs that bear the entirety of its backpack payload, as well as some of the human operator's weight. The XRL System must support its own balance and assist the operator stably while allowing them to move in selected directions. In some directions of the task space the XRL must constrain the human motion with position feedback for balance, while in other directions the XRL must have no position feedback, so that the human can move freely. Here, we present Hybrid Open-Loop / Closed-Loop Control Architecture for mixing the two control modes in a systematic manner. The system is reduced to individual joint feedback control that is simple to implement and reliable against failure. The method is applied to the XRL system that assists a human in conducting a nuclear waste decommissioning task. A prototype XRL system has been developed and demonstrated with a simulated human performing the transition from standing to crawling and back again while coupled to the prototype XRL system

IDCS J1426.5+3508: The Most Massive Galaxy Cluster at z>1.5z > 1.5

We present a deep (100 ks) Chandra observation of IDCS J1426.5+3508, a spectroscopically confirmed, infrared-selected galaxy cluster at $z = 1.75$. This cluster is the most massive galaxy cluster currently known at $z > 1.5$, based on existing Sunyaev-Zel'dovich (SZ) and gravitational lensing detections. We confirm this high mass via a variety of X-ray scaling relations, including $T_X$-M, $f_g$-M, $Y_X$-M and $L_X$-M, finding a tight distribution of masses from these different methods, spanning M$_{500}$ = 2.3-3.3 $\times 10^{14}$ M$_{\odot}$, with the low-scatter $Y_X$-based mass $M_{500,Y_X} = 2.6^{+1.5}_{-0.5} \times 10^{14}$ M$_\odot$. IDCS J1426.5+3508 is currently the only cluster at $z > 1.5$ for which X-ray, SZ and gravitational lensing mass estimates exist, and these are in remarkably good agreement. We find a relatively tight distribution of the gas-to-total mass ratio, employing total masses from all of the aforementioned indicators, with values ranging from $f_{gas,500}$ = 0.087-0.12. We do not detect metals in the intracluster medium (ICM) of this system, placing a 2$\sigma$ upper limit of $Z(r < R_{500}) < 0.18 Z_{\odot}$. This upper limit on the metallicity suggests that this system may still be in the process of enriching its ICM. The cluster has a dense, low-entropy core, offset by $\sim$30 kpc from the X-ray centroid, which makes it one of the few "cool core" clusters discovered at $z > 1$, and the first known cool core cluster at $z > 1.2$. The offset of this core from the large-scale centroid suggests that this cluster has had a relatively recent ($\lesssim$500 Myr) merger/interaction with another massive system.Comment: Minor changes to match accepted version, results unchanged; ApJ in pres

Modelling the impact of liner shipping network perturbations on container cargo routing: Southeast Asia to Europe application

Understanding how container routing stands to be impacted by different scenarios of liner shipping network perturbations such as natural disasters or new major infrastructure developments is of key importance for decision-making in the liner shipping industry. The variety of actors and processes within modern supply chains and the complexity of their relationships have previously led to the development of simulation-based models, whose application has been largely compromised by their dependency on extensive and often confidential sets of data. This study proposes the application of optimisation techniques less dependent on complex data sets in order to develop a quantitative framework to assess the impacts of disruptive events on liner shipping networks. We provide a categorization of liner network perturbations, differentiating between systemic and external and formulate a container assignment model that minimises routing costs extending previous implementations to allow feasible solutions when routing capacity is reduced below transport demand. We develop a base case network for the Southeast Asia to Europe liner shipping trade and review of accidents related to port disruptions for two scenarios of seismic and political conflict hazards. Numerical results identify alternative routing paths and costs in the aftermath of port disruptions scenarios and suggest higher vulnerability of intra-regional connectivity

The Spitzer South Pole Telescope Deep Field Survey: Linking galaxies and halos at z=1.5

We present an analysis of the clustering of high-redshift galaxies in the recently completed 94 deg$^2$ Spitzer-SPT Deep Field survey. Applying flux and color cuts to the mid-infrared photometry efficiently selects galaxies at $z\sim1.5$ in the stellar mass range $10^{10}-10^{11}M_\odot$, making this sample the largest used so far to study such a distant population. We measure the angular correlation function in different flux-limited samples at scales $>6^{\prime \prime}$ (corresponding to physical distances $>0.05$ Mpc) and thereby map the one- and two-halo contributions to the clustering. We fit halo occupation distributions and determine how the central galaxy's stellar mass and satellite occupation depend on the halo mass. We measure a prominent peak in the stellar-to-halo mass ratio at a halo mass of $\log(M_{\rm halo} / M_\odot) = 12.44\pm0.08$, 4.5 times higher than the $z=0$ value. This supports the idea of an evolving mass threshold above which star formation is quenched. We estimate the large-scale bias in the range $b_g=2-4$ and the satellite fraction to be $f_\mathrm{sat}\sim0.2$, showing a clear evolution compared to $z=0$. We also find that, above a given stellar mass limit, the fraction of galaxies that are in similar mass pairs is higher at $z=1.5$ than at $z=0$. In addition, we measure that this fraction mildly increases with the stellar mass limit at $z=1.5$, which is the opposite of the behavior seen at low-redshift.Comment: 32 pages, 22 figures. Published in MNRA