Combining symmetry collective states with coupled cluster theory: Lessons from the Agassi model Hamiltonian

The failures of single-reference coupled cluster for strongly correlated many-body systems is flagged at the mean-field level by the spontaneous breaking of one or more physical symmetries of the Hamiltonian. Restoring the symmetry of the mean-field determinant by projection reveals that coupled cluster fails because it factorizes high-order excitation amplitudes incorrectly. However, symmetry-projected mean-field wave functions do not account sufficiently for dynamic (or weak) correlation. Here we pursue a merger of symmetry projection and coupled cluster theory, following previous work along these lines that utilized the simple Lipkin model system as a testbed [J. Chem. Phys. 146, 054110 (2017)]. We generalize the concept of a symmetry-projected mean-field wave function to the concept of a symmetry projected state, in which the factorization of high-order excitation amplitudes in terms of low-order ones is guided by symmetry projection and is not exponential, and combine them with coupled cluster theory in order to model the ground state of the Agassi Hamiltonian. This model has two separate channels of correlation and two separate physical symmetries which are broken under strong correlation. We show how the combination of symmetry collective states and coupled cluster is effective in obtaining correlation energies and order parameters of the Agassi model throughout its phase diagram

Performance, emissions, and physical characteristics of a rotating combustion aircraft engine

The RC2-75, a liquid cooled two chamber rotary combustion engine (Wankel type), designed for aircraft use, was tested and representative baseline (212 KW, 285 BHP) performance and emissions characteristics established. The testing included running fuel/air mixture control curves and varied ignition timing to permit selection of desirable and practical settings for running wide open throttle curves, propeller load curves, variable manifold pressure curves covering cruise conditions, and EPA cycle operating points. Performance and emissions data were recorded for all of the points run. In addition to the test data, information required to characterize the engine and evaluate its performance in aircraft use is provided over a range from one half to twice its present power. The exhaust emissions results are compared to the 1980 EPA requirements. Standard day take-off brake specific fuel consumption is 356 g/KW-HR (.585 lb/BHP-HR) for the configuration tested

Research in the general area of non-linear dynamical systems Final report, 8 Jun. 1965 - 8 Jun. 1967

Nonlinear dynamical systems research on systems stability, invariance principles, Liapunov functions, and Volterra and functional integral equation

When flux standards go wild: white dwarfs in the age of Kepler

White dwarf stars have been used as flux standards for decades, thanks to their staid simplicity. We have empirically tested their photometric stability by analyzing the light curves of 398 high-probability candidates and spectroscopically confirmed white dwarfs observed during the original Kepler mission and later with K2 Campaigns 0-8. We find that the vast majority (>97 per cent) of non-pulsating and apparently isolated white dwarfs are stable to better than 1 per cent in the Kepler bandpass on 1-hr to 10-d timescales, confirming that these stellar remnants are useful flux standards. From the cases that do exhibit significant variability, we caution that binarity, magnetism, and pulsations are three important attributes to rule out when establishing white dwarfs as flux standards, especially those hotter than 30,000 K.Comment: Accepted for publication in MNRAS; 7 pages, 4 figures, 2 table

Discovery of an ultramassive pulsating white dwarf

We announce the discovery of the most massive pulsating hydrogen-atmosphere (DA) white dwarf (WD) ever discovered, GD 518. Model atmosphere fits to the optical spectrum of this star show it is a 12,030 +/- 210 K WD with a log(g) = 9.08 +/- 0.06, which corresponds to a mass of 1.20 +/- 0.03 Msun. Stellar evolution models indicate that the progenitor of such a high-mass WD endured a stable carbon-burning phase, producing an oxygen-neon-core WD. The discovery of pulsations in GD 518 thus offers the first opportunity to probe the interior of a WD with a possible oxygen-neon core. Such a massive WD should also be significantly crystallized at this temperature. The star exhibits multi-periodic luminosity variations at timescales ranging from roughly 425-595 s and amplitudes up to 0.7%, consistent in period and amplitude with the observed variability of typical ZZ Ceti stars, which exhibit non-radial g-mode pulsations driven by a hydrogen partial ionization zone. Successfully unraveling both the total mass and core composition of GD 518 provides a unique opportunity to investigate intermediate-mass stellar evolution, and can possibly place an upper limit to the mass of a carbon-oxygen-core WD, which in turn constrains SNe Ia progenitor systems.Comment: 5 pages, 3 figures, Astrophysical Journal Letters, 771, L2 (2013

