The Carter Constant for Inclined Orbits About a Massive Kerr Black Hole: I. circular orbits

In an extreme binary black hole system, an orbit will increase its angle of inclination (i) as it evolves in Kerr spacetime. We focus our attention on the behaviour of the Carter constant (Q) for near-polar orbits; and develop an analysis that is independent of and complements radiation reaction models. For a Schwarzschild black hole, the polar orbits represent the abutment between the prograde and retrograde orbits at which Q is at its maximum value for given values of latus rectum (l) and eccentricity (e). The introduction of spin (S = |J|/M2) to the massive black hole causes this boundary, or abutment, to be moved towards greater orbital inclination; thus it no longer cleanly separates prograde and retrograde orbits. To characterise the abutment of a Kerr black hole (KBH), we first investigated the last stable orbit (LSO) of a test-particle about a KBH, and then extended this work to general orbits. To develop a better understanding of the evolution of Q we developed analytical formulae for Q in terms of l, e, and S to describe elliptical orbits at the abutment, polar orbits, and last stable orbits (LSO). By knowing the analytical form of dQ/dl at the abutment, we were able to test a 2PN flux equation for Q. We also used these formulae to numerically calculate the di/dl of hypothetical circular orbits that evolve along the abutment. From these values we have determined that di/dl = -(122.7S - 36S^3)l^-11/2 -(63/2 S + 35/4 S^3) l^-9/2 -15/2 S l^-7/2 -9/2 S l^-5/2. Thus the abutment becomes an important analytical and numerical laboratory for studying the evolution of Q and i in Kerr spacetime and for testing current and future radiation back-reaction models for near-polar retrograde orbits.Comment: 51 pages, 8 figures, accepted by Classical and Quantum Gravity on September 22nd, 201

A Study of Elliptical Last Stable Orbits About a Massive Kerr Black Hole

The last stable orbit (LSO) of a compact object (CO) is an important boundary condition when performing numerical analysis of orbit evolution. Although the LSO is already well understood for the case where a test-particle is in an elliptical orbit around a Schwarzschild black hole (SBH) and for the case of a circular orbit about a Kerr black hole (KBH) of normalised spin, S (|J|/M^2, where J is the spin angular momentum of the KBH); it is worthwhile to extend our knowledge to include elliptical orbits about a KBH. This extension helps to lay the foundation for a better understanding of gravitational wave (GW) emission. The mathematical developments described in this work sprang from the use of an effective potential (V) derived from the Kerr metric, which encapsulates the Lense-Thirring precession. That allowed us to develop a new form of analytical expression to calculate the LSO Radius for circular orbits (R_LSO) of arbitrary KBH spin. We were then able to construct a numerical method to calculate the latus rectum (l_LSO) for an elliptical LSO. Abstract Formulae for E^2 (square of normalised orbital energy) and L^2 (square of normalised orbital angular momentum) in terms of eccentricity, e, and latus rectum, l, were previously developed by others for elliptical orbits around an SBH and then extended to the KBH case; we used these results to generalise our analytical l_LSO equations to elliptical orbits. LSO data calculated from our analytical equations and numerical procedures, and those previously published, are then compared and found to be in excellent agreement.Comment: 42 pages, 9 figures, accepted for publication in Classical and Quantum Gravit

Passive tracer in a flow corresponding to a two dimensional stochastic Navier Stokes equations

In this paper we prove the law of large numbers and central limit theorem for trajectories of a particle carried by a two dimensional Eulerian velocity field. The field is given by a solution of a stochastic Navier--Stokes system with a non-degenerate noise. The spectral gap property, with respect to Wasserstein metric, for such a system has been shown in [9]. In the present paper we show that a similar property holds for the environment process corresponding to the Lagrangian observations of the velocity. In consequence we conclude the law of large numbers and the central limit theorem for the tracer. The proof of the central limit theorem relies on the martingale approximation of the trajectory process

Nonequilibrium dynamics of a stochastic model of anomalous heat transport

We study the dynamics of covariances in a chain of harmonic oscillators with conservative noise in contact with two stochastic Langevin heat baths. The noise amounts to random collisions between nearest-neighbour oscillators that exchange their momenta. In a recent paper, [S Lepri et al. J. Phys. A: Math. Theor. 42 (2009) 025001], we have studied the stationary state of this system with fixed boundary conditions, finding analytical exact expressions for the temperature profile and the heat current in the thermodynamic (continuum) limit. In this paper we extend the analysis to the evolution of the covariance matrix and to generic boundary conditions. Our main purpose is to construct a hydrodynamic description of the relaxation to the stationary state, starting from the exact equations governing the evolution of the correlation matrix. We identify and adiabatically eliminate the fast variables, arriving at a continuity equation for the temperature profile T(y,t), complemented by an ordinary equation that accounts for the evolution in the bulk. Altogether, we find that the evolution of T(y,t) is the result of fractional diffusion.Comment: Submitted to Journal of Physics A, Mathematical and Theoretica

Revealing cell cycle control by combining model-based detection of periodic expression with novel cis-regulatory descriptors

