Some Congruence Modulo 2 Statements of Primitive Conway Vassiliev Invariants.

Polynomial knot invariants can often be used to define Vassiliev invariants on singu- lar knots. Here Vassiliev invariants form the Conway, Jones, HOMFLY, and Kauffman polynomials are explored. Also, some explanation is given about how symbols of the Jones and Conway polynomial can evaluated on suitable chord diagrams. These in- variants are further used to find expressions that are congruent modulo 2 to some low degree invariants derived from the Primitive Conway polynomial

MC2^2: Multi-wavelength and dynamical analysis of the merging galaxy cluster ZwCl 0008.8+5215: An older and less massive Bullet Cluster

We analyze a rich dataset including Subaru/SuprimeCam, HST/ACS and WFC3, Keck/DEIMOS, Chandra/ACIS-I, and JVLA/C and D array for the merging galaxy cluster ZwCl 0008.8+5215. With a joint Subaru/HST weak gravitational lensing analysis, we identify two dominant subclusters and estimate the masses to be M$_{200}=\text{5.7}^{+\text{2.8}}_{-\text{1.8}}\times\text{10}^{\text{14}}\,\text{M}_{\odot}$ and 1.2$^{+\text{1.4}}_{-\text{0.6}}\times10^{14}$ M$_{\odot}$. We estimate the projected separation between the two subclusters to be 924$^{+\text{243}}_{-\text{206}}$ kpc. We perform a clustering analysis on confirmed cluster member galaxies and estimate the line of sight velocity difference between the two subclusters to be 92$\pm$164 km s$^{-\text{1}}$. We further motivate, discuss, and analyze the merger scenario through an analysis of the 42 ks of Chandra/ACIS-I and JVLA/C and D polarization data. The X-ray surface brightness profile reveals a remnant core reminiscent of the Bullet Cluster. The X-ray luminosity in the 0.5-7.0 keV band is 1.7$\pm$0.1$\times$10$^{\text{44}}$ erg s$^{-\text{1}}$ and the X-ray temperature is 4.90$\pm$0.13 keV. The radio relics are polarized up to 40$\%$. We implement a Monte Carlo dynamical analysis and estimate the merger velocity at pericenter to be 1800$^{+\text{400}}_{-\text{300}}$ km s$^{-\text{1}}$. ZwCl 0008.8+5215 is a low-mass version of the Bullet Cluster and therefore may prove useful in testing alternative models of dark matter. We do not find significant offsets between dark matter and galaxies, as the uncertainties are large with the current lensing data. Furthermore, in the east, the BCG is offset from other luminous cluster galaxies, which poses a puzzle for defining dark matter -- galaxy offsets.Comment: 22 pages, 19 figures, accepted for publication in the Astrophysical Journal on March 13, 201

The effect of trim angle on the take-off performance

Data obtained at the N.A.C.A. tank from tests on the models of three flying-boat hulls - N.A.C.A. models 11-A, 16, and 22 - are used to demonstrate the effect of trim angle on water resistance. A specific example is taken, and data from Model 11-A are used to show that the trim angle giving the minimum water resistance will give minimum total air-plus-water resistance. Total-resistance curves for best trimmed angles and other angles are compared for the same example. The effect of wind on best trim angles and upon the take-off and run is shown by the working of an example. The possibility of using tank data on trim angles as aid in piloting is discussed, and an instrument for use in determining the trim angle of seaplanes is described. The importance of maintaining the best trim angle throughout the take-off is indicated

MC2^2: Subaru and Hubble Space Telescope Weak-Lensing Analysis of the Double Radio Relic Galaxy Cluster PLCK G287.0+32.9

