The effect of an isothermal atmosphere on the propagation of three-dimensional waves in a thermally stratified accretion disk

We extend our analysis of the three-dimensional response of a vertically polytropic disk to tidal forcing at Lindblad resonances by including the effects of a disk atmosphere. The atmosphere is modeled as an isothermal layer that joins smoothly on to an underlying polytropic layer. The launched wave progressively enters the atmosphere as it propagates away from the resonance. The wave never propagates vertically, however, and the wave energy rises to a (finite) characteristic height in the atmosphere. The increase of wave amplitude associated with this process of wave channeling is reduced by the effect of the atmosphere. For waves of large azimuthal mode number m generated by giant planets embedded in a disk, the increase in wave amplitude is still substantial enough to be likely to dissipate the wave energy by shocks for even modest optical depths (tau greater than about 10) over a radial distance of a few times the disk thickness. For low-m waves generated in circumstellar disks in binary stars, the effects of wave channeling are less important and the level of wave nonlinearity increases by less than a factor of 10 in going from the disk edge to the disk center. For circumbinary disks, the effects of wave channeling remain important, even for modest values of optical depth.Comment: 11 pages, 4 figures, submitted to the Astrophysical Journa

The Large-N Limit of PT-Symmetric O(N) Models

We study a $PT$-symmetric quantum mechanical model with an O(N)-symmetric potential of the form $m^{2}\vec{x}^{2}/2-g(\vec{x}^{2})^{2}/N$ using its equivalent Hermitian form. Although the corresponding classical model has finite-energy trajectories that escape to infinity, the spectrum of the quantum theory is proven to consist only of bound states for all $N$. We show that the model has two distinct phases in the large-$N$ limit, with different scaling behaviors as $N$ goes to infinity. The two phases are separated by a first-order phase transition at a critical value of the dimensionless parameter $m^{2}/g^{2/3}$, given by $3\cdot2^{1/3}$.Comment: 7 pages, 2 figure

Three-dimensional waves generated at Lindblad resonances in thermally stratified disks

We analyze the linear, 3D response to tidal forcing of a disk that is thin and thermally stratified in the direction normal to the disk plane. We model the vertical disk structure locally as a polytrope which represents a disk of high optical depth. We solve the 3D gas-dynamic equations semi-analytically in the neighborhood of a Lindblad resonance. These solutions match asymptotically on to those valid away from resonances and provide solutions valid at all radii. We obtain the following results. 1) A variety of waves are launched at resonance. However, the f mode carries more than 95% of the torque exerted at the resonance. 2) These 3D waves collectively transport exactly the amount of angular momentum predicted by the 2D torque formula. 3) Near resonance, the f mode occupies the full vertical extent of the disk. Away from resonance, the f mode becomes confined near the surface of the disk, and, in the absence of other dissipation mechanisms, damps via shocks. The radial length scale for this process is roughly r_L/m (for resonant radius r_L and azimuthal wavenumber m), independent of the disk thickness H. This wave channeling process is due to the variations of physical quantities in r and is not due to wave refraction. 4) However, the inwardly propagating f mode launched from an m=2 inner Lindblad resonance experiences relatively minor channeling. We conclude that for binary stars, tidally generated waves in highly optically thick circumbinary disks are subject to strong nonlinear damping by the channeling mechanism, while those in circumstellar accretion disks are subject to weaker nonlinear effects. We also apply our results to waves excited by young planets for which m is approximately r/H and conclude that the waves are damped on the scale of a few H.Comment: 15 pages, 3 figures, 2 colour plates, to be published in the Astrophysical Journa

A First Principles Estimate of Finite Size Effects in Quark-Gluon Plasma Formation

Using lattice simulations of quenched QCD we estimate the finite size effects present when a gluon plasma equilibrates in a slab geometry, i.e., finite width but large transverse dimensions. Significant differences are observed in the free energy density for the slab when compared with bulk behavior. A small shift in the critical temperature is also seen. The free energy required to liberate heavy quarks relative to bulk is measured using Polyakov loops; the additional free energy required is on the order of 30-40 MeV at 2-3 T_c.Comment: 10 pages, 5 figures, RevTeX; revised version includes comparison with the Bjorken model and various small improvement

