Mixing of Ground States in Vertex Models

We consider the analogue of the 6-vertex model constructed from alternating spin n/2 and spin m/2 lines, where $1\leq n<m$. We identify the transfer matrix and the space on which it acts in terms of the representation theory of $U_q(sl_2)$. We diagonalise the transfer matrix and compute the S-matrix. We give a trace formula for local correlation functions. When n=1, the 1-point function of a spin m/2 local variable for the alternating lattice with a particular ground state is given as a linear combination of the 1-point functions of the pure spin m/2 model with different ground states. The mixing ratios are calculated exactly and are expressed in terms of irreducible characters of $U_q(sl_2)$ and the deformed Virasoro algebra.Comment: 12 pages, LaTeX, typos correcte

Design Principles for Energy-Efficient Legged Locomotion and Implementation on the MIT Cheetah Robot

This paper presents the design principles for highly efficient legged robots, the implementation of the principles in the design of the MIT Cheetah, and the analysis of the high-speed trotting experimental results. The design principles were derived by analyzing three major energy-loss mechanisms in locomotion: heat losses from the actuators, friction losses in transmission, and the interaction losses caused by the interface between the system and the environment. Four design principles that minimize these losses are discussed: employment of high torque-density motors, energy regenerative electronic system, low loss transmission, and a low leg inertia. These principles were implemented in the design of the MIT Cheetah; the major design features are large gap diameter motors, regenerative electric motor drivers, single-stage low gear transmission, dual coaxial motors with composite legs, and the differential actuated spine. The experimental results of fast trotting are presented; the 33-kg robot runs at 22 km/h (6 m/s). The total power consumption from the battery pack was 973 W and resulted in a total cost of transport of 0.5, which rivals running animals' at the same scale. 76% of the total energy consumption is attributed to heat loss from the motor, and the remaining 24% is used in mechanical work, which is dissipated as interaction loss as well as friction losses at the joint and transmission.United States. Defense Advanced Research Projects Agency (M3 Program

Magnetoelectric effects of nanoparticulate Pb(Zr0.52Ti0.48)O3-NiFe2O4 composite films

We fabricated Pb(Zr0.52Ti0.48)O3-NiFe2O4 composite films consisting of randomly dispersed NiFe2O4 nanoparticles in the Pb(Zr0.52Ti0.48)O3 matrix. The structural analysis revealed that the crystal axes of the NiFe2O4 nanoparticles are aligned with those of the ferroelectric matrix. The composite has good ferroelectric and magnetic properties. We measured the transverse and longitudinal components of the magnetoelectric voltage coefficient, which supports the postulate that the magnetoelectric effect comes from direct stress coupling between magnetostrictive NiFe2O4 and piezoelectric Pb(Zr0.52Ti0.48)O3 grains.Comment: 11 pages, 4 figure

Super Helium-Rich Population and the Origin of Extreme Horizontal-Branch Stars in Globular Clusters

Recent observations for the color-magnitude diagrams (CMDs) of the massive globular cluster Omega Centauri have shown that it has a striking double main sequence (MS), with a minority population of bluer and fainter MS well separated from a majority population of MS stars. Here we confirm, with the most up-to-date Y2 isochrones, that this special feature can only be reproduced by assuming a large variation (Delta Y = 0.15) of primordial helium abundance among several distinct populations in this cluster. We further show that the same helium enhancement required for this special feature on the MS can by itself reproduce the extreme horizontal-branch (HB) stars observed in Omega Cen, which are hotter than normal HB stars. Similarly, the complex features on the HBs of other globular clusters, such as NGC 2808, are explained by large internal variations of helium abundance. Supporting evidence for the helium-rich population is also provided by the far-UV (FUV) observations of extreme HB stars in these clusters, where the enhancement of helium can naturally explain the observed fainter FUV luminosity for these stars. The presence of super helium-rich populations in some globular clusters suggests that the third parameter, other than metallicity and age, also influences CMD morphology of these clusters.Comment: 4 pages, 4 figures, accepted for publication in the Astrophysical Journal Letter

Human cell-camouflaged nanomagnetic scavengers restore immune homeostasis in a rodent model with bacteremia

Bloodstream infection caused by antimicrobial resistance pathogens is a global concern because it is difficult to treat with conventional therapy. Here, scavenger magnetic nanoparticles enveloped by nanovesicles derived from blood cells (MNVs) are reported, which magnetically eradicate an extreme range of pathogens in an extracorporeal circuit. It is quantitatively revealed that glycophorin A and complement receptor (CR) 1 on red blood cell (RBC)-MNVs predominantly capture human fecal bacteria, carbapenem-resistant (CR) Escherichia coli, and extended-spectrum beta-lactamases-positive (ESBL-positive) E. coli, vancomycin-intermediate Staphylococcus aureus (VISA), endotoxins, and proinflammatory cytokines in human blood. Additionally, CR3 and CR1 on white blood cell-MNVs mainly contribute to depleting the virus envelope proteins of Zika, SARS-CoV-2, and their variants in human blood. Supplementing opsonins into the blood significantly augments the pathogen removal efficiency due to its combinatorial interactions between pathogens and CR1 and CR3 on MNVs. The extracorporeal blood cleansing enables full recovery of lethally infected rodent animals within 7 days by treating them twice in series. It is also validated that parameters reflecting immune homeostasis, such as blood cell counts, cytokine levels, and transcriptomics changes, are restored in blood of the fatally infected rats after treatment