Complex charge ordering in CeRuSn

At ambient temperatures, CeRuSn exhibits an extraordinary structure with a coexistence of two types of Ce ions in a metallic environment, namely trivalent Ce3 and intermediate valent Ce 4 amp; 8722; amp; 948; . Charge ordering produces a doubling of the unit cell along the c axis with respect to the basic monoclinic CeCoAl type structure. Below room temperature, a phase transition with very broad hysteresis has been observed in various bulk properties like electrical resistivity, magnetic susceptibility, and specific heat. The present x ray diffraction results show that at low temperatures the doubling of the CeCoAl type structure is replaced by an ill defined modulated ground state. In this state, at least three different modulation periods compete, with the dominant mode close to a tripling of the basic cell. The transition is accompanied by a significant contraction of the c axis. XANES data suggest that the average Ce valence remains constant; thus the observed c axis contraction is not due to any valence transition. We propose a qualitative structure model with modified stacking sequences of Ce3 and Ce 4 amp; 8722; amp; 948; layers in the various modulated phases. Surprisingly, far below 100 K, the modulated state is sensitive to x ray irradiation at photon fluxes available at a synchrotron. With photon fluxes of order 1012 s amp; 8722;1, the modulated ground state can be destroyed on a time scale of minutes and the doubling of the CeCoAl cell observed at room temperature is recovered. The final state is metastable at 10 K. Heating the sample above 60 K again leads to a recovery of the modulated state. Thus CeRuSn exhibits both thermally and x ray induced reversible transformations of the Ce3 Ce 4 amp; 8722; amp; 948; charge ordering pattern. Such a behavior is unique among any known intermetallic compoun

The Shortest Period Detached Binary White Dwarf System

We identify SDSS J010657.39-100003.3 (hereafter J0106-1000) as the shortest period detached binary white dwarf (WD) system currently known. We targeted J0106-1000 as part of our radial velocity program to search for companions around known extremely low-mass (ELM, ~ 0.2 Msol) WDs using the 6.5m MMT. We detect peak-to-peak radial velocity variations of 740 km/s with an orbital period of 39.1 min. The mass function and optical photometry rule out a main-sequence star companion. Follow-up high-speed photometric observations obtained at the McDonald 2.1m telescope reveal ellipsoidal variations from the distorted primary but no eclipses. This is the first example of a tidally distorted WD. Modeling the lightcurve, we constrain the inclination angle of the system to be 67 +- 13 deg. J0106-1000 contains a pair of WDs (0.17 Msol primary + 0.43 Msol invisible secondary) at a separation of 0.32 Rsol. The two WDs will merge in 37 Myr and most likely form a core He-burning single subdwarf star. J0106-1000 is the shortest timescale merger system currently known. The gravitational wave strain from J0106-1000 is at the detection limit of the Laser Interferometer Space Antenna (LISA). However, accurate ephemeris and orbital period measurements may enable LISA to detect J0106-1000 above the Galactic background noise.Comment: MNRAS Letters, in pres

Rapid Orbital Decay in the 12.75-Minute Binary White Dwarf J0651+2844

We report the detection of orbital decay in the 12.75-minute, detached binary white dwarf (WD) SDSS J065133.338+284423.37 (hereafter J0651). Our photometric observations over a 13 month baseline constrain the orbital period to 765.206543(55) s and indicate that the orbit is decreasing at a rate of (-9.8 +/- 2.8) x 10(-12) s s(-1) (or -0.31 +/- 0.09 ms yr(-1)). We revise the system parameters based on our new photometric and spectroscopic observations: J0651 contains two WDs with M-1 = 0.26 +/- 0.04 M-circle dot and M-2 = 0.50 +/- 0.04 M-circle dot. General relativity predicts orbital decay due to gravitational wave radiation of (-8.2 +/- 1.7) x 10(-12) s s(-1) (or -0.26 +/- 0.05 ms yr(-1)). Our observed rate of orbital decay is consistent with this expectation. J0651 is currently the second-loudest gravitational wave source known in the milli-Hertz range and the loudest non-interacting binary, which makes it an excellent verification source for future missions aimed at directly detecting gravitational waves. Our work establishes the feasibility of monitoring this system's orbital period decay at optical wavelengths.NSF AST-0909107, AST-1008734Norman Hackerman Advanced Research Program 003658-0252-2009Astronom

Discovery of pulsations, including possible pressure modes, in two new extremely low mass, He-core white dwarfs

We report the discovery of the second and third pulsating extremely low mass white dwarfs (WDs), SDSS J111215.82+111745.0 (hereafter J1112) and SDSS J151826.68+065813.2 (hereafter J1518). Both have masses < 0.25 Msun and effective temperatures below 10,000 K, establishing these putatively He-core WDs as a cooler class of pulsating hydrogen-atmosphere WDs (DAVs, or ZZ Ceti stars). The short-period pulsations evidenced in the light curve of J1112 may also represent the first observation of acoustic (p-mode) pulsations in any WD, which provide an exciting opportunity to probe this WD in a complimentary way compared to the long-period g-modes also present. J1112 is a Teff = 9590 +/- 140 K and log(g) = 6.36 +/- 0.06 WD. The star displays sinusoidal variability at five distinct periodicities between 1792-2855 s. In this star we also see short-period variability, strongest at 134.3 s, well short of expected g-modes for such a low-mass WD. The other new pulsating WD, J1518, is a Teff = 9900 +/- 140 K and log(g) = 6.80 +/- 0.05 WD. The light curve of J1518 is highly non-sinusoidal, with at least seven significant periods between 1335-3848 s. Consistent with the expectation that ELM WDs must be formed in binaries, these two new pulsating He-core WDs, in addition to the prototype SDSS J184037.78+642312.3, have close companions. However, the observed variability is inconsistent with tidally induced pulsations and is so far best explained by the same hydrogen partial-ionization driving mechanism at work in classic C/O-core ZZ Ceti stars.Comment: 9 pages, 5 figures, accepted to The Astrophysical Journa