Growth of Perturbation in Gravitational Collapse and Accretion

When a self-gravitating spherical gas cloud collapses or accretes onto a central mass, the inner region of the cloud develops a density profile $\rho\propto r^{-3/2}$ and the velocity approaches free-fall. We show that in this region, nonspherical perturbations grow with decreasing radius. In the linear regime, the tangential velocity perturbation increases as $r^{-1}$, while the Lagrangian density perturbation, $\Delta\rho/\rho$, grows as $r^{-1/2}$. Faster growth occurs if the central collapsed object maintains a finite multiple moment, in which case $\Delta\rho/\rho$ increases as $r^{-l}$, where $l$ specifies the angular degree of the perturbation. These scaling relations are different from those obtained for the collapse of a homogeneous cloud. Our numerical calculations indicate that nonspherical perturbations are damped in the subsonic region, and that they grow and approach the asymptotic scalings in the supersonic region. The implications of our results to asymmetric supernova collapse and to black hole accretion are briefly discussed.Comment: 23 pages including 6 ps figures; Minor changes and update; To appear in ApJ, 200

An Extinction Study of the Taurus Dark Cloud Complex

We present a study of the detailed distribution of extinction in a region of the Taurus dark cloud complex. Our study uses new BVR images of the region, spectral classification data for 95 stars, and IRAS Sky Survey Atlas (ISSA) 60 and 100 micron images. We study the extinction of the region in four different ways, and we present the first inter-comparison of all these methods, which are: 1) using the color excess of background stars for which spectral types are known; 2) using the ISSA 60 and 100 micron images; 3) using star counts; and 4) using an optical (V and R) version of the average color excess method used by Lada et al. (1994). We find that all four methods give generally similar results, with important exceptions. To study the structure in the dust distribution, we compare the ISSA extinction and the extinction measured for individual stars. From the comparison, we conclude that in the relatively low extinction regions studied, with 0.9 < A_V < 3.0 mag (away from filamentary dark clouds and IRAS cores), there are no fluctuations in the dust column density greater than 45% (at the 99.7% confidence level), on scales smaller than 0.2 pc. We also report the discovery of a previously unknown stellar cluster behind the Taurus dark cloud near R.A 4h19m00s, Dec. 27:30:00 (B1950)Comment: 49 pages (which include 6 pages of tables and 6 pages of figures

Hysteretic and chaotic dynamics of viscous drops in creeping flows with rotation

It has been shown in our previous publication (Blawzdziewicz,Cristini,Loewenberg,2003) that high-viscosity drops in two dimensional linear creeping flows with a nonzero vorticity component may have two stable stationary states. One state corresponds to a nearly spherical, compact drop stabilized primarily by rotation, and the other to an elongated drop stabilized primarily by capillary forces. Here we explore consequences of the drop bistability for the dynamics of highly viscous drops. Using both boundary-integral simulations and small-deformation theory we show that a quasi-static change of the flow vorticity gives rise to a hysteretic response of the drop shape, with rapid changes between the compact and elongated solutions at critical values of the vorticity. In flows with sinusoidal temporal variation of the vorticity we find chaotic drop dynamics in response to the periodic forcing. A cascade of period-doubling bifurcations is found to be directly responsible for the transition to chaos. In random flows we obtain a bimodal drop-length distribution. Some analogies with the dynamics of macromolecules and vesicles are pointed out.Comment: 22 pages, 13 figures. submitted to Journal of Fluid Mechanic

Local Nature of Coset Models

The local algebras of the maximal Coset model C_max associated with a chiral conformal subtheory A\subset B are shown to coincide with the local relative commutants of A in B, provided A contains a stress energy tensor. Making the same assumption, the adjoint action of the unique inner-implementing representation U^A associated with A\subset B on the local observables in B is found to define net-endomorphisms of B. This property is exploited for constructing from B a conformally covariant holographic image in 1+1 dimensions which proves useful as a geometric picture for the joint inclusion A\vee C_max \subset B. Immediate applications to the analysis of current subalgebras are given and the relation to normal canonical tensor product subfactors is clarified. A natural converse of Borchers' theorem on half-sided translations is made accessible.Comment: 33 pages, no figures; typos, minor improvement

Representation-theoretic derivation of the Temperley-Lieb-Martin algebras

Explicit expressions for the Temperley-Lieb-Martin algebras, i.e., the quotients of the Hecke algebra that admit only representations corresponding to Young diagrams with a given maximum number of columns (or rows), are obtained, making explicit use of the Hecke algebra representation theory. Similar techniques are used to construct the algebras whose representations do not contain rectangular subdiagrams of a given size.Comment: 12 pages, LaTeX, to appear in J. Phys.

