Compact stellarators with modular coils

Compact stellarator designs with modular coils and only two or three field periods are now available; these designs have both good stability and quasiaxial symmetry providing adequate transport for a magnetic fusion reactor. If the bootstrap current assumes theoretically predicted values a three field period configuration is optimal, but if that net current turns out to be lower, a device with two periods and just 12 modular coils might be better. There are also attractive designs with quasihelical symmetry and four or five periods whose properties depend less on the bootstrap current. Good performance requires that there be a satisfactory magnetic well in the vacuum field, which is a property lacking in a stellarator-tokamak hybrid that has been proposed for a proof of principle experiment. In this paper, we present an analysis of stability for these configurations that is based on a mountain pass theorem asserting that, if two solutions of the problem of magnetohydrodynamic equilibrium can be found, then there has to be an unstable solution. We compare results of our theory of equilibrium, stability, and transport with recently announced measurements from the large LHD experiment in Japan.

Very-long-baseline radio interferometry surveys of the compact structure in active galactic nuclei.

Very-long-baseline radio interferometry (VLBI) imaging surveys have been undertaken since the late 1970s. The sample sizes were initially limited to a few tens of objects but the snapshot technique has now allowed samples containing almost 200 sources to be studied. The overwhelming majority of powerful compact sources are asymmetric corejects of one form or another, most of which exhibit apparent superluminal motion. However 5-10% of powerful flat-spectrum sources are 100-parsec (pc)-scale compact symmetric objects; these appear to form a continuum with the 1-kpc-scale double-lobed compact steep-spectrum sources, which make up 15-20% of lower frequency samples. It is likely that these sub-galactic-size symmetric sources are the precursors to the large-scale classical double sources. There is a surprising peak around 90 degrees in the histogram of misalignments between the dominant source axes on parsec and kiloparsec scales; this seems to be associated with sources exhibiting a high degree of relativistic beaming. VLBI snapshot surveys have great cosmological potential via measurements of both proper motion and angular size vs. redshift as well as searches for gravitational "millilensing."

Morphology of high-luminosity compact radio sources.

High-dynamic range imaging and monitoring with very-long-baseline interferometry reveal a rich morphology of luminous flat-spectrum radio sources. One-sided core-jet structures abound, and superluminal motion is frequently measured. In a few cases, both distinct moving features and diffuse underlying jet emission can be detected. Superluminal motion seen in such sources is typically complex, on curved trajectories or ridge lines, and with variable component velocities, including stationary features. The curved trajectories seen can be modeled by helical motion within the underlying jet flow. The very-long-baseline interferometry properties of the superluminal features in the jet of 3C 345 and other similar sources can be explained by models invoking the emission from shocks, at least within the vicinity of the compact core. Inverse-Compton calculations, constrained by x-ray observations, yield realistic estimates for the physical conditions in the parsec-scale jet. There is evidence for a transition region in this source beyond which other factors (e.g., plasma interactions and nonsynchrotron radiation processes) may become prominent. Multifrequency and polarization imaging (especially at high frequencies) are emerging as critical tools in testing model predictions.

Structure and evolution of the compact radio source in NGC 1275.

Investigations of the fine-scale structure in the compact nucleus of the radio source 3C 84 in NGC 1275 (New General Catalogue number) are reported. Structural monitoring observations beginning as early as 1976, and continuing to the present, revealed subluminal motions in a jet-like relatively diffuse region extending away from a flat-spectrum core. A counterjet feature was discovered in 1993, and very recent nearly simultaneous studies have detected the same feature at five frequencies ranging from 5 to 43 GHz. The counterjet exhibits a strong low-frequency cutoff, giving this region of the source an inverted spectrum. The observations are consistent with a physical model in which the cutoff arises from free-free absorption in a volume that surrounds the core but obscures only the counterjet feature. If such a model is confirmed, very-long-baseline radio interferometry observations can then be used to probe the accretion region, outside the radio jet, on parsec scales.

Bidirectional motion observed in the compact symmetric object 1946+708.

We present the first direct measurements of bidirectional motions in an extragalactic radio jet. The radio source 1946+708 is a compact symmetric object with striking S-symmetry identified with a galaxy at a redshift of 0.101. From observations 2 years apart we have determined the velocities of four compact components in the jet, the fastest of which has an apparent velocity of 1.09 h-1c. By pairing up the components, assuming they were simultaneously ejected in opposite directions, we derive a 1 lower limit on the Hubble constant, H0 > 42 km.s-1.Mpc-1.