On the tilting of protostellar disks by resonant tidal effects

We consider the dynamics of a protostellar disk surrounding a star in a circular-orbit binary system. Our aim is to determine whether, if the disk is initially tilted with respect to the plane of the binary orbit, the inclination of the system will increase or decrease with time. The problem is formulated in the binary frame in which the tidal potential of the companion star is static. We consider a steady, flat disk that is aligned with the binary plane and investigate its linear stability with respect to tilting or warping perturbations. The dynamics is controlled by the competing effects of the m=0 and m=2 azimuthal Fourier components of the tidal potential. In the presence of dissipation, the m=0 component causes alignment of the system, while the m=2 component has the opposite tendency. We find that disks that are sufficiently large, in particular those that extend to their tidal truncation radii, are generally stable and will therefore tend to alignment with the binary plane on a time-scale comparable to that found in previous studies. However, the effect of the m=2 component is enhanced in the vicinity of resonances where the outer radius of the disk is such that the natural frequency of a global bending mode of the disk is equal to twice the binary orbital frequency. Under such circumstances, the disk can be unstable to tilting and acquire a warped shape, even in the absence of dissipation. The outer radius corresponding to the primary resonance is always smaller than the tidal truncation radius. For disks smaller than the primary resonance, the m=2 component may be able to cause a very slow growth of inclination through the effect of a near resonance that occurs close to the disk center. We discuss these results in the light of recent observations of protostellar disks in binary systems.Comment: 21 pages, 7 figures, to be published in the Astrophysical Journa

Center clusters in the Yang-Mills vacuum

Properties of local Polyakov loops for SU(2) and SU(3) lattice gauge theory at finite temperature are analyzed. We show that spatial clusters can be identified where the local Polyakov loops have values close to the same center element. For a suitable definition of these clusters the deconfinement transition can be characterized by the onset of percolation in one of the center sectors. The analysis is repeated for different resolution scales of the lattice and we argue that the center clusters have a continuum limit.Comment: Table added. Final version to appear in JHE

An alpha theory of time-dependent warped accretion discs

The non-linear fluid dynamics of a warped accretion disc was investigated in an earlier paper by developing a theory of fully non-linear bending waves in a thin, viscous disc. That analysis is here extended to take proper account of thermal and radiative effects by solving an energy equation that includes viscous dissipation and radiative transport. The problem is reduced to simple one-dimensional evolutionary equations for mass and angular momentum, expressed in physical units and suitable for direct application. This result constitutes a logical generalization of the alpha theory of Shakura & Sunyaev to the case of a time-dependent warped accretion disc. The local thermal-viscous stability of such a disc is also investigated.Comment: 16 pages, 3 figures, to be published in MNRA

Warp propagation in astrophysical discs

Astrophysical discs are often warped, that is, their orbital planes change with radius. This occurs whenever there is a non-axisymmetric force acting on the disc, for example the Lense-Thirring precession induced by a misaligned spinning black hole, or the gravitational pull of a misaligned companion. Such misalignments appear to be generic in astrophysics. The wide range of systems that can harbour warped discs - protostars, X-ray binaries, tidal disruption events, quasars and others - allows for a rich variety in the disc's response. Here we review the basic physics of warped discs and its implications.Comment: To be published in Astrophysical Black Holes by Haardt et al., Lecture Notes in Physics, Springer 2015. 19 pages, 2 figure

PEComa of the Upper Extremity: A Unique Case and Description of an Initial Response to Neoadjuvant Chemotherapy

Purpose. Tumors of the perivascular epithelial cell tumor (PEComa), first described in 1992, represent a rare soft tissue neoplasm of varying malignant potential. Cases of PEComa have been previously described in a few somatic and visceral sites, most notably in the gastrointestinal tract, genitourinary tract, and one extremity case in the thigh. To date, most malignant cases of PEComa have been resistant to chemotherapy, and as such, an appropriate therapy is not known. Case report. Here we describe the first case of PEComa of the upper extremity. Open biopsy revealed a high-grade malignant lesion, and the patient subsequently underwent both neoadjuvant therapy with doxorubicin, ifosfamide and mensa, and radiation therapy prior to wide surgical resection. After six cycles of chemotherapy, the tumor underwent an 80% reduction in size. Subsequent neoadjuvant radiation therapy of 5000 cGy did not further reduce the size of the tumor. Following limb sparing radical resection, pathology showed 20% necrosis within a high-grade malignant lesion. Twenty one months after beginning treatment, the patient shows no sign of local recurrence, but metastatic disease was confirmed after resection of a lung nodule. Conclusion. Given the favorable albeit partial response seen in this patient, the course of therapy outlined here may represent a good starting point for neoadjuvant treatment in a tumor with a historically bleak prognosis. In addition, the diagnosis of PEComa must now be entertained in the differential diagnosis of upper extremity soft tissue sarcoma

Theory of Abelian Projection

Analytic methods for Abelian projection are developed. A number of results are obtained related to string tension measurements. It is proven that even without gauge fixing, abelian projection yields string tensions of the underlying non-Abelian theory. Strong arguments are given for similar results in the case where gauge fixing is employed. The methods used emphasize that the projected theory is derived from the underlying non-Abelian theory rather than vice versa. In general, the choice of subgroup used for projection is not very important, and need not be Abelian. While gauge fixing is shown to be in principle unnecessary for the success of Abelian projection, it is computationally advantageous for the same reasons that improved operators, e.g., the use of fat links, are advantageous in Wilson loop measurements. Two other issues, Casimir scaling and the conflict between projection and critical universality, are also discussed.Comment: Minor corrections, new section added, 14 pages, 3 figures, RevTe