Application of LANDSAT to Identify Potential On-shore Impact of Outer Continental Shelf Development

There are no author-identified significant results in this report

Rat mammary carcinogenesis following neutron- or X-radiation

Female 61 to 63 - day - old Sprague-Dawley rats were exposed once to a single dose of either 0.43 - MeV neutrons or 250 - kVX - rays . For neutrons 23 rats were exposed in plastic tubes rotated around and 31 c m from a water-cooled tritium impregnated target bombarded with 2.45 - MeV protons from a V a n de Graaff generator. The mean kerma was measured at the rat location by integrating the response of a rat - sized homogeneous tissue equivalent ionization chamber of minimum mass. The ratio between absorbed dose and kerma is under investigation and is anticipated to be approximately 0.7. A compensated GM gamma-ray dosimeter indicated that the gamma - ray doses were 3.5% of the total dose. All rats were examined weekly for the presence of breast tumours and these were removed, fixed, stained and verified histologically as mammary neoplasms. At 10 months after exposure 98<7ο of the rats were a live . The neutron kerma, the per cent of rats with mammary neoplasia, and the number of rats were, respectively: 0.125 rads, 8.2°}o, 182; 0.5 rads, 9.0^0, 89; 2 rads, 20. 6,68; and 8 rads, 31.1%, 45. The X - ray results were: 30 R, 1.4% 95; 60 R, 27. l°Io, 48; and 90 R, 35.4%, 48. A 3. O^o incidence was found in 167 control rats. At 10 months after exposure the mammary neoplastic response after 8 rads of neutrons corresponds approximately to that after 60 - 90 R of X - rays . Similarly, the response after 2 rads of neutrons was intermediate between 30 and 60 R of X - rays and the response after 0 . 125 and 0.5 rads of neutrons was similar to that after 30 R of X - rays . This demonstrates that the RBE for 0.43 - MeV neutrons is much lower at high doses than at low doses. Determination of the confidence limits for the dose-RBE dependence and dose-incidence relationship will be determined as additional data are collected

Molecular gyroscopes and biological effects of weak ELF magnetic fields

Extremely-low-frequency magnetic fields are known to affect biological systems. In many cases, biological effects display `windows' in biologically effective parameters of the magnetic fields: most dramatic is the fact that relatively intense magnetic fields sometimes do not cause appreciable effect, while smaller fields of the order of 10--100 $\mu$T do. Linear resonant physical processes do not explain frequency windows in this case. Amplitude window phenomena suggest a nonlinear physical mechanism. Such a nonlinear mechanism has been proposed recently to explain those `windows'. It considers quantum-interference effects on protein-bound substrate ions. Magnetic fields cause an interference of ion quantum states and change the probability of ion-protein dissociation. This ion-interference mechanism predicts specific magnetic-field frequency and amplitude windows within which biological effects occur. It agrees with a lot of experiments. However, according to the mechanism, the lifetime $\Gamma^{-1}$ of ion quantum states within a protein cavity should be of unrealistic value, more than 0.01 s for frequency band 10--100 Hz. In this paper, a biophysical mechanism has been proposed that (i) retains the attractive features of the ion interference mechanism and (ii) uses the principles of gyroscopic motion and removes the necessity to postulate large lifetimes. The mechanism considers dynamics of the density matrix of the molecular groups, which are attached to the walls of protein cavities by two covalent bonds, i.e., molecular gyroscopes. Numerical computations have shown almost free rotations of the molecular gyros. The relaxation time due to van der Waals forces was about 0.01 s for the cavity size of 28 angstr\"{o}ms.Comment: 10 pages, 7 figure