Compact steep-spectrum sources and the unified scheme.

The compact steep-spectrum sources (CSSs) are an interesting class of objects which are of subgalactic dimensions; they occur more frequently in high-frequency surveys because their spectra often turn over at lower frequencies. We have estimated the symmetry parameters of a well-defined sample of CSSs and compared these with the larger 3CR sources of similar luminosity to understand the evolution and the consistency of CSSs with the unified scheme. We suggest that the majority of CSSs are likely to be young sources advancing outward through an asymmetric, inhomogeneous environment to form the larger ones. The radio properties of the CSSs are consistent with the unified scheme, where the axes of the quasars are seen closer to the line of sight while the radio galaxies lie closer to the plane of the sky. We discuss how radio polarization observations may be used to probe whether the physical conditions in the central regions of the CSSs are different from the larger ones. We present a simple scenario where the depolarization and high rotation measures seen in many CSSs can be consistent with the low rotation measures of cores in the more extended quasars and suggest further observations to test this scenario.

Characterizations of logarithmic Besov spaces in terms of differences, Fourier-analytical decompositions, wavelets and semi-groups.

We work with Besov spaces Bp,q0,b defined by means of differences, with zero classical smoothness and logarithmic smoothness with exponent b. We characterize Bp,q0,b by means of Fourier-analytical decompositions, wavelets and semi-groups. We also compare those results with the well-known characterizations for classical Besov spaces Bp,qs.

Caught in the act: gas and stellar velocity dispersions in a fast Quenching compact star-forming galaxy at z ~ 1.7

We present Keck I MOSFIRE spectroscopy in the Y and H bands of GDN-8231, a massive, compact, star-forming galaxy at a redshift of z ~ 1.7. Its spectrum reveals both Hα and [Nii] emission lines and strong Balmer absorption lines. The Hα and Spitzer MIPS 24 μm fluxes are both weak, thus indicating a low star-formation rate of SFR≲5-10 M_⨀ yr−1. This, added to a relatively young age of ~700 Myr measured from the absorption lines, provides the first direct evidence for a distant galaxy being caught in the act of rapidly shutting down its star formation. Such quenching allows GDN-8231 to become a compact, quiescent galaxy, similar to three other galaxies in our sample, by z ~ 1.5. Moreover, the color profile of GDN-8231 shows a bluer center, consistent with the predictions of recent simulations for an early phase of inside-out quenching. Its line-of-sight velocity dispersion for the gas, σ_LOG^gas = 127 ± 32 km s^−1, is nearly 40% smaller than that of its stars, σ_LOG^* = 215 ± 35 km s^−1. High-resolution hydro-simulations of galaxies explain such apparently colder gas kinematics of up to a factor of ~1.5 with rotating disks being viewed at different inclinations and/or centrally concentrated star-forming regions. A clear prediction is that their compact, quiescent descendants preserve some remnant rotation from their star-forming progenitors.

On the nullstellensätze for stein spaces and C-analytic sets.

In this work we prove the real Nullstellensatz for the ring O(X) of analytic functions on a C-analytic set X ⊂ Rn in terms of the saturation of Łojasiewicz’s radical in O(X): The ideal I(Ƶ(a)) of the zero-set Ƶ(a) of an ideal a of O(X) coincides with the saturation (Formula presented) of Łojasiewicz’s radical (Formula presented). If Ƶ(a) has ‘good properties’ concerning Hilbert’s 17th Problem, then I(Ƶ(a)) = (Formula presented) where (Formula presented) stands for the real radical of a. The same holds if we replace (Formula presented) with the real-analytic radical (Formula presented) of a, which is a natural generalization of the real radical ideal in the C-analytic setting. We revisit the classical results concerning (Hilbert’s) Nullstellensatz in the framework of (complex) Stein spaces. Let a be a saturated ideal of O(Rn) and YRn the germ of the support of the coherent sheaf that extends aORn to a suitable complex open neighborhood of Rn. We study the relationship between a normal primary decomposition of a and the decomposition of YRn as the union of its irreducible components. If a:= p is prime, then I(Ƶ(p)) = p if and only if the (complex) dimension of YRn coincides with the (real) dimension of Ƶ(p).

