General relativistic hydrodynamics in curvilinear coordinates

In this paper we report on what we believe is the first successful implementation of relativistic hydrodynamics, coupled to dynamical spacetimes, in spherical polar coordinates without symmetry assumptions. We employ a high-resolution shock-capturing scheme, which requires that the equations be cast in flux-conservative form. One example of such a form is the :Valencia" formulation, which has been adopted in numerous applications, in particular in Cartesian coordinates. Here we generalize this formulation to allow for a reference-metric approach, which provides a natural framework for calculations in curvilinear coordinates. In spherical polar coordinates, for example, it allows for an analytical treatment of the singular r and sin(\theta) terms that appear in the equations. We experiment with different versions of our generalized Valencia formulation in numerical implementations of relativistic hydrodynamics for both fixed and dynamical spacetimes. We consider a number of different tests -- non-rotating and rotating relativistic stars, as well as gravitational collapse to a black hole -- to demonstrate that our formulation provides a promising approach to performing fully relativistic astrophysics simulations in spherical polar coordinates.Comment: 14 pages, 8 figures, version to be published in PR

Numerical Relativity in Spherical Polar Coordinates: Off-center Simulations

We have recently presented a new approach for numerical relativity simulations in spherical polar coordinates, both for vacuum and for relativistic hydrodynamics. Our approach is based on a reference-metric formulation of the BSSN equations, a factoring of all tensor components, as well as a partially implicit Runge-Kutta method, and does not rely on a regularization of the equations, nor does it make any assumptions about the symmetry across the origin. In order to demonstrate this feature we present here several off-centered simulations, including simulations of single black holes and neutron stars whose center is placed away from the origin of the coordinate system, as well as the asymmetric head-on collision of two black holes. We also revisit our implementation of relativistic hydrodynamics and demonstrate that a reference-metric formulation of hydrodynamics together with a factoring of all tensor components avoids problems related to the coordinate singularities at the origin and on the axes. As a particularly demanding test we present results for a shock wave propagating through the origin of the spherical polar coordinate system.Comment: 13 pages, 11 figures; matches version published in PR

Trumpet Slices in Kerr Spacetimes

We introduce a new time-independent family of analytical coordinate systems for the Kerr spacetime representing rotating black holes. We also propose a (2+1)+1 formalism for the characterization of trumpet geometries. Applying this formalism to our new family of coordinate systems we identify, for the first time, analytical and stationary trumpet slices for general rotating black holes, even for charged black holes in the presence of a cosmological constant. We present results for metric functions in this slicing and analyze the geometry of the rotating trumpet surface.Comment: 5 pages, 2 figures; version published in PR

Fully covariant and conformal formulation of the Z4 system in a reference-metric approach: comparison with the BSSN formulation in spherical symmetry

We adopt a reference-metric approach to generalize a covariant and conformal version of the Z4 system of the Einstein equations. We refer to the resulting system as ``fully covariant and conformal", or fCCZ4 for short, since it is well suited for curvilinear as well as Cartesian coordinates. We implement this fCCZ4 formalism in spherical polar coordinates under the assumption of spherical symmetry using a partially-implicit Runge-Kutta (PIRK) method and show that our code can evolve both vacuum and non-vacuum spacetimes without encountering instabilities. Our method does not require regularization of the equations to handle coordinate singularities, nor does it depend on constraint-preserving outer boundary conditions, nor does it need any modifications of the equations for evolutions of black holes. We perform several tests and compare the performance of the fCCZ4 system, for different choices of certain free parameters, with that of BSSN. Confirming earlier results we find that, for an optimal choice of these parameters, and for neutron-star spacetimes, the violations of the Hamiltonian constraint can be between 1 and 3 orders of magnitude smaller in the fCCZ4 system than in the BSSN formulation. For black-hole spacetimes, on the other hand, any advantages of fCCZ4 over BSSN are less evident.Comment: 13 pages, 10 figure

Exit times in non-Markovian drifting continuous-time random walk processes

By appealing to renewal theory we determine the equations that the mean exit time of a continuous-time random walk with drift satisfies both when the present coincides with a jump instant or when it does not. Particular attention is paid to the corrections ensuing from the non-Markovian nature of the process. We show that when drift and jumps have the same sign the relevant integral equations can be solved in closed form. The case when holding times have the classical Erlang distribution is considered in detail.Comment: 9 pages, 3 color plots, two-column revtex 4; new Appendix and references adde

How to reduce the number of rating scale items without predictability loss?

Rating scales are used to elicit data about qualitative entities (e.g., research collaboration). This study presents an innovative method for reducing the number of rating scale items without the predictability loss. The "area under the receiver operator curve method" (AUC ROC) is used. The presented method has reduced the number of rating scale items (variables) to 28.57\% (from 21 to 6) making over 70\% of collected data unnecessary. Results have been verified by two methods of analysis: Graded Response Model (GRM) and Confirmatory Factor Analysis (CFA). GRM revealed that the new method differentiates observations of high and middle scores. CFA proved that the reliability of the rating scale has not deteriorated by the scale item reduction. Both statistical analysis evidenced usefulness of the AUC ROC reduction method.Comment: 14 pages, 5 figure

Acquisition of anoikis resistance in human osteosarcoma cells does not alter sensitivity to chemotherapeutic agents

BACKGROUND: Chemotherapy-induced cell death can involve the induction of apoptosis. Thus, aberrant function of the pathways involved might result in chemoresistance. Since cell adhesion to the extracellular matrix acts as a survival factor that homeostatically maintains normal tissue architecture, it was tested whether acquisition of resistance to deadhesion-induced apoptosis (anoikis) in human osteosarcoma would result in resistance to chemotherapy. METHODS: Osteosarcoma cell lines (SAOS-2 and TE-85) obtained from ATCC and were maintained in complete Eagle's MEM medium. Suspension culture was established by placing cells in tissue culture wells coated with poly-HEMA. Cell cytotoxicity was determined using a live/dead cytotoxicity assay. Cell cycle/apoptosis analyses were performed using propidium iodide (PI) staining with subsequent FACS analysis. Apoptosis was also assayed by Annexin-FITC/PI staining. RESULTS: Etoposide, adriamycin, vinblastine, cisplatin and paclitaxel were able to induce apoptosis in human osteosarcoma cells SAOS-2 regardless of their anoikis resistance phenotype or the culture conditions (adhered vs. suspended). Moreover, suspended anoikis resistant TE-85 cells (TE-85ar) retained their sensitivity to chemotherapy as well. CONCLUSION: Acquisition of anoikis resistance in human osteosarcoma cells does not result in a generalized resistance to all apoptotic stimuli, including chemotherapy. Moreover, our results suggest that the pathways regulating anoikis resistance and chemotherapy resistance might involve the action of different mediators