Every countable model of set theory embeds into its own constructible universe

The main theorem of this article is that every countable model of set theory M, including every well-founded model, is isomorphic to a submodel of its own constructible universe. In other words, there is an embedding $j:M\to L^M$ that is elementary for quantifier-free assertions. The proof uses universal digraph combinatorics, including an acyclic version of the countable random digraph, which I call the countable random Q-graded digraph, and higher analogues arising as uncountable Fraisse limits, leading to the hypnagogic digraph, a set-homogeneous, class-universal, surreal-numbers-graded acyclic class digraph, closely connected with the surreal numbers. The proof shows that $L^M$ contains a submodel that is a universal acyclic digraph of rank $Ord^M$. The method of proof also establishes that the countable models of set theory are linearly pre-ordered by embeddability: for any two countable models of set theory, one of them is isomorphic to a submodel of the other. Indeed, they are pre-well-ordered by embedability in order-type exactly $\omega_1+1$. Specifically, the countable well-founded models are ordered by embeddability in accordance with the heights of their ordinals; every shorter model embeds into every taller model; every model of set theory $M$ is universal for all countable well-founded binary relations of rank at most $Ord^M$; and every ill-founded model of set theory is universal for all countable acyclic binary relations. Finally, strengthening a classical theorem of Ressayre, the same proof method shows that if $M$ is any nonstandard model of PA, then every countable model of set theory---in particular, every model of ZFC---is isomorphic to a submodel of the hereditarily finite sets $HF^M$ of $M$. Indeed, $HF^M$ is universal for all countable acyclic binary relations.Comment: 25 pages, 2 figures. Questions and commentary can be made at http://jdh.hamkins.org/every-model-embeds-into-own-constructible-universe. (v2 adds a reference and makes minor corrections) (v3 includes further changes, and removes the previous theorem 15, which was incorrect.

Radiative hydrodynamic modelling and observations of the X-class solar flare on 2011 March 9

We investigated the response of the solar atmosphere to non-thermal electron beam heating using the radiative transfer and hydrodynamics modelling code RADYN. The temporal evolution of the parameters that describe the non-thermal electron energy distribution were derived from hard X-ray observations of a particular flare, and we compared the modelled and observed parameters. The evolution of the non-thermal electron beam parameters during the X1.5 solar flare on 2011 March 9 were obtained from analysis of RHESSI X-ray spectra. The RADYN flare model was allowed to evolve for 110 seconds, after which the electron beam heating was ended, and was then allowed to continue evolving for a further 300s. The modelled flare parameters were compared to the observed parameters determined from extreme-ultraviolet spectroscopy. The model produced a hotter and denser flare loop than that observed and also cooled more rapidly, suggesting that additional energy input in the decay phase of the flare is required. In the explosive evaporation phase a region of high-density cool material propagated upward through the corona. This material underwent a rapid increase in temperature as it was unable to radiate away all of the energy deposited across it by the non-thermal electron beam and via thermal conduction. A narrow and high-density ($n_{e} \le 10^{15}$ cm$^{-3}$) region at the base of the flare transition region was the source of optical line emission in the model atmosphere. The collision-stopping depth of electrons was calculated throughout the evolution of the flare, and it was found that the compression of the lower atmosphere may permit electrons to penetrate farther into a flaring atmosphere compared to a quiet Sun atmosphere.Comment: 12 pages, 12 figure

The Strange New World of United States Export Controls Under the International Emergency Economic Powers Act