The second most significant detection of the Planck Sunyaev Zel'dovich survey, PLCK~G287.0+32.9 ($z=0.385$) boasts two similarly bright radio relics and a radio halo. One radio relic is located $\sim 400$ kpc northwest of the X-ray peak and the other $\sim 2.8$ Mpc to the southeast. This large difference suggests that a complex merging scenario is required. A key missing puzzle for the merging scenario reconstruction is the underlying dark matter distribution in high resolution. We present a joint Subaru Telescope and {\it Hubble Space Telescope} weak-lensing analysis of the cluster. Our analysis shows that the mass distribution features four significant substructures. Of the substructures, a primary cluster of mass $M_{200\text{c}}=1.59^{+0.25}_{-0.22}\times 10^{15} \ h^{-1}_{70} \ \text{M}_{\odot}$dominates the weak-lensing signal. This cluster is likely to be undergoing a merger with one (or more) subcluster whose mass is approximately a factor of 10 lower. One candidate is the subcluster of mass$M_{200\text{c}}=1.16^{+0.15}_{-0.13}\times 10^{14} \ h^{-1}_{70} \ \text{M}_{\odot}$located$\sim 400$kpc to the southeast. The location of this subcluster suggests that its interaction with the primary cluster could be the source of the NW radio relic. Another subcluster is detected$\sim 2$Mpc to the SE of the X-ray peak with mass$M_{200\text{c}}=1.68^{+0.22}_{-0.20}\times 10^{14} \ h^{-1}_{70} \ \text{M}_{\odot}$. This SE subcluster is in the vicinity of the SE radio relic and may have created the SE radio relic during a past merger with the primary cluster. The fourth subcluster,$M_{200\text{c}}=1.87^{+0.24}_{-0.22}\times 10^{14} \ h^{-1}_{70} \ \text{M}_{\odot}$, is northwest of the X-ray peak and beyond the NW radio relic.Comment: 19 pages, 14 figures; Accepted to Ap

Defect-Driven Anomalous Transport in Fast-Ion Conducting Solid Electrolytes

Solid-state ionic conduction is a key enabler of electrochemical energy storage and conversion. The mechanistic connections between material processing, defect chemistry, transport dynamics, and practical performance are of considerable importance, but remain incomplete. Here, inspired by studies of fluids and biophysical systems, we re-examine anomalous diffusion in the iconic two-dimensional fast-ion conductors, the $\beta$- and $\beta^{\prime\prime}$-aluminas. Using large-scale simulations, we reproduce the frequency dependence of alternating-current ionic conductivity data. We show how the distribution of charge-compensating defects, modulated by processing, drives static and dynamic disorder, which lead to persistent sub-diffusive ion transport at macroscopic timescales. We deconvolute the effects of repulsions between mobile ions, the attraction between the mobile ions and charge-compensating defects, and geometric crowding on ionic conductivity. Our quantitative framework based on these model solid electrolytes connects their atomistic defect chemistry to macroscopic performance with minimal assumptions and enables mechanism-driven 'atoms-to-device' optimization of fast-ion conductors.Comment: 45 pages, 23 figures. Additional code is available at https://github.com/apoletayev/anomalous_ion_conductio

The rise and fall of star-formation in z∼0.2\bf z\sim0.2 merging galaxy clusters

CIZA J2242.8+5301 (`Sausage') and 1RXS J0603.3+4213 (`Toothbrush') are two low-redshift ($z\sim0.2$), massive ($\sim2\times10^{15}M_\odot$), post-core passage merging clusters, which host shock waves traced by diffuse radio emission. To study their star-formation properties, we uniformly survey the `Sausage' and `Toothbrush' clusters in broad and narrow band filters and select a sample of $201$ and $463$ line emitters, down to a rest-frame equivalent width ($13${\AA}). We robustly separate between H$\alpha$ and higher redshift emitters using a combination of optical multi-band (B, g, V, r, i, z) and spectroscopic data. We build H$\alpha$ luminosity functions for the entire cluster region, near the shock fronts, and away from the shock fronts and find striking differences between the two clusters. In the dynamically younger, $1$ Gyr old `Sausage' cluster we find numerous ($59$) H$\alpha$ emitters above a star-formation rate (SFR) of $0.17$ M_{\sun} yr$^{-1}$ surprisingly located in close proximity to the shock fronts, embedded in very hot intra-cluster medium plasma. The SFR density for the cluster population is at least at the level of typical galaxies at $z\sim2$. Down to the same star-formation rate, the possibly dynamically more evolved `Toothbrush' cluster has only $9$ H$\alpha$ galaxies. The cluster H$\alpha$ galaxies fall on the SFR-stellar mass relation $z\sim0.2$ for the field. However, the `Sausage' cluster has an H$\alpha$ emitter density $>20$ times that of blank fields. If the shock passes through gas-rich cluster galaxies, the compressed gas could collapse into dense clouds and excite star-formation for a few $100$ Myr. This process ultimately leads to a rapid consumption of the molecular gas, accelerating the transformation of gas-rich field spirals into cluster S0s or ellipticals.Comment: Accepted for publication in MNRAS after minor referee report. 21 pages, 15 figures, 5 table