<p>Abstract</p> <p>Background</p> <p>We address the issue of explaining the presence or absence of phase-specific transcription in budding yeast cultures under different conditions. To this end we use a model-based detector of gene expression periodicity to divide genes into classes depending on their behavior in experiments using different synchronization methods. While computational inference of gene regulatory circuits typically relies on expression similarity (clustering) in order to find classes of potentially co-regulated genes, this method instead takes advantage of known time profile signatures related to the studied process.</p> <p>Results</p> <p>We explain the regulatory mechanisms of the inferred periodic classes with <it>cis</it>-regulatory descriptors that combine upstream sequence motifs with experimentally determined binding of transcription factors. By systematic statistical analysis we show that periodic classes are best explained by combinations of descriptors rather than single descriptors, and that different combinations correspond to periodic expression in different classes. We also find evidence for additive regulation in that the combinations of <it>cis</it>-regulatory descriptors associated with genes periodically expressed in fewer conditions are frequently subsets of combinations associated with genes periodically expression in more conditions. Finally, we demonstrate that our approach retrieves combinations that are more specific towards known cell-cycle related regulators than the frequently used clustering approach.</p> <p>Conclusion</p> <p>The results illustrate how a model-based approach to expression analysis may be particularly well suited to detect biologically relevant mechanisms. Our new approach makes it possible to provide more refined hypotheses about regulatory mechanisms of the cell cycle and it can easily be adjusted to reveal regulation of other, non-periodic, cellular processes.</p

Vesicle adhesion and fusion studied by small-angle x-ray scattering.

We have studied the adhesion state (also denoted by docking state) of lipid vesicles as induced by the divalent ions Ca2+ or Mg2+ at well-controlled ion concentration, lipid composition, and charge density. The bilayer structure and the interbilayer distance in the docking state were analyzed by small-angle x-ray scattering. A strong adhesion state was observed for DOPC:DOPS vesicles, indicating like-charge attraction resulting from ion correlations. The observed interbilayer separations of ∼1.6 nm agree quantitatively with the predictions of electrostatics in the strong coupling regime. Although this phenomenon was observed when mixing anionic and zwitterionic (or neutral) lipids, pure anionic membranes (DOPS) with highest charge density σ resulted in a direct phase transition to a multilamellar state, which must be accompanied by rupture and fusion of vesicles. To extend the structural assay toward protein-controlled docking and fusion, we have characterized reconstituted N-ethylmaleimide-sensitive factor attachment protein receptors in controlled proteoliposome suspensions by small-angle x-ray scattering

Neurotransmitter uptake of synaptic vesicles studied by X-ray diffraction

The size, polydispersity, and electron density profile of synaptic vesicles (SVs) can be studied by small-angle X-ray scattering (SAXS), i.e. by X-ray diffraction from purified SV suspensions in solution. Here we show that size and shape transformations, as they appear in the functional context of these important synaptic organelles, can also be monitored by SAXS. In particular, we have investigated the active uptake of neurotransmitters, and find a mean vesicle radius increase of about 12% after the uptake of glutamate, which indicates an unusually large extensibility of the vesicle surface, likely to be accompanied by conformational changes of membrane proteins and rearrangements of the bilayer. Changes in the electron density profile (EDP) give first indications for such a rearrangement. Details of the protein structure are screened, however, by SVs polydispersity. To overcome the limitations of large ensemble averages and heterogeneous structures, we therefore propose serial X-ray diffraction by single free electron laser pulses. Using simulated data for realistic parameters, we show that this is in principle feasible, and that even spatial distances between vesicle proteins could be assessed by this approach

A strand specific high resolution normalization method for chip-sequencing data employing multiple experimental control measurements

Background: High-throughput sequencing is becoming the standard tool for investigating protein-DNA interactions or epigenetic modifications. However, the data generated will always contain noise due to e. g. repetitive regions or non-specific antibody interactions. The noise will appear in the form of a background distribution of reads that must be taken into account in the downstream analysis, for example when detecting enriched regions (peak-calling). Several reported peak-callers can take experimental measurements of background tag distribution into account when analysing a data set. Unfortunately, the background is only used to adjust peak calling and not as a preprocessing step that aims at discerning the signal from the background noise. A normalization procedure that extracts the signal of interest would be of universal use when investigating genomic patterns. Results: We formulated such a normalization method based on linear regression and made a proof-of-concept implementation in R and C++. It was tested on simulated as well as on publicly available ChIP-seq data on binding sites for two transcription factors, MAX and FOXA1 and two control samples, Input and IgG. We applied three different peak-callers to (i) raw (un-normalized) data using statistical background models and (ii) raw data with control samples as background and (iii) normalized data without additional control samples as background. The fraction of called regions containing the expected transcription factor binding motif was largest for the normalized data and evaluation with qPCR data for FOXA1 suggested higher sensitivity and specificity using normalized data over raw data with experimental background. Conclusions: The proposed method can handle several control samples allowing for correction of multiple sources of bias simultaneously. Our evaluation on both synthetic and experimental data suggests that the method is successful in removing background noise

Reconstitution of SNARE proteins into solid-supported lipid bilayer stacks and X-ray structure analysis.

SNAREs are known as an important family of proteins mediating vesicle fusion. For various biophysical studies, they have been reconstituted into supported single bilayers via proteoliposome adsorption and rupture. In this study we extended this method to the reconstitution of SNAREs into supported multilamellar lipid membranes, i.e. oriented multibilayer stacks, as an ideal model system for X-ray structure analysis (X-ray reflectivity and diffraction). The reconstitution was implemented through a pathway of proteomicelle, proteoliposome and multibilayer. To monitor the structural evolution in each step, we used small-angle X-ray scattering for the proteomicelles and proteoliposomes, followed by X-ray reflectivity and grazing-incidence small-angle scattering for the multibilayers. Results show that SNAREs can be successfully reconstituted into supported multibilayers, with high enough orientational alignment for the application of surface sensitive X-ray characterizations. Based on this protocol, we then investigated the effect of SNAREs on the structure and phase diagram of the lipid membranes. Beyond this application, this reconstitution protocol could also be useful for X-ray analysis of many further membrane proteins