CB-norm estimates for maps between noncommutative Lp-spaces and quantum channel theory.

In the first part of this work, we show how certain techniques from quantum information theory can be used in order to obtain very sharp embeddings between noncommutative Lp-spaces. Then, we use these estimates to study the classical capacity with restricted assisted entanglement of the quantum erasure channel and the quantum depolarizing channel. In particular, we exactly compute the capacity of the first one and we show that certain nonmultiplicative results hold for the second one.

CANDELS: The progenitors of compact quiescent galaxies at z ~ 2

We combine high-resolution Hubble Space Telescope/WFC3 images with multi-wavelength photometry to track the evolution of structure and activity of massive (M_*> 10^10 M_☉) galaxies at redshifts z = 1.4-3 in two fields of the Cosmic Assembly Near-infrared Deep Extragalactic Legacy Survey. We detect compact, star-forming galaxies (cSFGs) whose number densities, masses, sizes, and star formation rates (SFRs) qualify them as likely progenitors of compact, quiescent, massive galaxies (cQGs) at z = 1.5-3. At z≲2, cSFGs present SFR = 100-200 M_☉ yr^–1, yet their specific star formation rates (sSFR ~ 10^–9 yr^–1) are typically half that of other massive SFGs at the same epoch, and host X-ray luminous active galactic nuclei (AGNs) 30 times (~30%) more frequently. These properties suggest that cSFGs are formed by gas-rich processes (mergers or disk-instabilities) that induce a compact starburst and feed an AGN, which, in turn, quench the star formation on dynamical timescales (few 10^8 yr). The cSFGs are continuously being formed at z = 2-3 and fade to cQGs down to z ~ 1.5. After this epoch, cSFGs are rare, thereby truncating the formation of new cQGs. Meanwhile, down to z = 1, existing cQGs continue to enlarge to match local QGs in size, while less-gas-rich mergers and other secular mechanisms shepherd (larger) SFGs as later arrivals to the red sequence. In summary, we propose two evolutionary tracks of QG formation: an early (z≲2), formation path of rapidly quenched cSFGs fading into cQGs that later enlarge within the quiescent phase, and a late-arrival (z≳2) path in which larger SFGs form extended QGs without passing through a compact state.

Student-Athlete Learning: How Learning Spaces Influence Athletic and Academic Success

This study will utilize case study inquiry to examine student-athlete learning opportunities in the athletic learning space and academic learning space in a higher education NCAA Division I collegiate institution. This study will assess what learning opportunities exist within the athletic and academic learning space to better understand effective learning practices. This study will utilize the sociocultural Learning Sciences literature, supported with critical pedagogy and inclusive excellence literature, to understand how different learning spaces contribute to student-athlete learning opportunities and educational success in college.

Central compact objects and the hidden magnetic field scenario

Central compact objects (CCOs) are X-ray sources lying close to the centre of supernova remnants, with inferred values of the surface magnetic fields significantly lower (≲1011 G) than those of standard pulsars. In this paper, we revise the hidden magnetic field scenario, presenting the first 2D simulations of the submergence and re-emergence of the magnetic field in the crust of a neutron star. A post-supernova accretion stage of about 10−4–10−3 M⊙ over a vast region of the surface is required to bury the magnetic field into the inner crust. When accretion stops, the field re-emerges on a typical time-scale of 1–100 kyr, depending on the submergence conditions. After this stage, the surface magnetic field is restored close to its birth values. A possible observable consequence of the hidden magnetic field is the anisotropy of the surface temperature distribution, in agreement with observations of several of these sources. We conclude that the hidden magnetic field model is viable as an alternative to the antimagnetar scenario, and it could provide the missing link between CCOs and the other classes of isolated neutron stars.

On some solutions of a functional equation related to the partial sums of the Riemann zeta function

In this paper, we prove that infinite-dimensional vector spaces of α-dense curves are generated by means of the functional equations f(x)+f(2x)+⋯+f(nx)=0, with n≥2, which are related to the partial sums of the Riemann zeta function. These curves α-densify a large class of compact sets of the plane for arbitrary small α, extending the known result that this holds for the cases n=2,3. Finally, we prove the existence of a family of solutions of such functional equation which has the property of quadrature in the compact that densifies, that is, the product of the length of the curve by the nth power of the density approaches the Jordan content of the compact set which the curve densifies.