This Article examines whether the President\u27s reauthorization of the Regulations is within the scope of the authority provided by IEEPA and explores the potential long term consequences of life under IEEPA for the United States system of export and boycott-related controls. Section I analyzes whether the President\u27s emergency powers under the IEEPA permit the maintenance of regulations originally promulgated under a statute that has since lapsed (i.e. the EAA). The Article demonstrates that when Congress promulgated the IEEPA, Congress expressly evinced its intent to give the President broad emergency authority to regulate exports and boycott-related practices during periods of the EAA lapse. Although there are serious doubts whether the lapse of the EAA rises to the level of an unusual and extraordinary threat to the national security, foreign policy, or the economy of the United States sufficient to allow the President to invoke the emergency powers under the IEEPA, the courts\u27 traditionally have been unwilling to review the validity of such Presidential determinations of an emergency. Thus, when the Regulations are maintained under the IEEPA during periods of EAA lapse, they nevertheless should be considered valid. Section II analyzes how the shift from the EAA to the IEEPA can affect the basic structure of United States export controls and boycott-related restrictions. It then examines the consequences of these changes for both businesses subject to the Regulations and for Congress, which traditionally has exercised a major role in the regulation of exports. Although Congress narrowly structured the EAA to provide a long-term framework for export and boycott-related controls, the broadly worded IEEPA does not contain such requirements or guidelines that limit the scope of the Administration\u27s discretion. Thus, under the guise of his emergency powers, the President can safely ignore the requirements and standards of the lapsed EAA, and unilaterally restructure the Commerce Department\u27s Regulations for the duration of the emergency. While the IEEPA permits greater judicial review of Commerce Department actions than did the EAA, such lawsuits rarely succeed in reversing the Commerce Department\u27s decisions and cannot limit the President\u27s discretion to reshape United States export controls and boycott-related restrictions in an emergency. Thus, a lengthy EAA lapse, like the recent one, allows the President to exercise unilateral emergency authority under the IEEPA, resulting in: (1) an unstable regulatory environment for international business transactions; and (2) an eclipse of the traditional role of Congress in structuring export controls. This article concludes by urging that when the EAA has lapsed, Congress should immediately reauthorize this important enabling statute in order to provide a more predictable regulatory environment for United States exporters and to reclaim its plenary authority in the regulation of foreign commerce. Moreover, with possible future lapses of the EAA in mind, Congress also should amend the IEEPA to require the maintenance of the Regulations without material change during future periods of lapse

Computer Simulation of Cytoskeleton-Induced Blebbing in Lipid Membranes

Blebs are balloon-shaped membrane protrusions that form during many physiological processes. Using computer simulation of a particle-based model for self-assembled lipid bilayers coupled to an elastic meshwork, we investigated the phase behavior and kinetics of blebbing. We found that blebs form for large values of the ratio between the areas of the bilayer and the cytoskeleton. We also found that blebbing can be induced when the cytoskeleton is subject to a localized ablation or a uniform compression. The results obtained are qualitatively in agreement with the experimental evidence and the model opens up the possibility to study the kinetics of bleb formation in detail.Comment: To appear in Physical Review

Many-body quantum dynamics of polarisation squeezing in optical fibre

We report new experiments that test quantum dynamical predictions of polarization squeezing for ultrashort photonic pulses in a birefringent fibre, including all relevant dissipative effects. This exponentially complex many-body problem is solved by means of a stochastic phase-space method. The squeezing is calculated and compared to experimental data, resulting in excellent quantitative agreement. From the simulations, we identify the physical limits to quantum noise reduction in optical fibres. The research represents a significant experimental test of first-principles time-domain quantum dynamics in a one-dimensional interacting Bose gas coupled to dissipative reservoirs.Comment: 4 pages, 4 figure

Nonlinear Development of the Secular Bar-mode Instability in Rotating Neutron Stars

We have modelled the nonlinear development of the secular bar-mode instability that is driven by gravitational radiation-reaction (GRR) forces in rotating neutron stars. In the absence of any competing viscous effects, an initially uniformly rotating, axisymmetric $n=1/2$ polytropic star with a ratio of rotational to gravitational potential energy $T/|W| = 0.181$ is driven by GRR forces to a bar-like structure, as predicted by linear theory. The pattern frequency of the bar slows to nearly zero, that is, the bar becomes almost stationary as viewed from an inertial frame of reference as GRR removes energy and angular momentum from the star. In this ``Dedekind-like'' state, rotational energy is stored as motion of the fluid in highly noncircular orbits inside the bar. However, in less than 10 dynamical times after its formation, the bar loses its initially coherent structure as the ordered flow inside the bar is disrupted by what appears to be a purely hydrodynamical, short-wavelength, ``shearing'' type instability. The gravitational waveforms generated by such an event are determined, and an estimate of the detectability of these waves is presented.Comment: 25 pages, 9 figures, accepted for publication in ApJ, refereed version, updated, for quicktime movie, see http://www.phys.lsu.edu/~ou/movie/fmode/new/fmode.b181.om4.2e5.mo

