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

Perturbations on steady spherical accretion in Schwarzschild geometry

The stationary background flow in the spherically symmetric infall of a compressible fluid, coupled to the space-time defined by the static Schwarzschild metric, has been subjected to linearized perturbations. The perturbative procedure is based on the continuity condition and it shows that the coupling of the flow with the geometry of space-time brings about greater stability for the flow, to the extent that the amplitude of the perturbation, treated as a standing wave, decays in time, as opposed to the amplitude remaining constant in the Newtonian limit. In qualitative terms this situation simulates the effect of a dissipative mechanism in the classical Bondi accretion flow, defined in the Newtonian construct of space and time. As a result of this approach it becomes impossible to define an acoustic metric for a conserved spherically symmetric flow, described within the framework of Schwarzschild geometry. In keeping with this view, the perturbation, considered separately as a high-frequency travelling wave, also has its amplitude reduced.Comment: 8 pages, no figur

Secular instability in quasi-viscous disc accretion

A first-order correction in the $\alpha$-viscosity parameter of Shakura and Sunyaev has been introduced in the standard inviscid and thin accretion disc. A linearised time-dependent perturbative study of the stationary solutions of this "quasi-viscous" disc leads to the development of a secular instability on large spatial scales. This qualitative feature is equally manifest for two different types of perturbative treatment -- a standing wave on subsonic scales, as well as a radially propagating wave. Stability of the flow is restored when viscosity disappears.Comment: 15 pages, 2 figures, AASTeX. Added some new material and upgraded the reference lis

Evolution of transonicity in an accretion disc

For inviscid, rotational accretion flows driven by a general pseudo-Newtonian potential on to a Schwarzschild black hole, the only possible fixed points are saddle points and centre-type points. For the specific choice of the Newtonian potential, the flow has only two critical points, of which the outer one is a saddle point while the inner one is a centre-type point. A restrictive upper bound is imposed on the admissible range of values of the angular momentum of sub-Keplerian flows through a saddle point. These flows are very unstable to any deviation from a necessarily precise boundary condition. The difficulties against the physical realisability of a solution passing through the saddle point have been addressed through a temporal evolution of the flow, which gives a non-perturbative mechanism for selecting a transonic solution passing through the saddle point. An equation of motion for a real-time perturbation about the stationary flows reveals a very close correspondence with the metric of an acoustic black hole, which is also an indication of the primacy of transonicity.Comment: 18 page

Self-Assembling Peptide Nanofiber Scaffolds Accelerate Wound Healing

Cutaneous wound repair regenerates skin integrity, but a chronic failure to heal results in compromised tissue function and increased morbidity. To address this, we have used an integrated approach, using nanobiotechnology to augment the rate of wound reepithelialization by combining self-assembling peptide (SAP) nanofiber scaffold and Epidermal Growth Factor (EGF). This SAP bioscaffold was tested in a bioengineered Human Skin Equivalent (HSE) tissue model that enabled wound reepithelialization to be monitored in a tissue that recapitulates molecular and cellular mechanisms of repair known to occur in human skin. We found that SAP underwent molecular self-assembly to form unique 3D structures that stably covered the surface of the wound, suggesting that this scaffold may serve as a viable wound dressing. We measured the rates of release of EGF from the SAP scaffold and determined that EGF was only released when the scaffold was in direct contact with the HSE. By measuring the length of the epithelial tongue during wound reepithelialization, we found that SAP scaffolds containing EGF accelerated the rate of wound coverage by 5 fold when compared to controls without scaffolds and by 3.5 fold when compared to the scaffold without EGF. In conclusion, our experiments demonstrated that biomaterials composed of a biofunctionalized peptidic scaffold have many properties that are well-suited for the treatment of cutaneous wounds including wound coverage, functionalization with bioactive molecules, localized growth factor release and activation of wound repair

Integrin-Blocking Antibodies Delay Keratinocyte Re-Epithelialization in a Human Three-Dimensional Wound Healing Model

The α6β4 integrin plays a significant role in tumor growth, angiogenesis and metastasis through modulation of growth factor signaling, and is a potentially important therapeutic target. However, α6β4-mediated cell-matrix adhesion is critical in normal keratinocyte attachment, signaling and anchorage to the basement membrane through its interaction with laminin-5, raising potential risks for targeted therapy. Bioengineered Human Skin Equivalent (HSE), which have been shown to mimic their normal and wounded counterparts, have been used here to investigate the consequences of targeting β4 to establish toxic effects on normal tissue homeostasis and epithelial wound repair. We tested two antibodies directed to different β4 epitopes, one adhesion-blocking (ASC-8) and one non-adhesion blocking (ASC-3), and determined that these antibodies were appropriately localized to the basal surface of keratinocytes at the basement membrane interface where β4 is expressed. While normal tissue architecture was not altered, ASC-8 induced a sub-basal split at the basement membrane in non-wounded tissue. In addition, wound closure was significantly inhibited by ASC-8, but not by ASC-3, as the epithelial tongue only covered 40 percent of the wound area at 120 hours post-wounding. These results demonstrate β4 adhesion-blocking antibodies may have adverse effects on normal tissue, whereas antibodies directed to other epitopes may provide safer alternatives for therapy. Taken together, we conclude that these three-dimensional tissue models provide a biologically relevant platform to identify toxic effects induced by candidate therapeutics, which will allow generation of findings that are more predictive of in vivo responses early in the drug development process

Tunable local polariton modes in semiconductors

We study the local states within the polariton bandgap that arise due to deep defect centers with strong electron-phonon coupling. Electron transitions involving deep levels may result in alteration of local elastic constants. In this case, substantial reversible transformations of the impurity polariton density of states occur, which include the appearance/disappearance of the polariton impurity band, its shift and/or the modification of its shape. These changes can be induced by thermo- and photo-excitation of the localized electron states or by trapping of injected charge carriers. We develop a simple model, which is applied to the $O_P$ center in $GaP$. Further possible experimental realizations of the effect are discussed.Comment: 7 pages, 3 figure

Exploring hypotheses of the actions of TGF-beta 1 in epidermal wound healing using a 3D computational multiscale model of the human epidermis

In vivo and in vitro studies give a paradoxical picture of the actions of the key regulatory factor TGF-beta 1 in epidermal wound healing with it stimulating migration of keratinocytes but also inhibiting their proliferation. To try to reconcile these into an easily visualized 3D model of wound healing amenable for experimentation by cell biologists, a multiscale model of the formation of a 3D skin epithelium was established with TGF-beta 1 literature-derived rule sets and equations embedded within it. At the cellular level, an agent-based bottom-up model that focuses on individual interacting units ( keratinocytes) was used. This was based on literature-derived rules governing keratinocyte behavior and keratinocyte/ECM interactions. The selection of these rule sets is described in detail in this paper. The agent-based model was then linked with a subcellular model of TGF-beta 1 production and its action on keratinocytes simulated with a complex pathway simulator. This multiscale model can be run at a cellular level only or at a combined cellular/subcellular level. It was then initially challenged ( by wounding) to investigate the behavior of keratinocytes in wound healing at the cellular level. To investigate the possible actions of TGF-beta 1, several hypotheses were then explored by deliberately manipulating some of these rule sets at subcellular levels. This exercise readily eliminated some hypotheses and identified a sequence of spatial-temporal actions of TGF-beta 1 for normal successful wound healing in an easy-to-follow 3D model. We suggest this multiscale model offers a valuable, easy-to-visualize aid to our understanding of the actions of this key regulator in wound healing, and provides a model that can now be used to explore pathologies of wound healing

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