Magnetic properties of geometrically frustrated SrGd2O4

A study of the magnetic properties of the frustrated rare earth oxide SrGd2O4 has been completed using bulk property measurements of magnetization, susceptibility and specific heat on single crystal samples. Two zero-field phase transitions have been identified at 2.73 and 0.48 K. For the field, H, applied along the a and b axes, a single boundary is identified that delineates the transition from a low field, low temperature magnetically ordered regime to a high field, high temperature paramagnetic phase. Several field-induced transitions, however, have been observed with H || c. The measurements have been used to map out the magnetic phase diagram of SrGd2O4, suggesting that it is a complex system with several competing magnetic interactions. The low-temperature magnetic behavior of SrGd2O4 is very different compared to the other SrLn2O4 (Ln = Lanthanide) compounds, even though all of the SrLn2O4 compounds are isostructural, with the magnetic ions forming a low-dimensional lattice of zigzag chains that run along the c axis. The differences are likely to be due to the fact that in the ground state Gd3+ has zero orbital angular momentum and therefore the spin-orbit interactions, which are crucial for other SrLn2O4 compounds, can largely be neglected. Instead, given the relatively short Gd3+-Gd3+ distances in SrGd2O4, dipolar interactions must be taken into account for this antiferromagnet alongside the Heisenberg exchange terms.Comment: 10 pages, 9 figure

Tiny Groups Tackle Byzantine Adversaries

A popular technique for tolerating malicious faults in open distributed systems is to establish small groups of participants, each of which has a non-faulty majority. These groups are used as building blocks to design attack-resistant algorithms. Despite over a decade of active research, current constructions require group sizes of $O(\log n)$, where $n$ is the number of participants in the system. This group size is important since communication and state costs scale polynomially with this parameter. Given the stubbornness of this logarithmic barrier, a natural question is whether better bounds are possible. Here, we consider an attacker that controls a constant fraction of the total computational resources in the system. By leveraging proof-of-work (PoW), we demonstrate how to reduce the group size exponentially to $O(\log\log n)$ while maintaining strong security guarantees. This reduction in group size yields a significant improvement in communication and state costs.Comment: This work is supported by the National Science Foundation grant CCF 1613772 and a C Spire Research Gif

Lattice dynamics of anharmonic solids from first principles

An accurate and easily extendable method to deal with lattice dynamics of solids is offered. It is based on first-principles molecular dynamics simulations and provides a consistent way to extract the best possible harmonic - or higher order - potential energy surface at finite temperatures. It is designed to work even for strongly anharmonic systems where the traditional quasiharmonic approximation fails. The accuracy and convergence of the method are controlled in a straightforward way. Excellent agreement of the calculated phonon dispersion relations at finite temperature with experimental results for bcc Li and bcc Zr is demonstrated

Proportional-integral-plus (PIP) control of time delay systems

The paper shows that the digital proportional-integral-plus (PIP) controller formulated within the context of non-minimum state space (NMSS) control system design methodology is directly equivalent, under certain non-restrictive pole assignment conditions, to the equivalent digital Smith predictor (SP) control system for time delay systems. This allows SP controllers to be considered within the context of NMSS state variable feedback control, so that optimal design methods can be exploited to enhance the performance of the SP controller. Alternatively, since the PIP design strategy provides a more flexible approach, which subsumes the SP controller as one option, it provides a superior basis for general control system design. The paper also discusses the robustness and disturbance response characteristics of the two PIP control structures that emerge from the analysis and demonstrates the efficacy of the design methods through simulation examples and the design of a climate control system for a large horticultural glasshouse system

Algebraic KK-theory and Grothendieck-Witt theory of monoid schemes

We study the algebraic $K$-theory and Grothendieck-Witt theory of proto-exact categories of vector bundles over monoid schemes. Our main results are the complete description of the algebraic $K$-theory space of an integral monoid scheme $X$ in terms of its Picard group $\operatorname{Pic}(X)$ and pointed monoid of regular functions $\Gamma(X, \mathcal{O}_X)$ and a description of the Grothendieck-Witt space of $X$ in terms of an additional involution on $\operatorname{Pic}(X)$. We also prove space-level projective bundle formulae in both settings

Group completion in the K-theory and Grothendieck-Witt theory of proto-exact categories

We study the algebraic $K$-theory and Grothendieck-Witt theory of proto-exact categories, with a particular focus on classes of examples of $\mathbb{F}_1$-linear nature. Our main results are analogues of theorems of Quillen and Schlichting, relating the $K$-theory or Grothendieck-Witt theories of proto-exact categories defined using the (hermitian) $Q$-construction and group completion

Locating Star-Forming Regions in Quasar Host Galaxies

We present a study of the morphology and intensity of star formation in the host galaxies of eight Palomar-Green quasars using observations with the Hubble Space Telescope. Our observations are motivated by recent evidence for a close relationship between black hole growth and the stellar mass evolution in its host galaxy. We use narrow-band [O II] $\lambda$3727, H$\beta$, [O III] $\lambda$5007 and Pa$\alpha$ images, taken with the WFPC2 and NICMOS instruments, to map the morphology of line-emitting regions, and, after extinction corrections, diagnose the excitation mechanism and infer star-formation rates. Significant challenges in this type of work are the separation of the quasar light from the stellar continuum and the quasar-excited gas from the star-forming regions. To this end, we present a novel technique for image decomposition and subtraction of quasar light. Our primary result is the detection of extended line-emitting regions with sizes ranging from 0.5 to 5 kpc and distributed symmetrically around the nucleus, powered primarily by star formation. We determine star-formation rates of order a few tens of M$_\odot$/yr. The host galaxies of our target quasars have stellar masses of order $10^{11}$ M$_\odot$ and specific star formation rates on a par with those of M82 and luminous infrared galaxies. As such they fall at the upper envelope or just above the star-formation mass sequence in the specific star formation vs stellar mass diagram. We see a clear trend of increasing star formation rate with quasar luminosity, reinforcing the link between the growth of the stellar mass of the host and the black hole mass found by other authors.Comment: Accepted for publication in M.N.R.A.