The Dependence of the Soft X-ray Properties of LMXBs on the Metallicity of Their Environment

We determine the X-ray spectral properties of a sample of low-mass X-ray binaries (LMXBs) which reside in globular clusters of M31, as well as five LMXBs in Galactic globular clusters and in the Large Magellanic Cloud using the ROSAT PSPC. We find a trend in the X-ray properties of the LMXBs as a function of globular cluster metallicity. The spectra of LMXBs become progressively softer as the metallicity of its environment increases. The one M31 globular cluster LMXB in our sample which has a metallicity greater than solar has spectral properties similar to those of LMXBs in the bulge of M31, but markedly different from those which reside in low metallicity globular clusters, both in M31 and the Galaxy. The spectral properties of this high metallicity LMXB is also similar to those of X-ray faint early-type galaxies. This lends support to the claim that a majority of the X-ray emission from these X-ray faint early-type galaxies results from LMXBs and not hot gas, as is the case in their X-ray bright counterparts.Comment: 5 pages, 2 embedded Postscript figures, uses emulateapj.sty, Astrophysical Journal Letters, in pres

Rock magnetic and geochemical evidence for authigenic magnetite formation via iron reduction in coal-bearing sediments offshore Shimokita Peninsula, Japan (IODP Site C0020)

Sediments recovered at Integrated Ocean Drilling Program (IODP) Site C0020, in a fore‐arc basin offshore Shimokita Peninsula, Japan, include numerous coal beds (0.3–7 m thick) that are associated with a transition from a terrestrial to marine depositional environment. Within the primary coal‐bearing unit (∼2 km depth below seafloor) there are sharp increases in magnetic susceptibility in close proximity to the coal beds, superimposed on a background of consistently low magnetic susceptibility throughout the remainder of the recovered stratigraphic sequence. We investigate the source of the magnetic susceptibility variability and characterize the dominant magnetic assemblage throughout the entire cored record, using isothermal remanent magnetization (IRM), thermal demagnetization, anhysteretic remanent magnetization (ARM), iron speciation, and iron isotopes. Magnetic mineral assemblages in all samples are dominated by very low‐coercivity minerals with unblocking temperatures between 350 and 580°C that are interpreted to be magnetite. Samples with lower unblocking temperatures (300–400°C), higher ARM, higher‐frequency dependence, and isotopically heavy δ56Fe across a range of lithologies in the coal‐bearing unit (between 1925 and 1995 mbsf) indicate the presence of fine‐grained authigenic magnetite. We suggest that iron‐reducing bacteria facilitated the production of fine‐grained magnetite within the coal‐bearing unit during burial and interaction with pore waters. The coal/peat acted as a source of electron donors during burial, mediated by humic acids, to supply iron‐reducing bacteria in the surrounding siliciclastic sediments. These results indicate that coal‐bearing sediments may play an important role in iron cycling in subsiding peat environments and if buried deeply through time, within the subsequent deep biosphere

Evidence for Accretion in the High-resolution X-ray Spectrum of the T Tauri Star System Hen 3-600

We present high-resolution X-ray spectra of the multiple T Tauri star system Hen 3-600, obtained with the High Energy Transmission Grating Spectrograph on the Chandra X-ray Observatory. Two binary components were detected in the zeroth-order image. Hen 3-600-A, which has a large mid-infrared excess, is a 2-3 times fainter in X-rays than Hen 3-600-B, due to a large flare on B. The dispersed X-ray spectra of the two primary components overlap spatially; spectral analysis was performed on the combined system. Analysis of the individual spectra was limited to regions where the contributions of A and B can be disentangled. This analysis results in two lines of evidence indicating that the X-ray emission from Hen 3-600 is derived from accretion processes: line ratios of O VII indicate that the characteristic density of its X-ray-emitting plasma is large; a significant component of low-temperature plasma is present and is stronger in component A. These results are consistent with results obtained from X-ray gratings spectroscopy of more rapidly accreting systems. All of the signatures of Hen 3-600 that are potential diagnostics of accretion activity -- X-ray emission, UV excess, H-alpha emission, and weak infrared excess -- suggest that its components represent a transition phase between rapidly accreting, classical T Tauri stars and non-accreting, weak-lined T Tauri stars.Comment: latex, 27 pages, 12 figures, 6 tables; accepted by Ap